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BEGIN:VEVENT
SUMMARY:Pavel Exner (Doppler Institute for Mathematical Physics and Applie
d Mathematics)
DTSTART:20201110T134500Z
DTEND:20201110T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/1
DESCRIPTION:Title: Spiral quantum wavegudies\nby Pavel Exner (Doppler Institute for Ma
thematical Physics and Applied Mathematics) as part of Quantum Circle\n\n\
nAbstract\nThe topic of this talk is a quantum particle confined to a spir
al-shaped region with Dirichlet boundary. As a case study we analyze in de
tail the Archimedean spiral and show that the spectrum above the continuum
threshold is absolutely continuous away from the thresholds. The subtle d
ifference between the radial and perpendicular width implies\, however\, t
hat in contrast to numerous examples of `less curved' waveguides\, the dis
crete spectrum is empty in this case. We also discuss modifications such a
multi-arm Archimedean spirals and spiral waveguides with a central cavity
\; in the latter case bound state already exist if the cavity exceeds a cr
itical size. For spiral regions of a more general type the spectral nature
depends substantially on whether their coil width is `expanding' or `shri
nking'. The most interesting situation occurs in the case we call asymptot
ically Archimedean\, where the existence of bound states depends on the di
rection from which the asymptotics is reached.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dale Frymark (Nuclear Physics Institute CAS)
DTSTART:20201124T134500Z
DTEND:20201124T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/2
DESCRIPTION:Title: Singular boundary conditions for Sturm-Liouville operators via perturba
tion theory\nby Dale Frymark (Nuclear Physics Institute CAS) as part o
f Quantum Circle\n\n\nAbstract\nWe show that all self-adjoint extensions o
f semi-bounded Sturm-Liouville operators with general limit-circle endpoin
t(s) can be obtained via an additive singular form bounded self-adjoint pe
rturbation of rank equal to the deficiency indices\, say d=1 or 2. This ch
aracterization generalizes the well-known analog for semi-bounded Sturm-Li
ouville operators with regular endpoints. Explicitly\, every self-adjoint
extension of the minimal operator can be written as\n$$\n A_{\\Theta} =
A_0 + B \\Theta B*\,\n$$\nwhere $A_0$ is a distinguished self-adjoint ext
ension and Theta is a self-adjoint linear relation in $\\mathbb{C}^d$. The
perturbation is singular in the sense that it does not belong to the unde
rlying Hilbert space but is form bounded with respect to $A_0$\, i.e. it
belongs to $H_{-1}(A_0)$. The construction of a boundary triple and compat
ible boundary pair for the symmetric operator ensure that the perturbation
is well-defined and self-adjoint extensions are in a one-to-one correspon
dence with self-adjoint relations $\\Theta$.\n\nAs an example\, self-adjoi
nt extensions of the classical symmetric Jacobi differential equation (whi
ch has two limit-circle endpoints) are obtained and their spectra is analy
zed with tools both from the theory of boundary triples and perturbation t
heory.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylwia Kondej (University of Zielona Gora)
DTSTART:20201201T134500Z
DTEND:20201201T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/3
DESCRIPTION:Title: Optimization problem for quantum system with star-shaped potential
\nby Sylwia Kondej (University of Zielona Gora) as part of Quantum Circle\
n\n\nAbstract\nWe discuss the spectral properties of singular Schr\\"oding
er operators in three dimensions with the interaction supported by an equi
lateral star. Our main result concerns spectral optimization: we show that
the principal eigenvalue is uniquely maximized when the arms are arranged
in one of the known five sharp configurations.\nThe results discussed i
n the talk are the joint work with Pavel Exner.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Lotoreichik (Nuclear Physics Institute CAS)
DTSTART:20201208T134500Z
DTEND:20201208T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/4
DESCRIPTION:Title: Szegö-type inequality for the 2-D Dirac operator with infinite mass bo
undary conditions\nby Vladimir Lotoreichik (Nuclear Physics Institute
CAS) as part of Quantum Circle\n\n\nAbstract\nIn this talk\, we will discu
ss spectral features of the Dirac operator with infinite mass boundary con
ditions in a smooth bounded domain of $\\mathbb{R}^2$. Motivated by spectr
al geometric inequalities\, we derive a non-linear variational formulation
to characterize its principal eigenvalue. This characterization turns ou
t to be very robust and allows for a simple proof of a Szeg\\H{o} type ine
quality as well as a new reformulation of a Faber-Krahn type inequality fo
r this operator. We will also present strong numerical evidence supporting
the validity of a Faber-Krahn type inequality.\n\nThis talk is based on a
joint work with Pedro Antunes\, Rafael Benguria\, and Thomas Ourmi\\`{e}r
es-Bonafos.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hynek Kovarik (Università degli studi di Brescia)
DTSTART:20201215T134500Z
DTEND:20201215T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/5
DESCRIPTION:Title: Absence of positive eigenvalues of magnetic Schroedinger operators\
nby Hynek Kovarik (Università degli studi di Brescia) as part of Quantum
Circle\n\n\nAbstract\nWe study sufficient conditions for the absence of po
sitive eigenvalues of magnetic Schroedinger operators in R^n. In our main
result we prove the absence of eigenvalues above certain threshold energy
which depends explicitly on the magnetic and electric field. A comparison
with the examples of Miller-Simon shows that our result is sharp as far as
the decay of the magnetic field is concerned.\nThe talk is based on a joi
nt work with Silvana Avramska-Lukarska and Dirk Hundertmark.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denis Borisov (Bashkir State Pedagogical University\, Ufa)
DTSTART:20201222T134500Z
DTEND:20201222T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/6
DESCRIPTION:Title: Accumulation of resonances and eigenvalues for operators with distant p
erturbations\nby Denis Borisov (Bashkir State Pedagogical University\,
Ufa) as part of Quantum Circle\n\n\nAbstract\nWe consider a model one-dim
ensional problem with distant perturbations\, for which we study a phenome
non of emerging of infinitely many eigenvalues and resonances near the bot
tom of the essential spectrum. We show that they accumulate to a certain s
egment of the essential spectrum. Then we discuss possible generalization
of this result to multi-dimensional models and various situations of reson
ances and eigenvalues distributions.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Pankrashkin (Universitaet Oldenburg)
DTSTART:20210105T134500Z
DTEND:20210105T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/7
DESCRIPTION:Title: On the discrete spectrum of a Schroedinger operator in a half-plane wit
h a potential localized along a line\nby Konstantin Pankrashkin (Unive
rsitaet Oldenburg) as part of Quantum Circle\n\n\nAbstract\nWe discuss the
the spectral properties of a Schrödinger operator in a half-plane with N
euman boundary condition and with a (regular or singular) potential which
only depends on the distance to a line. We discuss the cardinality of the
discrete spectrum for the case when the potential is attractive and the li
ne is not parallel to the boundary. Based in part on a joint work with Seb
astian Egger and Joachim Kerner.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aurel Gabris (Czech Technical University)
DTSTART:20210112T134500Z
DTEND:20210112T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/8
DESCRIPTION:Title: Classical and quantum coherences in photonic quantum networks\nby A
urel Gabris (Czech Technical University) as part of Quantum Circle\n\n\nAb
stract\nDiscerning quantum and classical features in a real-world scenario
is an intriguing task\, especially when the system under scrutiny has man
y degrees of freedom. In optics the notion of coherence is of central impo
rtance\, and it also comes in two flavours: classical and quantum. In this
talk I will present a simple yet powerful technique to control and discer
n classical and quantum coherences in a photonic quantum network\, an obje
ct that may encompass a large number of modes\, all possibly spatially sep
arated. Finally\, I will outline the experimental results from the applica
tion of this technique to photonic networks implemented in the time-domain
. \\\\[.2em]\nReference: Th.~Nitsche\, Syamsundar De\, S.~Barkhofen\, E.~M
eyer-Scott\, J.~Tiedau\, J.~Sperling\, A.~G\\'abris\, I.~Jex\, and Ch.~Sil
berhorn\, \\emph{Phys. Rev. Lett.} \\textbf{125}\, 213604 (2020)\n\nDiscer
ning quantum and classical features in a real-world scenario is an intrigu
ing task\, especially when the system under scrutiny has many degrees of f
reedom. In optics the notion of coherence is of central importance\, and i
t also comes in two flavours: classical and quantum. In this talk I will p
resent a simple yet powerful technique to control and discern classical an
d quantum coherences in a photonic quantum network\, an object that may en
compass a large number of modes\, all possibly spatially separated. Finall
y\, I will outline the experimental results from the application of this t
echnique to photonic networks implemented in the time-domain. \\\\[.2em]\n
Reference: Th.~Nitsche\, Syamsundar De\, S.~Barkhofen\, E.~Meyer-Scott\, J
.~Tiedau\, J.~Sperling\, A.~G\\'abris\, I.~Jex\, and Ch.~Silberhorn\, \\em
ph{Phys. Rev. Lett.} \\textbf{125}\, 213604 (2020)\n
LOCATION:https://researchseminars.org/talk/qc_seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brice Flamencourt (Universite d'Orsay)
DTSTART:20210216T134500Z
DTEND:20210216T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/9
DESCRIPTION:Title: On the convergence of Dirac operators with large masses\nby Brice F
lamencourt (Universite d'Orsay) as part of Quantum Circle\n\n\nAbstract\nW
e look at a class of Dirac operators with a potential that can be interpre
ted as masses in separated regions of the space. These operators arise nat
urally in the study of the MIT bag model in three dimensions\, and one can
generalize their construction to higher dimension. We are interested in t
he behavior of the operator’s eigenvalues in several asymptotic regimes
when the masses go to infinity. It can be shown that there is an effective
operator on the boundaries of the regions previously considered which gov
erns the convergence of the spectrum.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Stefanak (Czech Technical University)
DTSTART:20210323T134500Z
DTEND:20210323T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/10
DESCRIPTION:Title: Asymptotic properties of quantum walks on lattices\nby Martin Stef
anak (Czech Technical University) as part of Quantum Circle\n\n\nAbstract\
nWe provide an overview of results for evolution of discrete time quantum
walks on lattices. The focus is on homogeneous walks where Fourier analysi
s is applicable\, which allows to investigate the spectrum of the evolutio
n operator in detail. Most of the features of the probability distribution
generated by the quantum walk evolution\, e.g. the characteristic peaks a
nd ballistic spreading\, are captured in the limit density\, which can be
derived from the convergence moments of position rescalled with the number
of steps. The derivation of the limit density is illustrated on the examp
le of the quantum walk on a line with the Hadamard coin. We then turn to t
he examples of quantum walks on a line and a plane with the Grover coin\,
where the evolution operator has a non-empty point spectrum. This results
in the trapping effect\, where the walker remains localized in the vicinit
y of the starting point with non-vanishing probability.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrii Khrabustovskyi (University of Hradec Kralove)
DTSTART:20210316T134500Z
DTEND:20210316T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/11
DESCRIPTION:Title: Geometric approximation of delta interactions\nby Andrii Khrabusto
vskyi (University of Hradec Kralove) as part of Quantum Circle\n\n\nAbstra
ct\nIn this talk we demonstrate how to approximate $1d$ Schrodinger operat
ors with a $\\delta$-potential by the Neumann Laplacian on a narrow wavegu
ide-like domain. Namely\, we consider the domain consisting of a straight
narrow strip and a small protuberance with "room-and-passage" geometry. We
show that in the limit when perpendicular size of the strip tends to zero
and the protuberance is appropriated scaled the Neumann Laplacian on this
domain converges in (a kind of) norm resolvent sense to the above singula
r Schrodinger operator. The estimates on the rate of this convergence are
also derived. As an application we proof the Hausdorff convergence of spec
tra. This is a joint work with Olaf Post (Trier).\n
LOCATION:https://researchseminars.org/talk/qc_seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiri Lipovsky (University of Hradec Kralove)
DTSTART:20210309T134500Z
DTEND:20210309T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/12
DESCRIPTION:Title: Graphs with preferred-orientation coupling and their spectral properti
es\nby Jiri Lipovsky (University of Hradec Kralove) as part of Quantum
Circle\n\n\nAbstract\nAbstract: We investigate quantum graphs with the pr
eferred-orientation coupling conditions suggested by Exner and Tater [1].
In particular\, we are interested in the high-energy limit of their spectr
a. These coupling conditions violate the time-reversal symmetry\, for a pa
rticular energy\, the particle approaching the vertex from a given edge le
aves it through the neighbouring edge (for instance\, to the left of the i
ncoming edge) and this property is cyclical. It was previously shown that
the vertex scattering matrix depends on the degree of the vertex\; for an
odd-degree vertex\, the scattering matrix converges in the high-energy lim
it to the identity matrix\, while even-degree vertices behave differently.
This behaviour affects the transport properties of these graphs.\n\nWe st
udy two models. The first one is a finite graph consisting of edges of Pla
tonic solids. We find that the asymptotical distribution of the eigenvalue
s for the octahedron graph (having even degrees of vertices) is different
from the other Platonic solids (having odd degrees of vertices)\, for whic
h the eigenvalues approach the spectrum of the Neumann Laplacian on an int
erval. The second model consists of two types of infinite lattices. For on
e of them\, the transport at high energies is possible in the middle of th
e strip and is suppressed at the edges. For the other one\, the transport
is possible at the edge of the strip only.\n\nThe talk will be based on tw
o papers in collaboration with P. Exner [2\, 3].\n\nReferences:\n[1] P. Ex
ner\, M. Tater\, Quantum graphs with vertices of a preferred orientation\,
Phys. Lett. A 382 (2018) 283–287.\n[2] P. Exner\, J. Lipovsky\, Sp
ectral asymptotics of the Laplacian on Platonic solids graphs\, J. Math. P
hys. 60 (2019)\, 122101.\n[3] P. Exner\, J. Lipovsky\, Topological bulk-ed
ge effects in quantum graph transport\, Phys. Lett. A 384 (2020)\, 126390.
\n
LOCATION:https://researchseminars.org/talk/qc_seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Exner (Czech Academy of Sciences)
DTSTART:20210330T124500Z
DTEND:20210330T134500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/13
DESCRIPTION:Title: Product formulae and Zeno quantum dynamics\nby Pavel Exner (Czech
Academy of Sciences) as part of Quantum Circle\n\n\nAbstract\nWe present a
new product formula which involves a unitary group generated by a positiv
e self-adjoint operator and a continuous projection-valued function. The p
roblem is motivated by quantum description of decaying systems\, in partic
ular\, the Zeno effect coming from frequently repeated measurements. Appli
ed to it\, the formula expresses the dynamics of such a system. An example
of a permanent position ascertaining leading to the effective Dirichlet c
ondition is given.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Salzmann (University of Cambridge)
DTSTART:20210406T124500Z
DTEND:20210406T134500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/14
DESCRIPTION:Title: Quantum Zeno effect for open quantum systems\nby Robert Salzmann (
University of Cambridge) as part of Quantum Circle\n\n\nAbstract\nWe prove
the quantum Zeno effect in open quantum systems whose evolution\, governe
d by quantum dynamical semigroups\, is repeatedly and frequently interrupt
ed by the action of a quantum operation. For the case of a quantum dynamic
al semigroup with a bounded generator\, our analysis leads to a refinement
of existing results and extends them to a larger class of quantum operati
ons. We also prove the existence of a novel strong quantum Zeno limit for
quantum operations for which a certain spectral gap assumption\, which all
previous results relied on\, is lifted. The quantum operations are instea
d required to satisfy a weaker property of strong power-convergence. In ad
dition\, we establish\, for the first time\, the existence of a quantum Ze
no limit for the case of unbounded generators in the open system setup. We
also provide a variety of physically interesting examples of quantum oper
ations to which our results apply.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Schlosser (TU Graz)
DTSTART:20210413T124500Z
DTEND:20210413T134500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/15
DESCRIPTION:Title: Time evolution of superoscillations\nby Peter Schlosser (TU Graz)
as part of Quantum Circle\n\n\nAbstract\nhttp://gemma.ujf.cas.cz/%7Eexner/
Qcabs/schlosser21a.pdf\n
LOCATION:https://researchseminars.org/talk/qc_seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matej Tusek (Czech Technical University)
DTSTART:20210420T124500Z
DTEND:20210420T134500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/16
DESCRIPTION:Title: General delta-shell interactions for the two-dimensional Dirac operato
r: self-adjointness and approximation\nby Matej Tusek (Czech Technical
University) as part of Quantum Circle\n\n\nAbstract\nIn this talk the two
-dimensional Dirac operator with general local singular interactions suppo
rted on a closed curve is considered. A systematic study of the interactio
n is performed by decomposing it into a linear combination of four element
ary interactions: electrostatic\, Lorentz scalar\, magnetic\, and a fourth
one which can be absorbed by using unitary transformations. First\, the s
elf-adjointness and the spectral description of the underlying Dirac opera
tor will be adressed. This can be considered as a generalization of a rece
nt work of Behrndt\, Holzmann\, Ourmieres-Bonafos\, and Pankrashkin. The s
econd part of the talk will be devoted to a construction of approximations
of the studied operators by Dirac operators with regular potentials. The
talk is based on a joint work with Cassano\, Lotoreichik\, and Mas.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Marletta (Cardiff University)
DTSTART:20210427T124500Z
DTEND:20210427T134500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/17
DESCRIPTION:Title: A Laplace operator with boundary conditions singular at one point\
nby Marco Marletta (Cardiff University) as part of Quantum Circle\n\n\nAbs
tract\nIn this talk I will present some work with Rozenblum from 2009 and
some further results with my former student Freddy Symons from 2016. While
it has been known for more than half a century that the Laplace operator
on a smooth\, bounded domain may have essential spectrum if the boundary c
onditions are suitably chosen\, typical choices involved non-local operato
rs. In this talk I will show\, with very elementary arguments\, that even
local boundary conditions\, singular even just at a single point\, can hav
e a huge impact on the spectrum and eigenfunctions. The example we conside
r\, first proposed by Berry and Dennis\, still has empty essential spectru
m and compact resolvent. However Weyl’s law fails completely becaus
e the spectrum becomes unbounded below. The positive eigenvalues still obe
y Weyl asymptotics\, to leading order\; however the (absolute values of th
e) negative eigenvalues do not obey a power law distribution.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noema Nicolussi (Vienna University)
DTSTART:20210504T124500Z
DTEND:20210504T134500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/18
DESCRIPTION:Title: Laplacians on infinite graphs\nby Noema Nicolussi (Vienna Universi
ty) as part of Quantum Circle\n\n\nAbstract\nThere are two different notio
ns of a Laplacian operator associated with infinite graphs: discrete Lap
lacians and quantum graphs. Both objects have a venerable histor
y and their spectral theory relates to several diverse branches
of mathematics (random walks\, combinatorics\, geometric group theory\, ..
.). In our talk we explore connections between these two types of operator
s (spectral\, parabolic and geometric properties)\, and exploit these rela
tions to prove a number of new results in spectral theory for both setting
s. In particular\, we will present applications to the self-adjointness p
roblem on infinite graphs.Based on joint work with Aleksey Kostenko
(Ljubljana&Vienna) and Mark Malamud (Donetsk).\n
LOCATION:https://researchseminars.org/talk/qc_seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Larson (Caltech)
DTSTART:20210504T140000Z
DTEND:20210504T150000Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/19
DESCRIPTION:Title: On the spectrum of the Kronig-Penney model in a constant electric fiel
d\nby Simon Larson (Caltech) as part of Quantum Circle\n\n\nAbstract\n
\\documentclass[12pt\, a4paper]{article} % 11pt for all the article\n\\use
package{amsmath\,amsthm\,amsfonts\,amssymb}\n\\usepackage[affil-it]{authbl
k}\n\n\\begin{document}\n\n\\title{On the spectrum of the Kronig--Penney m
odel in a constant electric field}\n\\author{\\large\\sc Simon Larson}\n\\
affil{\\normalsize Caltech}\n\\date{}\n\\maketitle\n\n\\noindent \\textbf{
Abstract.} We are interested in the nature of the spectrum of the one-dime
nsional Schr\\"odinger operator\n\\begin{equation*}\n - \\frac{d^2}{dx^2}
-Fx + \\sum_{n \\in \\mathbb{Z}}g_n \\delta(x-n)\n\\end{equation*}\nwith $
F>0$ and two different choices of the coupling constants $\\{g_n\\}_{n\\in
\\mathbb{Z}}$. In the first model $g_n \\equiv \\lambda$ and we prove tha
t if $F\\in \\pi^2 \\mathbb{Q}$ then the spectrum is $\\mathbb{R}$ and is
furthermore absolutely continuous away from an explicit discrete set of po
ints. In the second model $g_n$ are independent random variables with mean
zero and variance $\\lambda^2$. Under certain assumptions on the distribu
tion of these random variables we prove that almost surely the spectrum is
dense pure point if $F < \\lambda^2/2$ and purely singular continuous if
$F> \\lambda^2/2$. Based on joint work with Rupert Frank.\n\\end{document}
\n
LOCATION:https://researchseminars.org/talk/qc_seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudio Cacciapuoti (Universita degli Studi dell'Insubria)
DTSTART:20210518T124500Z
DTEND:20210518T134500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/20
DESCRIPTION:Title: The nonlinear Schrödinger equation with isolated singularities\nb
y Claudio Cacciapuoti (Universita degli Studi dell'Insubria) as part of Qu
antum Circle\n\n\nAbstract\nI will discuss the well posedness of the nonli
near Schrödinger equation with power-type nonlinearity and in the prese
nce of a delta interaction\, both in dimension two and three. This is a mo
del of evolution for some singular solutions that are well known in the an
alysis of semilinear elliptic equations. I will consider local existence\,
uniqueness and continuous dependence from the initial data of strong (ope
rator domain) solutions of the associated Cauchy problem. In dimension two
well posedness holds for any power nonlinearity and global existence is p
roved for powers below the cubic. In dimension three local and global well
posedness are restricted to low powers.\nThe talk is based on a joint wor
k with Domenico Finco and Diego Noja.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vit Jakubsky (Nuclear Physics Institute CAS)
DTSTART:20210525T124500Z
DTEND:20210525T134500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/21
DESCRIPTION:Title: Reduction scheme for coupled Dirac systems\nby Vit Jakubsky (Nucle
ar Physics Institute CAS) as part of Quantum Circle\n\n\nAbstract\nWe anal
yze a class of coupled quantum systems whose dynamics can be understood vi
a two uncoupled\, lower-dimensional quantum settings with auxiliary intera
ctions. The general reduction scheme\, based on algebraic properties of th
e potential term\, is discussed in detail for two-dimensional Dirac Hamilt
onian. We discuss its possible application in description of Dirac fermion
s in graphene or bilayer graphene in presence of distortion scattering or
spin-orbit interaction. The framework is illustrated on the explicit examp
les where the interaction depends on two spatial coordinates or it is time
-dependent.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kyle Scarbrough (Czech Technical University)
DTSTART:20211005T124500Z
DTEND:20211005T134500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/22
DESCRIPTION:Title: Oscillation theory for canonical systems\nby Kyle Scarbrough (Czec
h Technical University) as part of Quantum Circle\n\n\nAbstract\nThis talk
will be about the spectral theory of canonical systems. After an introduc
tion to canonical systems\, a version of oscillation theory for them will
be discussed. Some applications of oscillation theory to semibounded syste
ms\, relations between diagonal and nondiagonal systems\, and the essentia
l spectrum will be highlighted.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dale Frymark (Czech Academy od Sciences)
DTSTART:20211019T124500Z
DTEND:20211019T134500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/23
DESCRIPTION:Title: Self-adjointness of the 2-D Dirac operator with singular interactions
supported on star-graphs\nby Dale Frymark (Czech Academy od Sciences)
as part of Quantum Circle\n\n\nAbstract\nWe present an analysis of the def
iciency indices of the 2-D Dirac Operator with Lorentz-scalar interactions
supported on a star-graph\, with different interaction strengths allowed
on different leads. In the general case\, we separate variables\, decompos
e the Dirac operator into an orthogonal sum and find that the deficiency i
ndices depend on the number of eigenvalues of the so-called spin-orbit ope
rator within an interval. For the simpler cases when there are two or thre
e leads much more can be said. Examples when the deficiency indices are (2
\,2) and when the spin-orbit operator has eigenvalues of multiplicity two
are included. It is also shown that there is a distinguished self-adjoint
extension whose domain lies in H^{1/2}.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michal Jex (Ceremade Paris)
DTSTART:20211026T124500Z
DTEND:20211026T134500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/24
DESCRIPTION:Title: Quantum Systems at The Brink: Critical Potentials and dimensionality\nby Michal Jex (Ceremade Paris) as part of Quantum Circle\n\n\nAbstract
\nThe existence of eigenfunctions for Schr\\"odinger operators are of utmo
st importance in quantum mechanics and its appllications. It is well known
that for eigenvalues below the threshold of the essential spectrum\, eige
nvectors exist and decay exponentially. However\, the situation at the thr
eshold is much more subtle. We present necessary and sufficient condition
for the Schrödinger operator to have zero energy ground state. We show th
at it critically depends on the asymptotic behaviour of the potential. We
derive necessary and sufficient conditions for the existence and absence o
f zero eigenvalue with respect to the dimension $d$. We show that the lead
ing order term has a strong dependence on the dimension\, namely $\\frac{d
(4-d)}{|x^2|}$ for $|x|\\rightarrow\\infty$. Furthermore our results are i
n the mathematical sense sharp.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Holzmann (TU Graz)
DTSTART:20211123T134500Z
DTEND:20211123T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/25
DESCRIPTION:Title: Approximation problems for Dirac operators with singular potentials\nby Markus Holzmann (TU Graz) as part of Quantum Circle\n\n\nAbstract\nI
n this talk two approximation problems for three dimensional Dirac operato
rs with singular $\\delta$-shell potentials supported on compact surfaces
are discussed. The first one is a generalization of a result by Gesztesy a
nd \\v{S}eba\, saying that a family of one dimensional Dirac operators wit
h a special combination of electrostatic and Lorentz scalar $\\delta$-inte
ractions converges in the nonrelativistic limit to a Schr\\"odinger operat
or with a $\\delta'$-interaction. In the higher dimensional setting a simi
lar convergence is obtained\, but the limit operator is a Schr\\"odinger o
perator with oblique jump conditions which is - for attractive interaction
strengths - not semibounded from below.\n\nThe second part of the talk is
devoted to the approximation of Dirac operators with $\\delta$-shell inte
ractions by Dirac operators with scaled regular potentials in the norm res
olvent sense. It will be explained how this can be achieved for special in
teraction strengths.\n\nThis talk is based on joint works with J.~Behrndt\
, C. Stelzer\, and G. Stenzel.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frantisek Štampach (Czech Technical University)
DTSTART:20211102T134500Z
DTEND:20211102T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/26
DESCRIPTION:Title: Spectral bounds and stability for 1D discrete Schrödinger operators w
ith complex potentials\nby Frantisek Štampach (Czech Technical Univer
sity) as part of Quantum Circle\n\n\nAbstract\nFirst\, we present optimal
spectral enclosures for discrete Laplacians on $\\mathbb{Z}$ and $\\mathbb
{N}$ with the Robin boundary condition perturbed by $\\ell^{1}$-complex po
tentials. Second\, we discuss results on a spectral stability of discrete
Schrödinger operators on $\\mathbb{N}$ with small complex potentials and
related discrete Hardy inequalities. The talk is based on joint projects w
ith O. O. Ibrogimov\, D. Krejčiřı́k\, and A. Laptev.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miloš Tater (Czech Academy of Sciences)
DTSTART:20211130T134500Z
DTEND:20211130T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/27
DESCRIPTION:Title: Spectral asymptotic of quasi-exactly solvable quartic potential\nb
y Miloš Tater (Czech Academy of Sciences) as part of Quantum Circle\n\n\n
Abstract\nWe discuss the asymptotics and the spectral monodromy of the qua
si-exactly solvable part of the spectrum of the quasi-exactly solvable qua
rtic. We formulate a conjecture on the coincidence of the asymptotic shape
of the level crossings of the latter oscillator with the asymptotic shape
of zeros of the Yablonskii-Vorob'ev polynomials. Jointly with B. Shapiro.
\n
LOCATION:https://researchseminars.org/talk/qc_seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Kandaurov (Czech Technical University)
DTSTART:20211214T134500Z
DTEND:20211214T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/28
DESCRIPTION:Title: Incremental learning of quantum generative adversarial network\nby
Artem Kandaurov (Czech Technical University) as part of Quantum Circle\n\
n\nAbstract\nMachine learning field has shown incredible impact on many ki
nds of optimization problems. Recently the power of machine learning was a
pplied to speed up the quantum states preparation. Although approximation
with quantum generative adversarial networks is one of the fastest ways to
prepare a generic quantum state\, training time for such models is still
significant and can easily impair quantum advantage. This thesis explores
incremental learning of quantum generative adversarial networks for the qu
antum states preparation problem and introduces learning use cases reducin
g the training time.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Malachov (Czech Technical University)
DTSTART:20211221T134500Z
DTEND:20211221T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/29
DESCRIPTION:Title: Chaotic features of purification protocol\nby Martin Malachov (Cze
ch Technical University) as part of Quantum Circle\n\n\nAbstract\nQuantum
information and communication has recently boomed into a promising discipl
ine offering secure communication and exponential speedup of certain algor
ithms. The basic elements of the quantum version of information/communicat
ion theory are qubits. A qubit is realised by a two-level quantum system a
nd two or more qubits can be entangled together to create a collective sta
te with information shared among its parts. Entanglement is a valuable res
ource used even in completely new algorithms like quantum teleportation. A
s a physical object\, qubit is subject to environment which makes its stat
e decay and disturb the entanglement. Purification protocols and error cor
rection codes aim on repairing the qubit states and retaining their entang
lement. One of proposed protocols use a copy of the qubit to act as a spec
ific environment but such action has been shown to induce chaotic behavior
\, particularly there are states undergoing deterministic chaos when the p
rotocol is iterated on them. Mathematically\, the protocol manifests as ra
tional polynomial functions of degree two. We propose a series of more gen
eral algorithms with polynomials of higher degree and investigate their pr
operties compared to the original algorithm whose features are also descri
bed in detail. We focus on fractal structures of chaotic states\, symmetri
es and other general properties of the protocols.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Zelaya (Nuclear Physics Institute CAS)
DTSTART:20220125T134500Z
DTEND:20220125T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/31
DESCRIPTION:Title: Fourth Painlevé and Ermakov equations: quantum invariants and new exa
ctly solvable time-dependent Hamiltonians\nby Kevin Zelaya (Nuclear Ph
ysics Institute CAS) as part of Quantum Circle\n\n\nAbstract\nAbstract: In
this talk\, I discuss a new realization of exactly solvable time-dependen
t Hamiltonians based on the solutions of the fourth Painlev\\'{e} and the
Ermakov equations. The latter is achieved by introducing a shape-invariant
condition between an unknown quantum invariant and a set of third-order i
ntertwining operators with time-dependent coefficients. The new quantum in
variant is constructed by adding a deformation term to the well-known para
metric oscillator invariant. Such a deformation depends explicitly on time
through the solutions of the Ermakov equation\, which ensures the regular
ity of the new time-dependent potential of the Hamiltonian at each time. T
he fourth Painlev\\'{e} equation appears naturally with the aid of the pro
per reparametrization\, whose parameters dictate the form of the discrete
spectrum of the quantum invariant. Some particular examples are presented
to illustrate the results.\nJoint work with Ian Marquete and V\\'{e}roniqu
e Hussin.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Lotoreichik (Nuclear Physics Institute)
DTSTART:20220301T134500Z
DTEND:20220301T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/32
DESCRIPTION:Title: Isoperimetric inequality for the two-dimensional magnetic Robin Laplac
ian\nby Vladimir Lotoreichik (Nuclear Physics Institute) as part of Qu
antum Circle\n\n\nAbstract\nIn this talk\, we consider the two-dimensional
magnetic Robin Laplacian with a negative boundary parameter on a bounded
and sufficiently smooth domain. The respective magnetic field is chosen to
be homogeneous. Among a certain class of domains\, we prove that the disk
maximizes the ground state energy under the fixed perimeter constraint pr
ovided that the magnetic field is of moderate strength. This class of doma
ins includes\, in particular\, all domains that are contained upon transla
tions in the disk of the same perimeter and all centrally symmetric domain
s. Our result generalizes the isoperimetric inequality for the Robin Lapla
cian without magnetic field due to Antunes\, Freitas\, and Krej\\v{c}i\\v{
r}\\'{i}k. \nThis talk is based on a joint work with Ayman Kachmar.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diana Barseghyan (University of Ostrava)
DTSTART:20220208T134500Z
DTEND:20220208T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/33
DESCRIPTION:Title: Spectral geometry in a rotating frame: properties of the ground state<
/a>\nby Diana Barseghyan (University of Ostrava) as part of Quantum Circle
\n\n\nAbstract\nWe investigate spectral properties of the operator describ
ing a quantum particle confined to a planar domain rotating around a fixed
point with certain angular velocity and demonstrate several properties of
its principal eigenvalue.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukas Heriban (Czech Technical University)
DTSTART:20220222T134500Z
DTEND:20220222T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/34
DESCRIPTION:by Lukas Heriban (Czech Technical University) as part of Quant
um Circle\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/qc_seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Md Fazlul Hoque (Czech Technical University)
DTSTART:20220503T124500Z
DTEND:20220503T134500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/35
DESCRIPTION:Title: Higher rank quadratic algebra of the $N$-dimensional quantum Smorodins
ky-Winternitz system\nby Md Fazlul Hoque (Czech Technical University)
as part of Quantum Circle\n\n\nAbstract\nAlgebraic methods are powerful to
ols in classical and quantum mechanics. Superintegrable systems are an imp
ortant class of classical and quantum systems which can be solved using al
gebraic approaches. In this talk\, I present higher rank quadratic algebra
of the $N$-dimensional quantum Smorodinsky-Winternitz system\, which is a
maximally superintegrable and exactly solvable model. It is shown that th
e model is multiseparable and the wave function can be expressed in terms
of Laguerre and Jacobi polynomials. We present a complete symmetry algebra
${\\cal SW}(N)$ of the system\, which it is a higher-rank quadratic one c
ontaining Racah algebra ${\\cal R}(N)$ as subalgebra. The substructures of
distinct quadratic Q(3) algebras and their related Casimirs are also stud
ied. The energy spectrum of the $N$-dimensional Smorodinsky-Winternitz sys
tem is obtained algebraically via the different set of subalgebras based o
n the Racah algebra ${\\cal R}(N)$. Joint work with Francisco Correa\, Ian
Marquette\, and Yao-Zhong Zhang.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiri Lipovsky (University of Hradec Kralove)
DTSTART:20220510T124500Z
DTEND:20220510T134500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/36
DESCRIPTION:Title: A Gelfand-Levitan Trace Formula for Generic Quantum Graphs\nby Jir
i Lipovsky (University of Hradec Kralove) as part of Quantum Circle\n\n\nA
bstract\nWe generalize the result given by Gelfand and Levitan for the Sch
roedinger operator on a segment with Neumann coupling condition. We give a
trace formula for the quantum graph with arbitrary edge lengths and gener
ic coupling conditions. The formula is reminiscent of the original Gelfand
-Levitan result on the segment with Neumann boundary conditions. The only
case of coupling conditions which is excluded is the condition with the un
itary coupling matrix having eigenvalue -1 (hence it is a set of measure z
ero in the set of all self-adjoint couplings). However\, the considered se
t does not include Dirichlet\, standard or delta-conditions.\n\nThis is jo
int work with prof. Pedro Freitas.\n\n[1] P. Freitas\, J. Lipovský\, A Ge
lfand-Levitan trace formula for generic quantum graphs\, Anal. Math. Phys.
11 (2021)\, 56 [mp_arc 19-4\; arXiv: 1901.07790 [math-ph]]\n
LOCATION:https://researchseminars.org/talk/qc_seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrii Khrabustovskyi (University of Hradec Kralove)
DTSTART:20221101T134500Z
DTEND:20221101T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/37
DESCRIPTION:Title: Domains with small resonators and what one can do with them\nby An
drii Khrabustovskyi (University of Hradec Kralove) as part of Quantum Circ
le\n\n\nAbstract\nhttp://gemma.ujf.cas.cz/%7Eexner/Qcabs/khrabustovskyi22a
.pdf\n
LOCATION:https://researchseminars.org/talk/qc_seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Md Fazlul Hoque (Czech Technical University)
DTSTART:20221108T134500Z
DTEND:20221108T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/38
DESCRIPTION:Title: Families of three-dimensional integrable and superintegrable classical
Hamiltonian systems in magnetic fields\nby Md Fazlul Hoque (Czech Tec
hnical University) as part of Quantum Circle\n\n\nAbstract\nThe talk prese
nts families of integrable and superintegrable classical Hamiltonian syste
ms in magnetic fields. We consider more general structure of their quadrat
ic commuting integrals of motion whose leading order terms are elements of
the universal enveloping algebra of the three--dimensional Euclidean alge
bra. We show how these pairs of commuting elements lead to distinct indepe
ndent integrals of motion in several nonvanishing magnetic fields. We also
search for additional first-- and second--order integrals of motion of th
ese systems to arrive at superintegrable systems. We construct the corresp
onding Poisson algebras of integrals of motion.\nThe talk is based on join
t work with Libor \\v{S}nobl.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylwia Kondej (University of Zielona Gora)
DTSTART:20221115T134500Z
DTEND:20221115T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/39
DESCRIPTION:Title: Quantum system with concentric circles and Aharonov-Bohm flux\nby
Sylwia Kondej (University of Zielona Gora) as part of Quantum Circle\n\n\n
Abstract\nIn this talk we discuss a class of two-dimensional Schrödinge
r operator with a singular interaction of the $\\delta$ type and a fixed s
trength supported by an infinite family of concentric\, equidistantly spac
ed circles. We analyze what happens below the essential spectrum after imp
lementing an Aharonov-Bohm flux $\\alpha \\in [0\,1/2]$ in the center. We
prove that there exists a critical value $\\alpha_{\\mathrm{cr}} \\in (0\,
1/2)$ such that the discrete spectrum has an accumulation point when $\\a
lpha < \\alpha_{\\mathrm{cr}}$\, while for $\\alpha \\geq \\alpha_{\\mathr
m{crit}}$ the number of eigenvalues is finite. The talk is based on a comm
on work with P. Exner.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davron Matrasulov (Turin Polytechnic University of Tashkent)
DTSTART:20221122T134500Z
DTEND:20221122T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/40
DESCRIPTION:Title: Dynamical confinement in low-dimensional quantum systems: Recent achie
vements and open problems\nby Davron Matrasulov (Turin Polytechnic Uni
versity of Tashkent) as part of Quantum Circle\n\n\nAbstract\nIn this talk
\, I will discuss the problem of dynamical quantum confinement\, described
in terms of Schrodinger and Dirac equations with time-dependent boundary
conditions. Practical applications in quantum optics\, atom optics and con
densed matter physics will be discussed. Open problems\, to be atatcked fr
om mathematicsal viewpoint will be also presented.\n
LOCATION:https://researchseminars.org/talk/qc_seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olena Atlasiuk (Mathematical Institute CAS)
DTSTART:20221129T134500Z
DTEND:20221129T144500Z
DTSTAMP:20260412T170858Z
UID:qc_seminar/41
DESCRIPTION:Title: Linear ordinary differential systems with generic boundary conditions
in Sobolev spaces\nby Olena Atlasiuk (Mathematical Institute CAS) as p
art of Quantum Circle\n\n\nAbstract\nhttp://gemma.ujf.cas.cz/%7Eexner/Qcab
s/atlasiuk22a.pdf\n
LOCATION:https://researchseminars.org/talk/qc_seminar/41/
END:VEVENT
END:VCALENDAR