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BEGIN:VEVENT
SUMMARY:Pavel Exner (Doppler Institute for Mathematical Physics and Applie
d Mathematics)
DTSTART;VALUE=DATE-TIME:20201110T134500Z
DTEND;VALUE=DATE-TIME:20201110T144500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20201124T134500Z
DTEND;VALUE=DATE-TIME:20201124T144500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20201201T134500Z
DTEND;VALUE=DATE-TIME:20201201T144500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20201208T134500Z
DTEND;VALUE=DATE-TIME:20201208T144500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20201215T134500Z
DTEND;VALUE=DATE-TIME:20201215T144500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20201222T134500Z
DTEND;VALUE=DATE-TIME:20201222T144500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20210105T134500Z
DTEND;VALUE=DATE-TIME:20210105T144500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20210112T134500Z
DTEND;VALUE=DATE-TIME:20210112T144500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20210216T134500Z
DTEND;VALUE=DATE-TIME:20210216T144500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20210323T134500Z
DTEND;VALUE=DATE-TIME:20210323T144500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20210316T134500Z
DTEND;VALUE=DATE-TIME:20210316T144500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20210309T134500Z
DTEND;VALUE=DATE-TIME:20210309T144500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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) 283â€“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;VALUE=DATE-TIME:20210330T124500Z
DTEND;VALUE=DATE-TIME:20210330T134500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20210406T124500Z
DTEND;VALUE=DATE-TIME:20210406T134500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20210413T124500Z
DTEND;VALUE=DATE-TIME:20210413T134500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20210420T124500Z
DTEND;VALUE=DATE-TIME:20210420T134500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20210427T124500Z
DTEND;VALUE=DATE-TIME:20210427T134500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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 Weylâ€™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;VALUE=DATE-TIME:20210504T124500Z
DTEND;VALUE=DATE-TIME:20210504T134500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20210504T140000Z
DTEND;VALUE=DATE-TIME:20210504T150000Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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;VALUE=DATE-TIME:20210518T124500Z
DTEND;VALUE=DATE-TIME:20210518T134500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
UID:qc_seminar/20
DESCRIPTION:Title: he nonlinear Schrödinger equation with isolated singularities\nby
Claudio Cacciapuoti (Universita degli Studi dell'Insubria) as part of Qua
ntum Circle\n\n\nAbstract\nI will discuss the well posedness of the nonlin
ear SchrĂ¶dinger equation with power-type nonlinearity and in the presen
ce of a delta interaction\, both in dimension two and three. This is a mod
el of evolution for some singular solutions that are well known in the ana
lysis of semilinear elliptic equations. I will consider local existence\,
uniqueness and continuous dependence from the initial data of strong (oper
ator domain) solutions of the associated Cauchy problem. In dimension two
well posedness holds for any power nonlinearity and global existence is pr
oved 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 work
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;VALUE=DATE-TIME:20210525T124500Z
DTEND;VALUE=DATE-TIME:20210525T134500Z
DTSTAMP;VALUE=DATE-TIME:20210514T202356Z
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
END:VCALENDAR