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BEGIN:VEVENT
SUMMARY:Serena Cenatiempo (GSSI L'Aquila)
DTSTART;VALUE=DATE-TIME:20210420T133000Z
DTEND;VALUE=DATE-TIME:20210420T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T051501Z
UID:UnibaMathPhys/1
DESCRIPTION:Title: Bogoliubov theory for weakly interacting bosons\nby Serena Cenat
iempo (GSSI L'Aquila) as part of UniBA Mathematical Physics Seminar\n\n\nA
bstract\nNon relativistic bosons at sufficiently low temperature exhibit a
celebrated critical phase – known as Bose-Einstein condensation (BEC) -
effectively corresponding to a macroscopic occupation of a one particle s
tate. While the prediction of BEC for non-interacting bosons dates back to
one century ago\, there are few\, quite special\, models where we are abl
e to prove that condensation survives in presence of interaction. In this
talk I will review the state of art on the problem and discuss a closely r
elated question\, namely the characterization of the low energy spectrum o
f weakly interacting bosons\, a problem that was first addressed in a pion
eering work by Bogoliubov in ‘47. I will then present recent results obt
ained in different regimes\, in two and three dimensions.\nBased on joint
works with G. Basti\, C. Boccato\, C.Brennecke\, C. Caraci and B.Schlein.\
n
LOCATION:https://researchseminars.org/talk/UnibaMathPhys/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcello Porta (SISSA Trieste)
DTSTART;VALUE=DATE-TIME:20210518T133000Z
DTEND;VALUE=DATE-TIME:20210518T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T051501Z
UID:UnibaMathPhys/2
DESCRIPTION:Title: Correlation energy of a weakly interacting Fermi gas\nby Marcell
o Porta (SISSA Trieste) as part of UniBA Mathematical Physics Seminar\n\n\
nAbstract\nIn this talk I will discuss the ground state properties of homo
geneous\, interacting Fermi gases\, in the mean-field regime. In this regi
me\, Hartree-Fock theory provides a good approximation for the ground stat
e energy of the system\; this approximation is based on the replacement of
the space of fermionic wave functions with the smaller set of Slater dete
rminants\, where the only correlations among the particles are those induc
ed by the Pauli principle. I will discuss a rigorous approach that allows
to go beyond the Hartree-Fock approximation\, and that in particular allow
s to compute the leading order of the correlation energy\, defined as the
difference between the many-body ground state energy and the Hartree-Fock
ground state energy. The expression we obtain reproduces the ground state
energy of a non-interacting Bose gas\, suggesting that the low energy exci
tations of high density Fermi gases are effectively described by a quasi-f
ree Bose gas. The method of proof consists in a rigorous formulation of th
e bosonization technique\, developed in the condensed matter physics in th
e 80s. Joint work with N. Benedikter\, P. T. Nam\, B. Schlein and R. Seiri
nger.\n
LOCATION:https://researchseminars.org/talk/UnibaMathPhys/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomaž Prosen (Ljubljana)
DTSTART;VALUE=DATE-TIME:20210608T133000Z
DTEND;VALUE=DATE-TIME:20210608T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T051501Z
UID:UnibaMathPhys/3
DESCRIPTION:Title: Exactly solved models of chaotic many-body dynamics\nby Tomaž P
rosen (Ljubljana) as part of UniBA Mathematical Physics Seminar\n\n\nAbstr
act\nOne should be amazed with an unreasonable effectiveness of random mat
rix theory to describe spectral fluctuations in simple non-integrable many
-body systems\, say one dimensional spin 1/2 chains with local interaction
s. I will discuss a class of Floquet (periodically driven) quantum spin ch
ains - specifically\, dual unitary Floquet circuits - where the random mat
rix result for the spectral form factor can be derived or even rigorously
proven. Several other nontrivial exactly solvable features of the presente
d models\, such as dynamical correlations or entanglement dynamics\, will
be discussed.\n
LOCATION:https://researchseminars.org/talk/UnibaMathPhys/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Michelangeli (Bonn)
DTSTART;VALUE=DATE-TIME:20210525T133000Z
DTEND;VALUE=DATE-TIME:20210525T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T051501Z
UID:UnibaMathPhys/4
DESCRIPTION:Title: Effective quantum dynamics of composite Bose-Einstein condensates\nby Alessandro Michelangeli (Bonn) as part of UniBA Mathematical Physics
Seminar\n\n\nAbstract\nAmong the most sophisticated\, recent experiments
with Bose-Einstein condensates\, a primary role is played by composite con
densation. This is like ordinary condensation\, with some kind of internal
structure: condensate samples consisting of two or more populations of di
fferent particle species (condensate mixtures)\, condensates of particles
whose spin is coupled with external radiation fields (pseudo-spinor conden
sates)\, condensates with interaction between different hyperfine states (
spinor condensates)\, or condensates with macroscopic occupation of differ
ent one-body orbitals (fragmented condensates). Their observed dynamics ob
ey multiple coupled non-linear Schrödinger equations\, and in this talk I
shall discuss recent rigorous derivations of such effective dynamics from
from the first-principle many-body (linear) Schrödinger equation. A spec
ial focus will be given to condensate mixtures\, for which the ground stat
e and the correctness of Bogolyubov's theory will be also shown.\n
LOCATION:https://researchseminars.org/talk/UnibaMathPhys/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva-Maria Graefe (London)
DTSTART;VALUE=DATE-TIME:20210615T133000Z
DTEND;VALUE=DATE-TIME:20210615T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T051501Z
UID:UnibaMathPhys/5
DESCRIPTION:Title: A non-Hermitian PT-symmetric kicked top\nby Eva-Maria Graefe (Lo
ndon) as part of UniBA Mathematical Physics Seminar\n\n\nAbstract\nA non-H
ermitian PT-symmetric version of the kicked top is introduced to study the
interplay of quantum chaos with balanced loss and gain. The classical dyn
amics arising from the quantum dynamics of the angular momentum expectatio
n values are derived. It is demonstrated that the presence of PT-symmetry
can lead to ''stable'' mixed regular chaotic behaviour without sinks or so
urces for subcritical values of the gain-loss parameter. For large values
of the kicking strength a strange attractor is observed that also persists
if PT-symmetry is broken. Classical structures are also identified in the
quantum dynamics. Finally\, some of the statistics of the eigenvalues of
the quantum system are analysed.\n
LOCATION:https://researchseminars.org/talk/UnibaMathPhys/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Życzkowski (Cracow\, Warsaw)
DTSTART;VALUE=DATE-TIME:20210622T133000Z
DTEND;VALUE=DATE-TIME:20210622T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T051501Z
UID:UnibaMathPhys/6
DESCRIPTION:Title: The spectra of random operations and random Lindblad operators\n
by Karol Życzkowski (Cracow\, Warsaw) as part of UniBA Mathematical Physi
cs Seminar\n\n\nAbstract\nWe analyze spectral properties of generic quantu
m operations\,\nwhich describe open systems under assumption of a strong\n
decoherence and a strong coupling with an environment.\nIn the case of dis
crete maps the spectrum of a quantum stochastic\nmap displays a universal
behaviour: it contains the leading eigenvalue \n\\lambda_1 = 1\, while al
l other eigenvalues are restricted to the disk of radius R<1. \nSimilar pr
operties are exhibited by spectra of their classical counterparts - rando
m stochastic matrices.\n\nIn the case of a generic dynamics in continuous
time\, we introduce an ensemble of \nrandom Lindblad operators\, which gen
erate Markov evolution in the space of density \nmatrices of a fixed size.
Universal spectral features of such operators\, \nincluding the lemon-lik
e shape of the spectrum in the complex plane\, are explained\nwith a non-h
ermitian random matrix model. The structure of the spectrum determines\nth
e transient behaviour of the quantum system and the convergence of the dyn
amics\ntowards the generically unique invariant state. The quantum-to-cla
ssical transition\nfor this model is also studied and the spectra of rando
m Kolmogorov operators \nare investigated.\n
LOCATION:https://researchseminars.org/talk/UnibaMathPhys/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cécilia Lancien (Toulouse)
DTSTART;VALUE=DATE-TIME:20210629T133000Z
DTEND;VALUE=DATE-TIME:20210629T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T051501Z
UID:UnibaMathPhys/7
DESCRIPTION:Title: Typical correlations and entanglement in random MPS and PEPS\nby
Cécilia Lancien (Toulouse) as part of UniBA Mathematical Physics Seminar
\n\n\nAbstract\nTensor network states are used extensively as a mathematic
ally convenient description of physically relevant states of many-body qua
ntum systems. Those built on regular lattices\, i.e. matrix product states
(MPS) in dimension 1 and projected entangled pair states (PEPS) in dimens
ion 2 or higher\, are of particular interest in condensed matter physics.
In this talk\, I will try to answer the following general question: which
features of MPS and PEPS are generic and which are\, on the contrary\, exc
eptional? Or to rephrase it: given an MPS or PEPS sampled at random\, what
are the features that it displays with either high or low probability? On
e property which we will focus on is that of having either rapidly decayin
g or long-range correlations. In a nutshell\, the main result I will state
is that translation-invariant MPS and PEPS typically exhibit exponential
decay of correlations at a high rate. I will show two distinct ways of get
ting to this conclusion\, depending on the dimensional regime under consid
eration. Both yield intermediate results which are of independent interest
\, namely: the parent Hamiltonian and the transfer operator of such MPS an
d PEPS typically have a large spectral gap. If time allows\, I will also p
resent on-going attempts at quantifying the amount of genuinely multiparti
te entanglement in such random MPS and PEPS.\nThe talk will be based mainl
y on a joint work with David Perez-Garcia\, available at arXiv:1906.11682\
, and on some work in progress with Ion Nechita.\n
LOCATION:https://researchseminars.org/talk/UnibaMathPhys/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Seiringer (IST Austria)
DTSTART;VALUE=DATE-TIME:20211103T143000Z
DTEND;VALUE=DATE-TIME:20211103T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T051501Z
UID:UnibaMathPhys/8
DESCRIPTION:Title: Quantum fluctuations and dynamics of a strongly coupled polaron\
nby Robert Seiringer (IST Austria) as part of UniBA Mathematical Physics S
eminar\n\n\nAbstract\nWe review old and new results on the Fröhlich polar
on model. The discussion includes the validity of the (classical) Landau--
Pekar equations for the dynamics in the strong coupling limit\, quantum co
rrections to this limit\, as well as the divergence of the effective polar
on mass.\n
LOCATION:https://researchseminars.org/talk/UnibaMathPhys/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Exner (Prague)
DTSTART;VALUE=DATE-TIME:20211124T143000Z
DTEND;VALUE=DATE-TIME:20211124T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T051501Z
UID:UnibaMathPhys/9
DESCRIPTION:Title: A product formula and its application to Zeno quantum dynamics\n
by Pavel Exner (Prague) as part of UniBA Mathematical Physics Seminar\n\n\
nAbstract\nWe present a new product formula which involves a unitary group
generated by a positive self-adjoint operator and a continuous projection
-valued function. The question has a direct physical motivation coming fro
m treatment of decaying quantum systems and\, in particular\, the Zeno eff
ect associated with frequently repeated measurements. Used in this context
\, the formula expresses the dynamics of such a system. We describe the ba
ckground of the problem\, sketch the proof of the formula\, and present an
example of a permanent position ascertaining which leads to an effective
constraint given by the Dirichlet condition.\n
LOCATION:https://researchseminars.org/talk/UnibaMathPhys/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Pepe (Bari)
DTSTART;VALUE=DATE-TIME:20211214T143000Z
DTEND;VALUE=DATE-TIME:20211214T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T051501Z
UID:UnibaMathPhys/10
DESCRIPTION:Title: The many facets of quantum decay in a simple hopping model\nby
Francesco Pepe (Bari) as part of UniBA Mathematical Physics Seminar\n\n\nA
bstract\nThe decay of an unstable system is usually described by an expone
ntial function\, following a classical statistical assumption. In a quantu
m mechanical context\, the exponential law emerges in the context of pertu
rbation theory\, and is characterized by a decay rate fixed by the Fermi g
olden rule. However\, quantum mechanics generally predicts deviations from
the exponential: the survival probability is characterized by an initial
regime of quadratic decrease\, while at large times it must follow\, in a
very wide range of physical systems\, a power law\, with possible superimp
osed oscillations. In this seminar\, I will describe how all these feature
s can be identified in the behavior of a semi-analytically solvable neares
t-neigbor hopping model. Specifically\, I will analyze the quantum decay o
f an initial state in which the first site of a semi-infinite linear array
is populated\, showing that the model parameters can be tuned in order to
enhance the relevance of the quadratic and the power-law decay regime.\n
LOCATION:https://researchseminars.org/talk/UnibaMathPhys/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Hall (Notre Dame)
DTSTART;VALUE=DATE-TIME:20220330T133000Z
DTEND;VALUE=DATE-TIME:20220330T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T051501Z
UID:UnibaMathPhys/11
DESCRIPTION:Title: PDE methods in random matrix theory\nby Brian Hall (Notre Dame)
as part of UniBA Mathematical Physics Seminar\n\n\nAbstract\nGirko’s me
thod for analyzing random matrix models is to study the log potential of t
he eigenvalue distribution. It is then sometimes useful to put in a regula
rization parameter $\\epsilon$ that avoids the singularity in the log func
tion. In recent work of mine with Driver and Kemp\, we studied a “multip
licative” random matrix model—Brownian motion in the general linear gr
oup—by showing that the regularized log potential satisfies a PDE. This
PDE can then be analyzed by the method of characteristics to compute the l
imiting eigenvalue distribution\, which has a beautiful structure.\n\nI wi
ll discuss the PDE method and several random matrix models that can be ana
lyzed using it. The talk will be self-contained and have lots of pictures.
\n
LOCATION:https://researchseminars.org/talk/UnibaMathPhys/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Zamparo (Bari)
DTSTART;VALUE=DATE-TIME:20220302T143000Z
DTEND;VALUE=DATE-TIME:20220302T153000Z
DTSTAMP;VALUE=DATE-TIME:20240329T051501Z
UID:UnibaMathPhys/12
DESCRIPTION:Title: Large deviation principles in renewal-reward processes\nby Marc
o Zamparo (Bari) as part of UniBA Mathematical Physics Seminar\n\nLecture
held in Aula XI - Dipartimento di Matematica.\n\nAbstract\nRenewal-reward
processes describe some event that is continuously renewed over time\, \ni
nvolving a reward at each occurrence. In this seminar\, I will establish a
sharp large deviation \nprinciple for renewal-reward processes supposing
that rewards take values in a separable \nBanach space. My large deviation
principle extends Cramér’s theorem to renewal theory. \nSome applicati
ons will be reviewed with special focus on renewal models of statistical p
hysics\, \nsuch as the Poland-Scheraga model of DNA denaturation\, which a
re Gibbs changes of measure \nof a renewal process.\n\nReferences:\n- M. Z
amparo\, Large deviations in discrete-time renewal theory\,\nStoch. Proces
s. Their Appl. 139 (2021) 80-109 \n- M. Zamparo\, Large deviations in rene
wal models of statistical mechanics\,\nJ. Phys. A: Math. Theor. 52 (2019)
495004\n- M. Zamparo\, Critical fluctuations in renewal models of statisti
cal mechanics\,\nJ. Math. Phys. 62 (2021) 113301\n- M. Zamparo\, Large dev
iation principles for renewal-reward processes\,\nsubmitted to Ann. Appl.
Probab. (arXiv:2111.01679)\n
LOCATION:https://researchseminars.org/talk/UnibaMathPhys/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elia Bisi (Vienna)
DTSTART;VALUE=DATE-TIME:20220406T133000Z
DTEND;VALUE=DATE-TIME:20220406T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T051501Z
UID:UnibaMathPhys/13
DESCRIPTION:Title: Matsumoto-Yor and Dufresne type theorems for a random walk on posit
ive definite matrices\nby Elia Bisi (Vienna) as part of UniBA Mathemat
ical Physics Seminar\n\n\nAbstract\nWe establish analogues of the geometri
c Pitman 2M-X theorem of Matsumoto and Yor and of the classical Dufresne i
dentity\, for a multiplicative random walk on positive definite matrices w
ith Beta type II distributed increments. The Dufresne type identity provid
es also an example of a stochastic matrix recursion that admits an explici
t solution.\nJoint work with J. Arista and N. O'Connell.\n
LOCATION:https://researchseminars.org/talk/UnibaMathPhys/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregory Berkolaiko (Texas)
DTSTART;VALUE=DATE-TIME:20220427T133000Z
DTEND;VALUE=DATE-TIME:20220427T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T051501Z
UID:UnibaMathPhys/14
DESCRIPTION:Title: Nodal deficiency\, spectral minimal partitions and the Dirichlet-to
-Neumann map\nby Gregory Berkolaiko (Texas) as part of UniBA Mathemati
cal Physics Seminar\n\n\nAbstract\nIn this overview talk we will explore c
onnections between the subjects\nmentioned in the title as well as some ot
her notions such as the\nspectral shift and the Schur complement. For an
eigenfunction of the\nDirichlet Laplacian\, the nodal deficiency is the di
fference between\nthe label of an eigenfunction (starting with 1 for the g
round state)\nand the number of its nodal domains. It is known to be equa
l to the\nMorse index of a critical point of a certain spectral functional
\ndefined on the space of partitions of the manifold. The connection\nbet
ween the two is easier understood via the introduction of a two-sided\nDir
ichlet-to-Neumann map. On one hand\, the number of its negative\neigenval
ues is related to the spectral shift (which is a natural\ninterpretation o
f the nodal deficiency). On the other hand\, the DtN\nmap is unitarily eq
uivalent to the Hessian of the spectral functional\nat the critical point.
\n\nThe talk is based on several papers of Yaiza Canzani\, Graham Cox\,\nB
ernard Helffer\, Peter Kuchment\, Jeremy Marzuola\, Uzy Smilansky and\nMik
ael Sundqvist\, with and without the speaker.\n
LOCATION:https://researchseminars.org/talk/UnibaMathPhys/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nilanjana Datta (Cambridge)
DTSTART;VALUE=DATE-TIME:20220608T133000Z
DTEND;VALUE=DATE-TIME:20220608T143000Z
DTSTAMP;VALUE=DATE-TIME:20240329T051501Z
UID:UnibaMathPhys/16
DESCRIPTION:Title: Majorization and entropic continuity bounds\nby Nilanjana Datta
(Cambridge) as part of UniBA Mathematical Physics Seminar\n\n\nAbstract\n
We employ majorization theory to obtain a powerful tool for deriving simpl
e and universal proofs\nof continuity bounds for various entropies which a
re relevant in information theory. In obtaining this\, we first derive a m
ore general result which may be of independent interest: a necessary and s
ufficient condition under which a state maximizes a concave\, continuous\,
Gateaux-differentiable function in an epsilon-ball in trace distance. Exa
mples of such a function include the von Neumann entropy\, and the conditi
onal entropy of bipartite states. This is joint work with Eric Hanson.\n
LOCATION:https://researchseminars.org/talk/UnibaMathPhys/16/
END:VEVENT
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