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SUMMARY:Weighted models for level statistics across the many--body localiz
ation transition
DTSTART;VALUE=DATE-TIME:20180903T133500Z
DTEND;VALUE=DATE-TIME:20180903T135500Z
DTSTAMP;VALUE=DATE-TIME:20220809T225027Z
UID:indico-contribution-37-217@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Piotr Sierant (Jagiellonian University in Kraków)\n
We study level statistics across the many-body localization transition. An
analysis of the gap ratio statistics from the perspective of inter- and i
ntra-sample randomness allows us to pin point differences between transiti
ons in random and quasi-random disorder\, showing effects due to Griffiths
rare events for the former case. Defining a mean gap ratio for a single r
ealization of disorder we show that it has a broad\, system specific distr
ibution across the whole transition. That explains the necessity of introd
ucing weighted random matrix ensembles that correctly grasp the sample-to-
sample variation of system properties including the rare events. We consid
er two such approaches. One is a weighted short-range plasma model\, the o
ther a weighted power--law random banded matrix model. Treating the single
sample gap ratio distribution as input\, the considered weighted models y
ield a very good agreement both for spacing distribution including its exp
onential tail and the number variance up to tens of level spacings. We sho
w explicitly that our weighted models describe the level statistics across
the whole ergodic to many-body localized transition much more faithfully
than earlier predictions. We also demonstrate that our model describes lev
el statistics in variety of spin\, bosonic and fermionic systems. The rema
ining deviations for long-range spectral correlations are discussed and at
tributed mainly to the intricacies of level unfolding. \n\n[1] P. Sierant
and J. Zakrzewski\, *Intermediate spectral statistics in the many--body lo
calization transition*\, arXiv:1807.06983\n\n[2] P. Sierant and J. Zakrzew
ski\, *Weighted models for level statistics across the many--body localiza
tion transition*\, arXiv:1808.02795\n\nhttps://zakopane.if.uj.edu.pl/event
/6/contributions/217/
LOCATION:
URL:https://zakopane.if.uj.edu.pl/event/6/contributions/217/
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SUMMARY:Two distinguishable impurities in BEC: squeezing and entanglement
of two Bose polarons
DTSTART;VALUE=DATE-TIME:20180903T131500Z
DTEND;VALUE=DATE-TIME:20180903T133500Z
DTSTAMP;VALUE=DATE-TIME:20220809T225027Z
UID:indico-contribution-37-194@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Christos Charalambous (ICFO)\nWe apply the quantum o
pen system formalism to describe the physics of two impurities immersed in
a Bose-Einstein condensate. Here\, the impurities are considered to be t
wo quantum Brownian particles interacting with a bath of oscillators corre
sponding to the Bogoliubov modes of the condensate. We characterize the dy
namics of the Brownian impurities with Langevin-like quantum stochastic e
quations carrying an account of memory effects. The Langevin equations are
solved to evaluate the covariance matrix. We find that the presence of th
e bath induces an interaction between the impurities\, which leads to enta
nglement among them. Whether or not the impurities are trapped in an exter
nal potential gives rise to different behaviours of such entanglement: (i)
In the absence of external potential\, we observe sudden death of entangl
ement\, i.e.\, entanglement disappears at long enough times\; (ii) In the
presence of external harmonic potential\, entanglement survives even at as
ymptotic time limit. Our study puts the behaviour of entanglement under sc
rutiny and captures its response to experimentally tunable parameters.\nBe
sides entanglement\, we study the squeezing as well. Interestingly\, we fi
nd that the mean-square-displacement is super-diffusive\, which as we prov
e\, is due to non-Markovianity of the dynamics. Further\, a full analysis
of squeezing is provided\, which explains how experimentally tunable para
meters create or destroy squeezing. We emphasize that all of our analysis
is rigorously obtained from a realistic physical model\; in particular\,
we avoid manipulating it by introducing artificial Hamiltonians\, or by in
troducing arbitrary spectral densities.\n\nhttps://zakopane.if.uj.edu.pl/e
vent/6/contributions/194/
LOCATION:
URL:https://zakopane.if.uj.edu.pl/event/6/contributions/194/
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SUMMARY:Quantum law for partition of kinetic energy
DTSTART;VALUE=DATE-TIME:20180903T123000Z
DTEND;VALUE=DATE-TIME:20180903T131500Z
DTSTAMP;VALUE=DATE-TIME:20220809T225027Z
UID:indico-contribution-37-184@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Jerzy Luczka (University of Silesia)\nOne of the fun
damental laws of classical statistical physics is the energy equipartition
theorem which states that for each degree of freedom the average kinetic
energy equals $E_k=k_B T/2$\, where $k_B$ is the Boltzmann constant and $
T$ is temperature of the system. Despite the fact that quantum mechanics h
as already been developed for more than 100 years still there is no quantu
m counterpart of this theorem. We attempt to fill this far-reaching gap an
d formulate the \\emph{quantum law for equipartition of energy} in the app
ealing form $E_k = \\langle \\mathcal E_k \\rangle$\, where $\\mathcal E_k
$ is thermal kinetic energy per one degree of freedom of the thermostat co
nsisting of harmonic oscillators and $\\langle ...\\rangle$ denotes averag
ing over frequencies $\\omega$ of those thermostat oscillators which contr
ibute to $E_k$ according to the probability distribution $\\mathbb P(\\ome
ga)$. \n %It is valid for an arbitrary strength of the system-thermostat c
oupling. \nWe derive it for two paradigmatic and exactly solvable models o
f quantum open systems: a free Brownian particle and a harmonic oscillator
. We formulate conditions for validity of the relation $E_k = \\langle \\
mathcal E_k \\rangle$ for other quantum systems.\n\nhttps://zakopane.if.uj
.edu.pl/event/6/contributions/184/
LOCATION:
URL:https://zakopane.if.uj.edu.pl/event/6/contributions/184/
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