pinecone/core-2020-05-10-deduplication huggingface dataset:
Macroscopic and Microscopic Thermal Equilibrium

We study the nature of and approach to thermal equilibrium in isolated
quantum systems. An individual isolated macroscopic quantum system in a pure or
mixed state is regarded as being in thermal equilibrium if all macroscopic
observables assume rather sharply the values obtained from thermodynamics. Of
such a system (or state) we say that it is in macroscopic thermal equilibrium
(MATE). A stronger requirement than MATE is that even microscopic observables
(i.e., ones referring to a small subsystem) have a probability distribution in
agreement with that obtained from the micro-canonical, or equivalently the
canonical, ensemble for the whole system. Of such a system we say that it is in
microscopic thermal equilibrium (MITE). The distinction between MITE and MATE
is particularly relevant for systems with many-body localization (MBL) for
which the energy eigenfuctions fail to be in MITE while necessarily most of
them, but not all, are in MATE. However, if we consider superpositions of
energy eigenfunctions (i.e., typical wave functions $\psi$) in an energy shell,
then for generic macroscopic systems, including those with MBL, most $\psi$ are
in both MATE and MITE. We explore here the properties of MATE and MITE and
compare the two notions, thereby elaborating on ideas introduced in [Goldstein
et al., Phys.Rev.Lett. 115: 100402 (2015)].Comment: 36 pages LaTeX, 2 figures; v3 minor improvement
Localization due to interaction-enhanced disorder in bosonic systems

Localization in interacting systems caused by disorder, known as many-body
localization (MBL), has attracted a lot of attention in recent years. Most
systems studied in this context also show single-particle localization, and the
question of MBL is whether the phenomena survives the effects of interactions.
It is intriguing to consider a system with no single-particle localization but
which does localize in the presence of many particles. The localization
phenomena occurs "due to" rather than "in spite of" interactions in such
systems. We consider a simple bosonic system and show that interactions enhance
the effects of very weak disorder and result in localization when many
particles are present. We provide physical insights into the mechanism involved
and support our results with analytical and numerical calculations.Comment: 8 pages, 4 figure
Coherent backscattering in the Fock space of ultracold bosonic atoms

We present numerical evidence for the occurrence of coherent backscattering
in the Fock space of a small disordered Bose-Hubbard system consisting of four
sites and containing five particles. This many-body interference phenomenon can
most conveniently be seen in time evolution processes that start from a Fock
state of the Bose-Hubbard system. It manifests itself in an enhanced detection
probability of this initial state as compared to other Fock states with
comparable total energy. We argue that coherent backscattering in Fock space
can be experimentally measured with ultracold bosonic atoms in optical lattices
using state-of-the-art single-site detection techniques. A synthetic gauge
field can be induced in order to break time-reversal symmetry within the
lattice and thereby destroy coherent backscattering. While this many-body
interference effect is most prominently visible in the presence of eigenstate
thermalization, we briefly discuss its significance in the opposite regime of
many-body localization.Comment: 7 pages, 4 figure
Beta-functions of non-linear $\sigma$-models for disordered and
  interacting electron systems

We provide and study complete sets of one-loop renormalization group
equations of several Finkel'stein non-linear $\sigma$-models, the effective
field theories describing the diffusive quantum fluctuations in correlated
disordered systems. We consider different cases according to the presence of
certain symmetries induced by the original random Hamiltonians, and we show
that, for interacting systems, the Cartan's classification of symmetry classes
is not enough to uniquely determine their scaling behaviors.Comment: 16 pages, 4 figures, final version for the special issue "Many-Body
  Localization" in Annalen der Physi
Out-of-time-ordered correlators in many-body localized systems

In many-body localized systems, propagation of information forms a light cone
that grows logarithmically with time. However, local changes in energy or other
conserved quantities typically spread only within a finite distance. Is it
possible to detect the logarithmic light cone generated by a local perturbation
from the response of a local operator at a later time? We numerically calculate
various correlators in the random-field Heisenberg chain. While the equilibrium
retarded correlator $A(t=0)B(t>0)$ is not sensitive to the unbounded
information propagation, the out-of-time-ordered correlator
$A(t=0)B(t>0)A(t=0)B(t>0)$ can detect the logarithmic light cone. We relate
out-of-time-ordered correlators to the Lieb-Robinson bound in many-body
localized systems, and show how to detect the logarithmic light cone with
retarded correlators in specially designed states. Furthermore, we study the
temperature dependence of the logarithmic light cone using out-of-time-ordered
correlators.Comment: published version with updated reference
Rare region effects and dynamics near the many-body localization
  transition

The low-frequency response of systems near the many-body localization phase
transition, on either side of the transition, is dominated by contributions
from rare regions that are locally "in the other phase", i.e., rare localized
regions in a system that is typically thermal, or rare thermal regions in a
system that is typically localized. Rare localized regions affect the
properties of the thermal phase, especially in one dimension, by acting as
bottlenecks for transport and the growth of entanglement, whereas rare thermal
regions in the localized phase act as local "baths" and dominate the
low-frequency response of the MBL phase. We review recent progress in
understanding these rare-region effects, and discuss some of the open questions
associated with them: in particular, whether and in what circumstances a single
rare thermal region can destabilize the many-body localized phase.Comment: Review Article, 14 pages + acknowledgements + Ref
Models for a multimode bosonic tunneling junction

We discuss the relaxation dynamics for a bosonic tunneling junction with two
modes in the central potential well. We use a master equation description for
ultracold bosons tunneling in the presence of noise and incoherent coupling
processes into the two central modes. Whilst we cannot quantitatively reproduce
the experimental data of the setup reported in [Phys. Rev. Lett. {\bf 115},
050601 (2015)], we find a reasonable qualitative agreement of the refilling
process of the initially depleted central site. Our results may pave the way
for the control of bosonic tunneling junctions by the simultaneous presence of
decoherence processes and atom-atom interaction
Quasinormal modes of BTZ black hole and Hawking-like radiation in
  graphene

The Ba\~{n}ados-Teitelboim-Zanelli (BTZ) black hole model corresponds to a
solution of (2+1)-dimensional Einstein gravity with negative cosmological
constant, and by a conformal rescaling its metric can be mapped onto the
hyperbolic pseudosphere surface (Beltrami trumpet) with negative curvature.
Beltrami trumpet shaped graphene sheets have been predicted to emit Hawking
radiation that is experimentally detectable by a scanning tunnelling
microscope. Here, for the first time we present an analytical algorithm that
allows variational solutions to the Dirac Hamiltonian of graphene
pseudoparticles in BTZ black hole gravitational field by using an approach
based on the formalism of pseudo-Hermitian Hamiltonians within a
discrete-basis-set method. We show that our model not only reproduces the exact
results for the real part of quasinormal mode frequencies of (2+1)-dimensional
spinless BTZ black hole, but also provides analytical results for the real part
of quasinormal modes of spinning BTZ black hole, and also offers some
predictions for the observable effects with a view to gravity-like phenomena in
a curved graphene sheet.Comment: 5 pages,1 figur
Out-of-time-order correlations in many-body localized and thermal phases

We use the out-of-time-order (OTO) correlators to study the slow dynamics in
the many-body localized (MBL) phase. We investigate OTO correlators in the
effective ("l-bit") model of the MBL phase, and show that their amplitudes
after disorder averaging approach their long-time limits as power-laws of time.
This power-law dynamics is due to dephasing caused by interactions between the
localized operators that fall off exponentially with distance. The long-time
limits of the OTO correlators are determined by the overlaps of the local
operators with the conserved l-bits. We demonstrate numerically our results in
the effective model and three other more "realistic" spin chain models.
Furthermore, we extend our calculations to the thermal phase and find that for
a time-independent Hamiltonian, the OTO correlators also appear to vanish as a
power law at long time, perhaps due to coupling to conserved densities. In
contrast, we find that in the thermal phase of a Floquet spin model with no
conserved densities the OTO correlator decays exponentially at long times.Comment: 24 pages, 12 figure
Dynamical Many-body Localization and Delocalization in Periodically
  Driven Closed Quantum Systems

Quantum interference lies at the heart of several surprising equilibrium and
non-equilibrium phenomena in many-body Physics. Here we discuss two recently
explored non-equilibrium scenarios where external periodic drive applied to
closed (i.e., not attached to any external bath) quantum many-body systems have
apparently opposite effects in respective cases. In one case it
freezes/localizes a disorder free system dynamically, while in the other it
delocalizes a disordered many-body localized system, and quantum interference
is responsible for both the effects. We review these in the perspective of more
general questions of ergodicity, energy absorption, asymptotic behavior, and
finally the essential role of quantum mechanics in understanding these issues
in periodically driven closed many-body systems. In this article we intend to
deliver a non-technical account of some recent developments in this field in a
manner accessible to a broad readership.Comment: Invited Feature Article for Annalen der Physik Special Issue on
  Many-body Localization (accepted on Feb. 1, 2017
Hamiltonian ratchets with ultra-cold atoms

Quantum-resonance ratchets have been realized over the last ten years for the
production of directed currents of atoms. These non-dissipative systems are
based on the interaction of a Bose-Einstein condensate with an optical standing
wave potential to produce a current of atoms in momentum space. In this paper
we provide a review of the important features of these ratchets with a
particular emphasis on their optimization using more complex initial states. We
also examine their stability close to resonance conditions of the kicking.
Finally we discuss the way in which these ratchets may pave the way for
applications in quantum (random) walks and matter-wave interferometry
Out-of-equilibrium fluctuation-dissipation relations verified by the
  electrical and thermoelectrical ac-conductances in a quantum dot

The electrical and heat currents flowing through a quantum dot are calculated
in the presence of a time-modulated gate voltage with the help of the
out-of-equilibrium Green function technique. From the first harmonics of the
currents, we extract the electrical and thermoelectrical trans-admittances and
ac-conductances. Next, by a careful comparison of the ac-conductances with the
finite-frequency electrical and mixed electrical-heat noises, we establish the
fluctuation-dissipation relations linking these quantities, which are thus
generalized out-of-equilibrium for a quantum system. It is shown that the
electrical ac-conductance associated to the displacement current is directly
linked to the electrical noise summed over reservoirs, whereas the relation
between the thermoelectrical ac-conductance and the mixed noise contains an
additional term proportional to the energy step that the electrons must
overcome when traveling through the junction. A numerical study reveals however
that a fluctuation-dissipation relation involving a single reservoir applies
for both electrical and thermoelectrical ac-conductances when the frequency
dominates over the other characteristic energies.Comment: 10 pages, 5 figure
Quantum ratchet in disordered quantum walk

Symmetrically evolving discrete quantum walk results in dynamic localization
with zero mean displacement when the standard evolution operations are replaced
by a temporal disorder evolution operation. In this work we show that the
quantum ratchet action, that is, a directed transport in standard or disordered
discrete-time quantum walk can be realized by introducing a pawl like effect
realized by using a fixed coin operation at marked positions that is, different
from the ones used for evolution at other positions. We also show that the
combination of standard and disordered evolution operations can be optimized to
get the mean displacement of order $\propto$ t (number of walk steps). This
model of quantum ratchet in quantum walk is defined using only a set of
entangling unitary operators resulting in the coherent quantum transport.Comment: 7 pages, 7 figure
The Ergodic Side of the Many-Body Localization Transition

Recent studies point towards nontriviality of the ergodic phase in systems
exhibiting many-body localization (MBL), which shows subexponential relaxation
of local observables, subdiffusive transport and sublinear spreading of the
entanglement entropy. Here we review the dynamical properties of this phase and
the available numerically exact and approximate methods for its study. We
discuss in which sense this phase could be considered ergodic and present
possible phenomenological explanations of its dynamical properties. We close by
analyzing to which extent the proposed explanations were verified by numerical
studies and present the open questions in this field.Comment: Review article (25 pages, 2 figures). Adds missing references to the
  Appendix on the relation between the mean-square displacement and the
  current-current correlation function
Physics of quantum light emitters in disordered photonic nanostructures

Nanophotonics focuses on the control of light and the interaction with matter
by the aid of intricate nanostructures. Typically, a photonic nanostructure is
carefully designed for a specific application and any imperfections may reduce
its performance, i.e., a thorough investigation of the role of unavoidable
fabrication imperfections is essential for any application. However, another
approach to nanophotonic applications exists where fabrication disorder is used
to induce functionalities by enhancing light-matter interaction. Disorder leads
to multiple scattering of light, which is the realm of statistical optics where
light propagation requires a statistical description. We review here the recent
progress on disordered photonic nanostructures and the potential implications
for quantum photonics devices.Comment: Review accepted for publication in Annalen der Physi
Three-phonon and four-phonon interaction processes in a pair-condensed
  Fermi gas

We study the interactions among phonons and the phonon lifetime in a
pair-condensed Fermi gas in the BEC-BCS crossover in the collisionless regime.
To compute the phonon-phonon coupling amplitudes we use a microscopic model
based on a generalized BCS Ansatz including moving pairs, which allows for a
systematic expansion around the mean field BCS approximation of the ground
state. We show that the quantum hydrodynamic expression of the amplitudes
obtained by Landau and Khalatnikov apply only on the energy shell, that is for
resonant processes that conserve energy. The microscopic model yields the same
excitation spectrum as the Random Phase Approximation, with a linear (phononic)
start and a concavity at low wave number that changes from upwards to downwards
in the BEC-BCS crossover. When the concavity of the dispersion relation is
upwards at low wave number, the leading damping mechanism at low temperature is
the Beliaev-Landau process 2 phonons $\leftrightarrow$ 1 phonon while, when the
concavity is downwards, it is the Landau-Khalatnikov process 2 phonons
$\leftrightarrow$ 2 phonons. In both cases, by rescaling the wave vectors to
absorb the dependence on the interaction strength, we obtain a universal
formula for the damping rate. This universal formula corrects and extends the
original analytic results of Landau and Khalatnikov [ZhETF {\bf 19}, 637
(1949)] for the $2\leftrightarrow2$ processes in the downward concavity case.
In the upward concavity case, for the Beliaev 1$\leftrightarrow$ 2 process for
the unitary gas at zero temperature, we calculate the damping rate of an
excitation with wave number $q$ including the first correction proportional to
$q^7$ to the $q^5$ hydrodynamic prediction, which was never done before in a
systematic way.Comment: in english (published version except for single column presentation,
  44 pages) and in french (35 pages, double column
One-particle density matrix characterization of many-body localization

We study a model of interacting fermions in one dimension subject to random,
uncorrelated onsite disorder. The model realizes an interaction-driven quantum
phase transition between an ergodic and a many-body localized phase (MBL). We
propose a single-particle framework to characterize these phases by the
eigenstates (the natural orbitals) and the eigenvalues (the occupation
spectrum) of the one-particle density matrix (OPDM) in many-body eigenstates.
As a main result, we find that the natural orbitals are localized in the MBL
phase, but delocalized in the ergodic phase. This qualitative change in these
single-particle states is a many-body effect, since without interactions the
single-particle energy eigenstates are all localized. The occupation spectrum
in the ergodic phase is thermal in agreement with the eigenstate thermalization
hypothesis, while in the MBL phase the occupations preserve a discontinuity at
an emergent Fermi edge. This suggests that the MBL eigenstates are weakly
dressed Slater determinants, with the eigenstates of the underlying Anderson
problem as reference states. We discuss the statistical properties of the
natural orbitals and of the occupation spectrum in the two phases and as the
transition is approached. Our results are consistent with the existing picture
of emergent integrability and localized integrals of motion, or quasiparticles,
in the MBL phase. We emphasize the close analogy of the MBL phase to a
zero-temperature Fermi liquid: in the studied model, the MBL phase is
adiabatically connected to the Anderson insulator and the occupation-spectrum
discontinuity directly indicates the presence of quasiparticles localized in
real space. Finally, we show that the same picture emerges for interacting
fermions in the presence of an experimentally-relevant bichromatic lattice and
thereby demonstrate that our findings are not limited to a specific model.Comment: 19 pages, 20 figure
Optimizing weak measurements to detect angular deviations

We analyze and compare the angular deviations for an optical beam reflected
by and transmitted through a dielectric triangular prism. The analytic
expressions derived for the angular deviations hold for arbitrary incidence
angles. For incidence approaching the internal and external Brewster angles,
the angular deviations transverse magnetic waves present the same behavior
leading to the well-known giant Goos-Haenchen angular shift. For incidence near
the critical angle a new region of large shift is seen both for transverse
magnetic and transverse electric waves. While a direct measuring procedure is
better in the vicinity of the Brewster region, a weak measurement breaks off
the giant Goos-Haenchen effect, preserving the amplification in the critical
region. We discuss under which conditions it is possible to optimize the
amplification and we also determine when a weak measurement is preferred to a
direct measuring procedure.Comment: 28 pages, 6 figure
Density correlations and transport in models of many-body localization

We present a review of recent theoretical results concerning the many-body
localization (MBL) phenomenon, with the emphasis on dynamical density
correlations and transport quantities. They are shown to be closely related,
providing a comprehensive description of the ergodic-to-nonergodic transition,
consistent with experimental findings. While the focus is set mostly on the
one-dimensional model of interacting spinless fermions, we also present
evidence for the absence of full MBL in the one-dimensional Hubbard model and
for the density-wave decay induced by the inter-chain coupling.Comment: Feature Article of the special issue Annalen der Physik: "Many-Body
  Localization
Absence of many-body localization in a continuum

We show that many-body localization, which exists in tight-binding models, is
unstable in a continuum. Irrespective of the dimensionality of the system,
many-body localization does not survive the unbounded growth of the
single-particle localization length with increasing energy that is
characteristic of the continuum limit. The system remains delocalized down to
arbitrarily small temperature $T$, although its dynamics slows down as $T$
decreases. Remarkably, the conductivity vanishes with decreasing $T$ faster
than in the Arrhenius law. The system can be characterized by an effective
$T$-dependent single-particle mobility edge which diverges in the limit of
$T\to 0$. Delocalization is driven by interactions between hot electrons above
the mobility edge and the "bath" of thermal electrons in the vicinity of the
Fermi level
Localization Lifetime of a Many-Body System with Periodic Constructed
  Disorder

We show that, in a many-body system, all particles can be strongly confined
to the initially occupied sites for a time that scales as a high power of the
ratio of the bandwidth of site energies to the hopping amplitude. Such
time-domain formulation is complementary to the formulation of the many-body
localization of all stationary states with a large localization length. The
long localization lifetime is achieved by constructing a periodic sequence of
site energies with a large period in a one-dimensional chain. The scaling of
the localization lifetime is independent of the number of particles for a broad
range of the coupling strength. The analytical results are confirmed by
numerical calculations
Transient dynamics of a one-dimensional Holstein polaron under the
  influence of an external electric field

Following the Dirac-Frenkel time-dependent variational principle, transient
dynamics of a one-dimensional Holstein polaron with diagonal and off-diagonal
exciton-phonon coupling in an external electric field is studied by employing
the multi-D$_2$ {\it Ansatz}, also known as a superposition of the usual
Davydov D$_2$ trial states. Resultant polaron dynamics has significantly
enhanced accuracy, and is in perfect agreement with that derived from the
hierarchy equations of motion method. Starting from an initial broad wave
packet, the exciton undergoes typical Bloch oscillations. Adding weak
exciton-phonon coupling leads to a broadened exciton wave packet and a reduced
current amplitude. Using a narrow wave packet as the initial state, the bare
exciton oscillates in a symmetric breathing mode, but the symmetry is easily
broken by weak coupling to phonons, resulting in a non-zero exciton current.
For both scenarios, temporal periodicity is unchanged by exciton-phonon
coupling. In particular, at variance with the case of an infinite linear chain,
no steady state is found in a finite-sized ring within the anti-adiabatic
regime. For strong diagonal coupling, the multi-$\rm D_2$ {\it Anstaz} is found
to be highly accurate, and the phonon confinement gives rise to exciton
localization and decay of the Bloch oscillations