6,245 research outputs found
Exploring local quantum many-body relaxation by atoms in optical superlattices
We establish a setting - atoms in optical superlattices with period 2 - in
which one can experimentally probe signatures of the process of local
relaxation and apparent thermalization in non-equilibrium dynamics without the
need of addressing single sites. This opens up a way to explore the convergence
of subsystems to maximum entropy states in quenched quantum many-body systems
with present technology. Remarkably, the emergence of thermal states does not
follow from a coupling to an environment, but is a result of the complex
non-equilibrium dynamics in closed systems. We explore ways of measuring the
relevant signatures of thermalization in this analogue quantum simulation of a
relaxation process, exploiting the possibilities offered by optical
superlattices.Comment: 4 pages, 3 figures, version to published in Physical Review Letter
Hydrodynamic Waves in Regions with Smooth Loss of Convexity of Isentropes. General Phenomenological Theory
General phenomenological theory of hydrodynamic waves in regions with smooth
loss of convexity of isentropes is developed based on the fact that for most
media these regions in p-V plane are anomalously small. Accordingly the waves
are usually weak and can be described in the manner analogous to that for weak
shock waves of compression. The corresponding generalized Burgers equation is
derived and analyzed. The exact solution of the equation for steady shock waves
of rarefaction is obtained and discusses.Comment: RevTeX, 4 two-column pages, no figure
On single-copy entanglement
The largest eigenvalue of the reduced density matrix for quantum chains is
shown to have a simple physical interpretation and power-law behaviour in
critical systems. This is verified numerically for XXZ spin chains.Comment: 4 pages, 2 figures, note added, typo correcte
Half the entanglement in critical systems is distillable from a single specimen
We establish that the leading critical scaling of the single-copy
entanglement is exactly one half of the entropy of entanglement of a block in
critical infinite spin chains in a general setting, using methods of conformal
field theory. Conformal symmetry imposes that the single-copy entanglement for
critical many-body systems scales as E_1(\rho_L)=(c/6) \log L- (c/6)
(\pi^2/\log L) + O(1/L), where L is the number of constituents in a block of an
infinite chain and c corresponds to the central charge. This proves that from a
single specimen of a critical chain, already half the entanglement can be
distilled compared to the rate that is asymptotically available. The result is
substantiated by a quantitative analysis for all translationally invariant
quantum spin chains corresponding to general isotropic quasi-free fermionic
models. An analytic example of the XY model shows that away from criticality
the above simple relation is only maintained near the quantum phase transition
point.Comment: 4 pages RevTeX, 1 figure, final versio
Flashing annihilation term of a logistic kinetic as a mechanism leading to Pareto distributions
It is shown analytically that the flashing annihilation term of a Verhulst
kinetic leads to the power--law distribution in the stationary state. For the
frequency of switching slower than twice the free growth rate this provides the
quasideterministic source of a Levy noises at the macroscopic level.Comment: 1 fi
Area laws for the entanglement entropy - a review
Physical interactions in quantum many-body systems are typically local:
Individual constituents interact mainly with their few nearest neighbors. This
locality of interactions is inherited by a decay of correlation functions, but
also reflected by scaling laws of a quite profound quantity: The entanglement
entropy of ground states. This entropy of the reduced state of a subregion
often merely grows like the boundary area of the subregion, and not like its
volume, in sharp contrast with an expected extensive behavior. Such "area laws"
for the entanglement entropy and related quantities have received considerable
attention in recent years. They emerge in several seemingly unrelated fields,
in the context of black hole physics, quantum information science, and quantum
many-body physics where they have important implications on the numerical
simulation of lattice models. In this Colloquium we review the current status
of area laws in these fields. Center stage is taken by rigorous results on
lattice models in one and higher spatial dimensions. The differences and
similarities between bosonic and fermionic models are stressed, area laws are
related to the velocity of information propagation, and disordered systems,
non-equilibrium situations, classical correlation concepts, and topological
entanglement entropies are discussed. A significant proportion of the article
is devoted to the quantitative connection between the entanglement content of
states and the possibility of their efficient numerical simulation. We discuss
matrix-product states, higher-dimensional analogues, and states from
entanglement renormalization and conclude by highlighting the implications of
area laws on quantifying the effective degrees of freedom that need to be
considered in simulations.Comment: 28 pages, 2 figures, final versio
Correlations, spectral gap, and entanglement in harmonic quantum systems on generic lattices
We investigate the relationship between the gap between the energy of the
ground state and the first excited state and the decay of correlation functions
in harmonic lattice systems. We prove that in gapped systems, the exponential
decay of correlations follows for both the ground state and thermal states.
Considering the converse direction, we show that an energy gap can follow from
algebraic decay and always does for exponential decay. The underlying lattices
are described as general graphs of not necessarily integer dimension, including
translationally invariant instances of cubic lattices as special cases. Any
local quadratic couplings in position and momentum coordinates are allowed for,
leading to quasi-free (Gaussian) ground states. We make use of methods of
deriving bounds to matrix functions of banded matrices corresponding to local
interactions on general graphs. Finally, we give an explicit entanglement-area
relationship in terms of the energy gap for arbitrary, not necessarily
contiguous regions on lattices characterized by general graphs.Comment: 26 pages, LaTeX, published version (figure added
Single-copy entanglement in critical spin chains
We introduce the single-copy entanglement as a quantity to assess quantum
correlations in the ground state in quantum many-body systems. We show for a
large class of models that already on the level of single specimens of spin
chains, criticality is accompanied with the possibility of distilling a
maximally entangled state of arbitrary dimension from a sufficiently large
block deterministically, with local operations and classical communication.
These analytical results -- which refine previous results on the divergence of
block entropy as the rate at which EPR pairs can be distilled from many
identically prepared chains, and which apply to single systems as encountered
in actual experimental situations -- are made quantitative for general
isotropic translationally invariant spin chains that can be mapped onto a
quasi-free fermionic system, and for the anisotropic XY model. For the XX
model, we provide the asymptotic scaling of ~(1/6) log_2(L), and contrast it
with the block entropy. The role of superselection rules on single-copy
entanglement in systems consisting of indistinguishable particles is
emphasized.Comment: 5 pages, RevTeX, final versio
Divergences in the Effective Action for Acausal Spacetimes
The 1--loop effective Lagrangian for a massive scalar field on an arbitrary
causality violating spacetime is calculated using the methods of Euclidean
quantum field theory in curved spacetime. Fields of spin 1/2, spin 1 and
twisted field configurations are also considered. In general, we find that the
Lagrangian diverges to minus infinity at each of the nth polarised
hypersurfaces of the spacetime with a structure governed by a DeWitt-Schwinger
type expansion.Comment: 17 pages, Late
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