610 research outputs found
Chaos and thermalization in small quantum systems
Chaos and ergodicity are the cornerstones of statistical physics and
thermodynamics. While classically even small systems like a particle in a
two-dimensional cavity, can exhibit chaotic behavior and thereby relax to a
microcanonical ensemble, quantum systems formally can not. Recent theoretical
breakthroughs and, in particular, the eigenstate thermalization hypothesis
(ETH) however indicate that quantum systems can also thermalize. In fact ETH
provided us with a framework connecting microscopic models and macroscopic
phenomena, based on the notion of highly entangled quantum states. Such
thermalization was beautifully demonstrated experimentally by A. Kaufman et.
al. who studied relaxation dynamics of a small lattice system of interacting
bosonic particles. By directly measuring the entanglement entropy of
subsystems, as well as other observables, they showed that after the initial
transient time the system locally relaxes to a thermal ensemble while globally
maintaining a zero-entropy pure state.Comment: Perspectiv
On non-coercive mixed problems for parameter-dependent elliptic operators
We consider a (generally, non-coercive) mixed boundary value problem in a
bounded domain of for a second order parameter-dependent
elliptic differential operator with complex-valued
essentially bounded measured coefficients and complex parameter . The
differential operator is assumed to be of divergent form in , the boundary
operator is of Robin type with possible pseudo-differential
components on . The boundary of is assumed to be a Lipschitz
surface. Under these assumptions the pair induces
a holomorphic family of Fredholm operators in
suitable Hilbert spaces , of Sobolev type. If the argument
of the complex-valued multiplier of the parame\-ter in is continuous and the coefficients related to second order
derivatives of the operator are smooth then we prove that the operators
are conti\-nu\-ously invertible for all with
sufficiently large modulus on each ray on the complex plane
where the differential operator is
parameter-dependent elliptic. We also describe reasonable conditions for the
system of root functions related to the family to be (doubly)
complete in the spaces , and the Lebesgue space
Integrable Floquet dynamics
We discuss several classes of integrable Floquet systems, i.e. systems which
do not exhibit chaotic behavior even under a time dependent perturbation. The
first class is associated with finite-dimensional Lie groups and
infinite-dimensional generalization thereof. The second class is related to the
row transfer matrices of the 2D statistical mechanics models. The third class
of models, called here "boost models", is constructed as a periodic interchange
of two Hamiltonians - one is the integrable lattice model Hamiltonian, while
the second is the boost operator. The latter for known cases coincides with the
entanglement Hamiltonian and is closely related to the corner transfer matrix
of the corresponding 2D statistical models. We present several explicit
examples. As an interesting application of the boost models we discuss a
possibility of generating periodically oscillating states with the period
different from that of the driving field. In particular, one can realize an
oscillating state by performing a static quench to a boost operator. We term
this state a "Quantum Boost Clock". All analyzed setups can be readily realized
experimentally, for example in cod atoms.Comment: 18 pages, 2 figures; revised version. Submission to SciPos
Universal Dynamics Near Quantum Critical Points
We give an overview of the scaling of density of quasi-particles and excess
energy (heat) for nearly adiabatic dynamics near quantum critical points
(QCPs). In particular we discuss both sudden quenches of small amplitude and
slow sweeps across the QCP. We show close connection between universal scaling
of these quantities with the scaling behavior of the fidelity susceptibility
and its generalizations. In particular we argue that the Kibble-Zurek scaling
can be easily understood using this concept. We discuss how these scalings can
be derived within the adiabatic perturbation theory and how using this approach
slow and fast quenches can be treated within the same framework. We also
describe modifications of these scalings for finite temperature quenches and
emphasize the important role of statistics of low-energy excitations. In the
end we mention some connections between adiabatic dynamics near critical points
with dynamics associated with space-time singularities in the metrics, which
naturally emerges in such areas as cosmology and string theory.Comment: 19 pages, Contribution to the book "Developments in Quantum Phase
Transitions", edited by Lincoln Carr; revised version, acknowledgement adde
Efficiency bounds for nonequilibrium heat engines
We analyze the efficiency of thermal engines (either quantum or classical)
working with a single heat reservoir like atmosphere. The engine first gets an
energy intake, which can be done in arbitrary non-equilibrium way e.g.
combustion of fuel. Then the engine performs the work and returns to the
initial state. We distinguish two general classes of engines where the working
body first equilibrates within itself and then performs the work (ergodic
engine) or when it performs the work before equilibrating (non-ergodic engine).
We show that in both cases the second law of thermodynamics limits their
efficiency. For ergodic engines we find a rigorous upper bound for the
efficiency, which is strictly smaller than the equivalent Carnot efficiency.
I.e. the Carnot efficiency can be never achieved in single reservoir heat
engines. For non-ergodic engines the efficiency can be higher and can exceed
the equilibrium Carnot bound. By extending the fundamental thermodynamic
relation to nonequilibrium processes, we find a rigorous thermodynamic bound
for the efficiency of both ergodic and non-ergodic engines and show that it is
given by the relative entropy of the non-equilibrium and initial equilibrium
distributions.These results suggest a new general strategy for designing more
efficient engines. We illustrate our ideas by using simple examples.Comment: updated version, 16 pages, 3 figure
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