151 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
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
Localized phase structures growing out of quantum fluctuations in a quench of tunnel-coupled atomic condensates
We investigate the relative phase between two weakly interacting 1D
condensates of bosonic atoms after suddenly switching on the tunnel-coupling.
The following phase dynamics is governed by the quantum sine-Gordon equation.
In the semiclassical limit of weak interactions, we observe the parametric
amplification of quantum fluctuations leading to the formation of breathers
with a finite lifetime. The typical lifetime and density of the these
'quasibreathers' are derived employing exact solutions of the classical
sine-Gordon equation. Both depend on the initial relative phase between the
condensates, which is considered as a tunable parameter.Comment: 7 pages, 5 figure
Dynamic trapping near a quantum critical point
The study of dynamics in closed quantum systems has recently been revitalized
by the emergence of experimental systems that are well-isolated from their
environment. In this paper, we consider the closed-system dynamics of an
archetypal model: spins near a second order quantum critical point, which are
traditionally described by the Kibble-Zurek mechanism. Imbuing the driving
field with Newtonian dynamics, we find that the full closed system exhibits a
robust new phenomenon -- dynamic critical trapping -- in which the system is
self-trapped near the critical point due to efficient absorption of field
kinetic energy by heating the quantum spins. We quantify limits in which this
phenomenon can be observed and generalize these results by developing a
Kibble-Zurek scaling theory that incorporates the dynamic field. Our findings
can potentially be interesting in the context of early universe physics, where
the role of the driving field is played by the inflaton or a modulus.Comment: 4 pages, 3 figures + 5 page supplemen
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