Related papers: Relaxation Fluctuations in Quantum Chaos
Numerous pivotal concepts have been introduced to clarify the puzzle of relaxation and/or equilibration in closed quantum systems. All of these concepts rely in some way on specific conditions on Hamiltonians $H$, observables $A$, and…
A new master equation to mimic the dynamics of a collection of interacting random walkers in an open system is proposed and solved numerically.In this model, the random walkers interact through excluded volume interaction (single-file…
In a frequency range where a microwave resonator simulates a chaotic quantum billiard, we have measured moduli and phases of reflection and transmission amplitudes in the regimes of both isolated and of weakly overlapping resonances and for…
We discuss a general and efficient approach for "bootstrapping" short-time correlation data in chaotic or complex quantum systems to obtain information about long-time dynamics and stationary properties, such as the local density of states.…
We consider isolated many-body quantum systems which do not thermalize, i.e., expectation values approach an (approximately) steady longtime limit which disagrees with the microcanonical prediction of equilibrium statistical mechanics. A…
We introduce the notion of the relaxation time for noisy quantum maps on the 2d-dimensional torus - a generalization of previously studied dissipation time. We show that relaxation time is sensitive to the chaotic behavior of the…
The relation between relaxation and diffusion is investigated in a Hamiltonian system of globally coupled rotators. Diffusion is anomalous if and only if the system is going towards equilibrium. The anomaly in diffusion is not anomalous…
We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…
Earlier two of us (J.L. and L.P.) considered a matrix model for a two-level system interacting with a $n\times n$ reservoir and assuming that the interaction is modelled by a random matrix. We presented there a formula for the reduced…
We derive a general fluctuation theorem for quantum maps. The theorem applies to a broad class of quantum dynamics, such as unitary evolution, decoherence, thermalization, and other types of evolution for quantum open systems. The theorem…
We discuss the intimate connection between the chaotic dynamics of a classical field theory and the instability of the one-loop effective action of the associated quantum field theory. Using the example of massless scalar electrodynamics,…
A simple class of chaotic systems in a random environment is considered and the fluctuation theorem is extended under the assumption of reversibility.
For many classically chaotic systems, it is believed that in the semiclassical limit, the matrix elements of smooth observables approach the phase space average of the observable. In the approach to the limit the matrix elements can…
Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix…
We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal…
Quantum fluctuation of the energy is studied for an ultracold gas of interacting fermions trapped in a three-dimensional potential. Periodic-orbit theory is explored, and energy fluctuations are studied versus particle number for generic…
In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null…
The Floquet operator, defined as the time-evolution operator over one period, plays a central role in the work presented in this thesis on periodically perturbed quantum systems. Knowledge of the spectral nature of the Floquet operator…
Quantum Chaos has originally emerged as the field which studies how the properties of classical chaotic systems arise in their quantum counterparts. The growing interest in quantum many-body systems, with no obvious classical meaning has…
For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space average of the observable. In this paper we study…