Related papers: Relaxation Time of Quantized Toral Maps
We show that the quantum relaxation process in a classically chaotic open dynamical system is characterized by a quantum relaxation time scale t_q. This scale is much shorter than the Heisenberg time and much larger than the Ehrenfest time:…
We define a class of dynamical systems on the sphere analogous to the baker map on the torus. The classical maps are characterized by dynamical entropy equal to ln 2. We construct and investigate a family of the corresponding quantum maps.…
In general, classical fully-connected systems are known to undergo violent relaxation. This phenomenon refers to the relaxation of observables to stationary, non-thermal, values on a finite timescale, despite their long-time dynamics being…
We give a polynomial time classical algorithm for sampling from the output distribution of a noisy random quantum circuit in the regime of anti-concentration to within inverse polynomial total variation distance. This gives strong evidence…
The Quantum Loschmidt Echo is a measurement of the sensitivity of a quantum system to perturbations of the Hamiltonian. In the case of the standard 2-torus, we derive some explicit formulae for this quantity in the transition regime where…
Classical quasi-integrable systems are known to have Lyapunov times much shorter than their ergodicity time -- the most clear example being the Solar System -- but the situation for their quantum counterparts is less well understood. As a…
A generalized approach to the quantization of a large class of maps on a torus, i.e. quantization via the von Neumann Equation, is described and a number of issues related to the quantization of model systems are discussed. The approach…
We reveal several distinct regimes of the relaxation dynamics of a small quantum system coupled to an environment within the plane of the dissipation strength and the reservoir temperature. This is achieved by discriminating between…
We provide an overview of our numerical and analytical studies of isolated interacting quantum systems that are quenched out of equilibrium instantaneously. We describe the relaxation process to a new equilibrium and obtain lower bounds for…
Temporal evolutions toward thermal equilibria are numerically investigated in a Hamiltonian system with many degrees of freedom which has second order phase transition. Relaxation processes are studied through local order parameter, and…
Recently we have shown that slow relaxations in the electron glass system can be understood in terms of the spectrum of a matrix describing the relaxation of the system close to a metastable state. The model focused on the electron glass…
Decoherence in quantum systems which are classically chaotic is studied. The Arnold cat map and the quantum kicked rotor are chosen as examples of linear and nonlinear chaotic systems. The Feynman-Vernon influence functional formalism is…
Quantum nanomagnets can show a field dependence of the relaxation time very different from their classical counterparts, due to resonant tunneling via excited states (near the anisotropy barrier top). The relaxation time then shows minima…
We investigate the classical and quantum dynamics of an electron confined to a circular quantum dot in the presence of homogeneous $B_{dc}+B_{ac}$ magnetic fields. The classical motion shows a transition to chaotic behavior depending on the…
Exactly solvable models that exhibit quantum signatures of classical chaos are both rare as well as important - more so in view of the fact that the mechanisms for ergodic behavior and thermalization in isolated quantum systems and its…
Operators in ergodic spin-chains are found to grow according to hydrodynamical equations of motion. The study of such operator spreading has aided our understanding of many-body quantum chaos in spin-chains. Here we initiate the study of…
Coherent control of a spin is limited by both the decoherence due to coupling with the environment and noise coming from the quantized control. The quantum noise study of this system is particularly important in fault tolerant quantum…
Quantum circuits have become a powerful tool in the study of many-body quantum physics, providing insights into both fast-thermalizing chaotic and non-thermalizing integrable many-body dynamics. In this work, we explore a distinct…
The approach to equilibrium of quantum mechanical systems is a topic as old as quantum mechanics itself, but has recently seen a surge of interest due to applications in quantum technologies, including, but not limited to, quantum…
The paper addresses the problem of relaxation of open quantum systems. Using the path integral methods we found an analytical expression for time-dependent density matrix of two coupled quantum oscillators interacting with different baths…