Related papers: An initial value representation for the Loschmidt …
The density operator for a quantum system in thermal equilibrium with its environment depends on Planck's constant, as well as the temperature. At high temperatures, the Weyl representation, that is, the thermal Wigner function, becomes…
We elucidate the basic physical mechanisms responsible for the quantum-classical transition in one-dimensional, bounded chaotic systems subject to unconditioned environmental interactions. We show that such a transition occurs due to the…
We analyze quantal Brownian motion in $d$ dimensions using the unified model for diffusion localization and dissipation, and Feynman-Vernon formalism. At high temperatures the propagator possess a Markovian property and we can write down an…
An exact general formula for the matrix elements of the evolution operator in quantum theory is established. The formul ("ABC-formula") has the form <U(t)>=exp(At+B+C(t)). The constants A and B and the decreasing function C(t) are computed…
Semiclassical transformation theory implies an integral representation for stationary-state wave functions $\psi_m(q)$ in terms of angle-action variables ($\theta,J$). It is a particular solution of Schr\"{o}dinger's time-independent…
Based on a quantum Langevin equation and its corresponding Hamiltonian within a c-number formalism we calculate the vibrational dephasing rate of a cubic oscillator. It is shown that leading order quantum correction due to anharmonicity of…
An initial coherent state is propagated exactly by a kicked quantum Hamiltonian and its associated classical stroboscopic map. The classical trajectories within the initial state are regular for low kicking strengths, then bifurcate and…
We describe a quantum perturbative approach to evaluating the phase shift of an atom interferometer in a weakly anharmonic trap. This provides a simple way to evaluate quantum corrections to the standard semi-classical approximation. The…
We unveil the role of the long time average of Loschmidt echo in the characterization of nonequilibrium quantum phase transitions by studying sudden quench processes across quantum phase transitions in various quantum systems. While the…
We develop a new semiclassical approach, which starts with the density matrix given by the Euclidean time path integral with fixed coinciding endpoints, and proceed by identifying classical (minimal Euclidean action) path, to be referred to…
We show that the number of harmonics of the Wigner function, recently proposed as a measure of quantum complexity, can be also used to characterize quantum phase transitions. The non-analytic behavior of this quantity in the neighborhood of…
We show that in the classical interaction picture the echo-dynamics, namely the composition of perturbed forward and unperturbed backward hamiltonian evolution, can be treated as a time-dependent hamiltonian system. For strongly chaotic…
We show that phase transitions in the quantum $q$-state clock model for $q \leq 4$ can be characterized by an enhanced decay behavior of the Loschmidt echo via a small quench. The quantum criticality of the quantum $q$-state clock model is…
We consider the quantum evolution of classically chaotic systems in contact with surroundings. Based on $\hbar$-scaling of an equation for time evolution of the Wigner's quasi-probability distribution function in presence of dissipation and…
We review some aspects of the quantization of the damped harmonic oscillator. We derive the exact action for a damped mechanical system in the frame of the path integral formulation of the quantum Brownian motion problem developed by…
We construct the integrals of motion for several models of the quantum damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic…
An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one dimensional chaotic dynamical systems. Environmental fluctuations -- characteristic of all realistic dynamical systems -- suppress…
We study the Loschmidt echo for a system of electrons interacting through mean-field Coulomb forces. The electron gas is modeled by a self-consistent set of hydrodynamic equations. It is observed that the quantum fidelity drops abruptly…
We consider the dephasing rate of an electron level in a quantum dot, placed next to a fluctuating edge current in the fractional quantum Hall effect. Using perturbation theory, we show that this rate has an anomalous dependence on the bias…
Fidelity decay is studied for quantum many-body systems with a dominant independent particle Hamiltonian resulting e.g. from a mean field theory with a weak two-body interaction. The diagonal terms of the interaction are included in the…