Related papers: Fidelity Decay as an Efficient Indicator of Quantu…
We study the ultimate limits to the decoherence rate associated with dephasing processes. Fluctuating chaotic quantum systems are shown to exhibit extreme decoherence, with a rate that scales exponentially with the particle number, thus…
The operator fidelity is a measure of the information-theoretic distinguishability between perturbed and unperturbed evolutions. The response of this measure to the perturbation may be formulated in terms of the operator fidelity…
We study quantum Loschmidt echo, or fidelity, in the triangle map whose classical counterpart has linear instability and weak chaos. Numerically, three regimes of fidelity decay have been found with respect to the perturbation strength…
We propose a formalism which defines chaos in both quantum and classical systems in an equivalent manner by means of \textit{adiabatic transformations}. The complexity of adiabatic transformations which preserve classical time-averaged…
Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic…
We introduce a novel method to investigate the stability of wave packet dynamics under perturbations of the Hamiltonian. Our approach relies on semiclassical approximations, but is non-perturbative. Two separate contributions to the quantum…
We discuss the dephasing induced by the internal classical chaotic motion in the absence of any external environment. To this end we consider a suitable extension of fidelity for mixed states which is measurable in a Ramsey interferometry…
In this paper we review our recent work on the theoretical approach to quantum Loschmidt echoes, i.e. various properties of the so called echo dynamics -- the composition of forward and backward time evolutions generated by two slightly…
We propose to study echo dynamics in a random matrix framework, where we assume that the perturbation is time independent, random and orthogonally invariant. This allows to use a basis in which the unperturbed Hamiltonian is diagonal and…
Environment-induced decoherence has long been recognised as being of crucial importance in the study of chaos in quantum systems. In particular, the exact form and strength of the system-environment interaction play a major role in the…
The Loschmidt echo -- also known as fidelity -- is a very useful tool to study irreversibility in quantum mechanics due to perturbations or imperfections. Many different regimes, as a function of time and strength of the perturbation, have…
By considering correlations between classical orbits we derive semiclassical expressions for the decay of the quantum fidelity amplitude for classically chaotic quantum systems, as well as for its squared modulus, the fidelity or Loschmidt…
We study the decay rate of the Loschmidt echo or fidelity in a chaotic system under a time-dependent perturbation $V(q,t)$ with typical strength $\hbar/\tau_{V}$. The perturbation represents the action of an uncontrolled environment…
We prove spatial decay estimates on disorder-averaged position-momentum correlations in a gapless class of random oscillator models. First, we prove a decay estimate on dynamic correlations for general eigenstates with a bound that depends…
The scattering matrix was measured for a flat microwave cavity with classically chaotic dynamics. The system can be perturbed by small changes of the geometry. We define the "scattering fidelity" in terms of parametric correlation functions…
Decoherence in quantum systems which are classically chaotic is studied. It is well-known that a classically chaotic system when quantized loses many prominent chaotic traits. We show that interaction of the quantum system with an…
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…
A new generic dynamical phenomenon of pseudochaos and its relevance to the statistical physics both modern as well as traditional one are considered and explained in some detail. The pseudochaos is defined as a statistical behavior of the…
We consider stability of a general quantum algorithm with respect to a fixed but unknown residual interaction between qubits, and show a surprising fact, namely that the average fidelity of quantum computation increases by decreasing…
Using the methods of quantum trajectories we investigate the effects of dissipative decoherence in a quantum computer algorithm simulating dynamics in various regimes of quantum chaos including dynamical localization, quantum ergodic regime…