Decay of the Loschmidt echo in a time-dependent environment

Abstract

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 Planck's/tau(v) . The perturbation represents the action of an uncontrolled environment interacting with the system, and is characterized by a correlation length xi(0) and a correlation time tau(0). For small perturbation strengths or rapid fluctuating perturbations, the Loschmidt echo decays exponentially with a rate predicted by the Fermi "golden rule," 1/approximately tau =tau(c)/tau(v)(2), where tau(c) approximately min[tau(0), xi(0)/upsilon] and upsilon is the typical particle velocity. Whenever the rate 1/approximately tau is larger than the Lyapunov exponent of the system, a perturbation independent Lyapunov decay regime arises. We also find that by speeding up the fluctuations (while keeping the perturbation strength fixed) the fidelity decay becomes slower, and hence one can protect the system against decoherence.

Quantum corrections to fidelity decay in chaotic systems

“…Furthermore, we assume in this section, as in Ref. [46], a Gaussian form of the spatial and the time-dependent perturbation…”

Entanglement of an impurity in a few-body one-dimensional ideal Bose system

“…Just to mention a few studies and effects in this area one can mention the Landau-Pekar polaron [14,15] and a magnetic impurity in a metal resulting in the Kondo effect [16]. Moreover, the impurity atom interacting with a Bose-Einstein condensate has been found to have a bound ground state in which the impurity is self-localized in the so-called polaron-like state [17][18][19][20]. There has been considerable recent interest in the physics of polarons in quasi-condensates [21][22][23], also in the case where the mass of the impurity is different from the mass of the bosons [24][25][26].…”

Observation of Coherent Precursors in Pulsed Mode-Stirred Reverberation Fields

“…They are applied in studies of reflection, scattering and diffusion of acoustic or EM waves in complex (multipath) time-varying propagation environments, power radiated by rf sources, antenna characterization, spectroscopy, tunable high-intensity random fields, etc. Their dynamics involve aspects relating to fidelity [18][19][20][21], diffusing wave spectroscopy [22 -24], and scattering and transport in opened absorbing chaotic systems [25][26][27]. The extreme sensitivity of the interior field to small perturbations of the configuration warrants a statistical characterization of the field and the cavity's intrinsic parameters (relaxation time, quality factor, mode density, etc.).…”

“…2(e)]. The functional dependence of the decay of correlations with increasing perturbation strength has been studied in a variety of quantum and classical dynamic systems [21]. Just after onset [ Fig.…”