Related papers: Loschmidt Echo and Lyapunov Exponent in a Quantum …
Motivated by rapid developments in the field of quantum computing and the increasingly diverse nature of qubits, we theoretically study the influence that quenched outside disturbances have in an intermediately long time limit. We consider…
We consider a one-dimensional spin chain system with quenched disorder and in the presence of a local periodic drive. We study the time evolution of the system in the Floquet basis and evaluate the fidelity susceptibility, which is a…
In this paper we consider the problem of minimizing a quadratic functional for a discrete-time linear stochastic system with multiplicative noise, on a standard probability space, in infinite time horizon. We show that the necessary and…
General semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial…
We define a quantity, the so-called purity fidelity, which measures the rate of dynamical irreversibility due to decoherence, observed e.g in echo experiments, in the presence of an arbitrary small perturbation of the total (system +…
This paper develops a quantitatively accurate first-principles description for the frequency and the linewidth of collective electronic excitations in inhomogeneous weakly disordered systems. A finite linewidth in general has intrinsic and…
The sensitive dependence of chaos on parameters is a topic of great interest in the study of integrability and stability of dynamical systems. Previous work has proposed ways to identify the sensitive dependence on parameters by topological…
We study the influence of disorder on propagation of waves in one-dimensional structures. Transmission properties of the process governed by the Schr\"{o}dinger equation with the white noise potential can be expressed through the Lyapunov…
Finite-time Lyapunov exponents of generic chaotic dynamical systems fluctuate in time. These fluctuations are due to the different degree of stability across the accessible phase-space. A recent numerical study of spatially-extended systems…
A recently proposed statistical model for the effects of decoherence on electron transport manifests a decoherence-driven transition from quantum-coherent localized to ohmic behavior when applied to the one-dimensional Anderson model. Here…
In order to study the chaotic behavior of a system with non-local interactions, we will consider weakly coupled non-commutative field theories. We compute the Lyapunov exponent of this exponential growth in the large Moyal-scale limit to…
We investigate the extent to which the probabilistic properties of a chaotic scattering system with dissipation can be understood from the properties of the dissipation-free system. For large energies $E$, a fully chaotic scattering leads…
A strong analogy is found between the evolution of localized disturbances in extended chaotic systems and the propagation of fronts separating different phases. A condition for the evolution to be controlled by nonlinear mechanisms is…
The phase space trajectories of many body systems charateristic of simple fluids are highly unstable. We quantify this instability by a set of Lyapunov exponents, which are the rates of exponential divergence, or convergence, of initial…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
Diffusion of electrons in a two-dimensional system with time-dependent random potentials is investigated numerically. In the absence of spin-orbit scattering, the conductivity shows universal weak localization correction. In the presence of…
Transport properties of disordered electron system can be characterized by the conductance, Lyapunov exponent, or level spacing. Two additional parameters, $K_{11}$ and $\gamma $ were introduced recently which measure the non-homogeneity of…
The analysis of dissipation and dephasing in driven mesoscopic devices requires a distinction between two notions of quantum irreversibility. One ("Loschmidt echo") is related to "time reversal", while the other is related to "driving…
The Loschmidt echo is investigated to track the effect of the local QDP. It is also quite sensitive to whether the background dynamics is integrable or not. For the integrable case, viz. the Heisenberg model, the Loschmidt echo depends on…
We point out that the low temperature saturation of the electron phase decoherence time in a disordered conductor can be explained within the existing theory of weak localization provided the effect of quantum (high frequency) fluctuations…