Quantum two-state dynamics driven by stationary non-Markovian discrete noise: Exact results

Abstract

We consider the problem of stochastic averaging of a quantum two-state dynamics driven by non-Markovian, discrete noises of the continuous time random walk type (multistate renewal processes). The emphasis is put on the proper averaging over the stationary noise realizations corresponding, e.g., to a stationary environment. A two-state non-Markovian process with an arbitrary non-exponential distribution of residence times (RTDs) in its states with a finite mean residence time provides a paradigm. For the case of a two-state quantum relaxation caused by such a classical stochastic field we obtain the explicit exact, analytical expression for the averaged Laplace-transformed relaxation dynamics. In the limit of Markovian noise (implying an exponential RTD), all previously known results are recovered. We exemplify new more general results for the case of non-Markovian noise with a biexponential RTD. The averaged, real-time relaxation dynamics is obtained in this case by numerically exact solving of a resulting algebraic polynomial problem. Moreover, the case of manifest non-Markovian noise with an infinite range of temporal autocorrelation (which in principle is not accessible to any kind of perturbative treatment) is studied, both analytically (asymptotic long-time dynamics) and numerically (by a precise numerical inversion of the Laplace-transformed averaged quantum relaxation).

Non-Markovian dynamics of single- and two-qubit systems interacting with Gaussian and non-Gaussian fluctuating transverse environments

“…Analytic solutions for a qubit interacting with RTN with an arbitrary direction are known [50][51][52]. By following [50], we consider the time evolution of the Bloch vector n(t), which can be written by means of a transfer matrix T applied to the initial Bloch vector n(0) as…”

Superdiffusion of a random walk driven by an ergodic Markov process with switching

“…Stochastic switching has been of much interest since it is one of the basic processes in many areas of natural sciences, e.g., switching between two metastable states in stochastic resonance theory [10,18], two-state model for anomalous diffusion [27,29], two-state gating process for ion channels [11], stochastically driven two-level quantum systems [12], etc. The standard model for switching is a continuous time Markov chain with an exponential distribution of residence times.…”

Controlled decoherence in a quantum Lévy kicked rotator

“…The relaxation of a quantum two-level system subjected to stationary and nonstationary power-law noise has been respectively examined in Refs. [35] and [36]. In the latter work, the presence of aging dephasing has been demonstrated.…”