The time-fractional kinetic equation for the non-equilibrium processes

In this study, we consider the non-Markovian dynamics of the generic non-equilibrium kinetic process. We summarize the generalized master equation, the continuous and discrete forms of the time-fractional diffusion equation. Using path integral formulation, we generalized the solutions of the Markovian system to the non-Markovian for the non-equilibrium kinetic processes. Then, we obtain the time-fractional kinetic equation for the non-equilibrium systems in terms of free energy. Finally, we introduce a time-fractional equation to analyse time evolution of the open probability for the deformed voltage-gated ion-channel system as an example.

Quantum dephasing induced by non-Markovian random telegraph noise

We theoretically study the dynamical dephasing of a quantum two level system interacting with an environment which exhibits non-Markovian random telegraph fluctuations. The time evolution of the conditional probability of the environmental noise is governed by a generalized master equation depending on the environmental memory effect. The expression of the dephasing factor is derived exactly which is closely associated with the memory kernel in the generalized master equation for the conditional probability of the environmental noise. In terms of three important types memory kernels, we discuss the quantum dephasing dynamics of the system and the non-Markovian character exhibiting in the dynamical dephasing induced by non-Markovian random telegraph noise. We show that the dynamical dephasing of the quantum system does not always exhibit non-Markovian character which results from that the non-Markovian character in the dephasing dynamics depends both on the environmental non-Markovian character and the interaction between the system and environment. In addition, the dynamical dephasing of the quantum system can be modulated by the external modulation frequency of the environment. This result is significant to quantum information processing and helpful for further understanding non-Markovian dynamics of open quantum systems.

Generalized Master Equation Approach to Time-Dependent Many-Body Transport

We recall theoretical studies on transient transport through interacting mesoscopic systems.It is shown that a generalized master equation (GME) written and solved in terms of many-body statesprovides the suitable formal framework to capture both the effects of the Coulomb interaction andelectron–photon coupling due to a surrounding single-mode cavity. We outline the derivation of thisequation within the Nakajima–Zwanzig formalism and point out technical problems related to itsnumerical implementation for more realistic systems which can neither be described by non-interactingtwo-level models nor by a steady-stateMarkov–Lindblad equation. We first solve the GME for a latticemodel and discuss the dynamics of many-body states in a two-dimensional nanowire, the dynamicalonset of the current-current correlations in electrostatically coupled parallel quantum dots and transientthermoelectric properties. Secondly, we rely on a continuous model to get the Rabi oscillations ofthe photocurrent through a double-dot etched in a nanowire and embedded in a quantum cavity.A many-bodyMarkovian version of the GME for cavity-coupled systems is also presented.

Approach to equilibrium of a quantum system and generalization of the Montroll–Shuler equation for vibrational relaxation of a molecular oscillator

The approach to equilibrium of a quantum mechanical system in interaction with a bath is studied from a practical as well as a conceptual point of view. Explicit memory functions are derived for given models of bath couplings. If the system is a harmonic oscillator representing a molecule in interaction with a reservoir, the generalized master equation derived becomes an extension into the coherent domain of the well-known Montroll–Shuler equation for vibrational relaxation and unimolecular dissociation. A generalization of the Bethe–Teller result regarding energy relaxation is found for short times. The theory has obvious applications to relaxation dynamics at ultra-short times as in observations on the femtosecond time scale and to the investigation of quantum coherence at those short times. While vibrational relaxation in chemical physics is a primary target of the study, another system of interest in condensed matter physics, an electron or hole in a lattice subjected to a strong DC electric field that gives rise to well-known Wannier–Stark ladders, is naturally addressed with the theory. Specific system–bath interactions are explored to obtain explicit details of the dynamics. General phenomenological descriptions of the reservoir are considered rather than specific microscopic realizations.