Non-Markovianity measure using two-time correlation functions

Abstract

We investigate non-Markovianity measure using two-time correlation functions for open quantum systems. We define non-Markovianity measure as the difference between the exact two-time correlation function and the one obtained in the Markov limit. Such non-Markovianity measure can easily be measured in experiments. We found that the non-Markovianity dynamics in different time scale crucially depends on the system-environment coupling strength and other physical parameters such as the initial temperature of the environment and the initial state of the system. In particular, we obtain the short-time and long-time behaviors of non-Markovianity for different spectral densities. We also find that the thermal fluctuation always reduce the non-Markovian memory effect. Also, the non-Markovianity measure shows non-trivial initial state dependence in different time scales.

Signature of the transition to a bound state in thermoelectric quantum transport

“…38 By comparing the initial state in Eq. (12) with an adiabatic preparation 30,31,35 of the dot-lead system, we will see that the steady-state DC currents are the same, suggesting that DC currents are insensitive to the initial preparation.…”

“…[24][25][26], and more recently for finite-temperature. [27][28][29][30][31] It stops an atom's excited state fully decaying into the continuum, as recently observed in an NV centre in a waveguide, 32 and is predicted to lead to perfect subradiance. 33 The bound state (or localized mode) was extensively studied in the context of a quantum dot coupled to finite temperature fermionic reservoirs, 27,29,[34][35][36][37][38][39][40][41] exhibiting the same absence of decay, and even infinite-time oscillations.…”

“…By comparing adiabatic preparation 30,31 to the case of an initial quench, we show that the steady-state DC currents do not depend on the type of preparation, even if many other observables do. 38 We also clarify why Eq.…”

Exact master equation and general non-Markovian dynamics in open quantum systems

“…The measure of non-Markovian dynamics in terms of two-time correlation function[29] for a bosonic system coupled to a thermal reservoir with Ohmic-type spectral density J( ) = 2πη ( / c ) s−1 e − / c . The energy cut-off c = 5ε s and the system is initially in Fock state with n = 1, and t = 0.…”

“…The general solution of the propagating Green function consists of nonexponential decays and dissipationless oscillations (localized bound states in open quantum systems)[12], which is indeed a universal property of the propagating Green functions in arbitrary interacting many-body systems, according to the general principle of quantum field theory[45]. The non-exponential decays described by time-dependent decay rates oscillate between positive (dissipation) and negative (back flowing) values in a short time, resulting in the short-time non-Markovian dynamics[9,29]. The localized bound states give dissipationless oscillations that make the states of open systems depend forever to its initial state, as a long-time non-Markovian dynamics.…”