Time correlation functions in quantum systems

Dave Thirumalai, B. J. Berne

Sudhir R. Jain, Pierre Gaspard

R. Dümcke

Masashi Ban

Dave Thirumalai, B. J. Berne

A Monte Carlo method for calculating quantum mechanical time correlation functions is presented. In this method the time correlation function is calculated at several values along the pure imaginary axis of the complex time plane such that 0<it<β, where (β)−1 is the temperature of the system. Using the periodicity of the imaginary time correlation function, the real time behavior is inferred by analytic continuation. The method is used to calculate the absorption spectra of two model systems.

Yifan Shi, Yusui Chen, Kaiqi Xiong

Abstract The two-time correlation function (TTCF) is a fundamental tool in precision detection and quantum measurement. In this work, we present a theoretical study of the dynamical behavior of a cavity optomechanical system. Employing the stochastic Schrödinger equation formalism, we systematically investigate both the long-time steady-state and time-dependent two-time correlation functions under different environmental conditions. Our numerical results reveal that the steady-state TTCFs exhibit qualitatively distinct features in Markovian and non-Markovian environments. Moreover, we show that finite-time TTCFs provide a more sensitive and detailed characterization of environmental properties compared to conventional spectral-function-based approaches. Importantly, we demonstrate that the stability of the system is jointly determined by the eigenfrequency of the system and the environmental memory parameter. These results establish a unified framework for the analysis of two-time correlation functions in non-Markovian regimes, offering deeper physical insight into the role of environmental effects in quantum measurement and system stability.