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Two-Time Correlation Functions : Bohm Theory and Conventional Quantum Mechanics

L. Feligioni, Y. Srivastava, Orlando Panella +1 more

An investigation of two-time correlation functions is reported within the framework of (i) the Bohm theory of stochastic quantum mechanics and (ii) conventional Heisenberg-Schroedinger quantum mechanics. The spectral functions associated with the two-time electric dipole correlation functions are worked out in detail for the case of the hydrogen atom. While the single time averages are identical for Bohm stochastic quantum mechanics and the conventional Heisenberg-Schroedinger quantum mechanics, differences arise in the two approaches for multiple time correlation functions.An investigation of two-time correlation functions is reported within the framework of (i) the Bohm theory of stochastic quantum mechanics and (ii) conventional Heisenberg-Schroedinger quantum mechanics. The spectral functions associated with the two-time electric dipole correlation functions are worked out in detail for the case of the hydrogen atom. While the single time averages are identical for Bohm stochastic quantum mechanics and the conventional Heisenberg-Schroedinger quantum mechanics, differences arise in the two approaches for multiple time correlation functions.

Feb 7, 20021 citation

Stochastic Quantum Mechanics

Ramabhadra Vasudevan

Lecture notes in economics and mathematical systemsJan 1, 19913 citations

Stochastic Quantum Mechanics

WORLD SCIENTIFIC eBooksMar 1, 20250 citations

Non-Markovian two-time correlation functions for optomechanical 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.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.

arXiv:2501.07678Optics ExpressAug 7, 20260 citations

Stochastics and Quantum Mechanics

Aubrey Truman, Ian M Davies

May 1, 199215 citations

Quantum State Diffusion and Time Correlation Functions

Todd A. Brun, Physics Department Queen, Nicolas Gisin

In computing the spectra of quantum mechanical systems one encounters the Fourier transforms of time correlation functions, as given by the quantum regression theorem for systems described by master equations. Quantum state diffusion (QSD) gives a useful method of solving these problems by unraveling the master equation into stochastic trajectories; but there is no generally accepted definition of a time correlation function for a single QSD trajectory. In this paper we show how QSD can be used to calculate these spectra directly; by formally solving the equations which arise, we arrive at a natural definition for a two-time correlation function in QSD, which depends explicitly on both the stochastic noise of the particular trajectory and the time of measurement, and which agrees in the mean with the ensemble average definition of correlation functions. 1 1In computing the spectra of quantum mechanical systems one encounters the Fourier transforms of time correlation functions, as given by the quantum regression theorem for systems described by master equations. Quantum state diffusion (QSD) gives a useful method of solving these problems by unraveling the master equation into stochastic trajectories; but there is no generally accepted definition of a time correlation function for a single QSD trajectory. In this paper we show how QSD can be used to calculate these spectra directly; by formally solving the equations which arise, we arrive at a natural definition for a two-time correlation function in QSD, which depends explicitly on both the stochastic noise of the particular trajectory and the time of measurement, and which agrees in the mean with the ensemble average definition of correlation functions. 1 1

Dec 11, 19956 citations

Two-time correlation functions: stochastic and conventional quantum mechanics

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