Quantum dynamical correlations: Effective potential analytic continuation approach

Abstract

We propose a new quantum dynamics method called the effective potential analytic continuation (EPAC) to calculate the real time quantum correlation functions at finite temperature. The method is based on the effective action formalism which includes the standard effective potential. The basic notions of the EPAC are presented for a one-dimensional double well system in comparison with the centroid molecular dynamics (CMD) and the exact real time quantum correlation function. It is shown that both the EPAC and the CMD well reproduce the exact short time behavior, while at longer time their results deviate from the exact one. The CMD correlation function damps rapidly with time because of ensemble dephasing. The EPAC correlation function, however, can reproduce the long time oscillation inherent in the quantum double well systems. It is also shown that the EPAC correlation function can be improved toward the exact correlation function by means of the higher order derivative expansion of the effective action.

Effective potential analytic continuation calculations of real time quantum correlation functions: Asymmetric systems

“…Then by means of the analytic continuation [28] real time quantum correlation functions can be readily obtained from the imaginary time quantities. This is the EPAC [8], an approximation method based on the effective action formalism. Following the EPAC method, for example, the real time position autocorrelation function C β (t) = q(t)q(0) β can be expressed as [8]…”

“…In our previous paper [8], the usefulness of the EPAC method has been shown for a Z 2 (q ↔ −q) symmetric double well potential system in comparison with the CMD result. We expect that the EPAC method may also be useful for general anharmonic quantum systems.…”

“…As new quantum dynamics methods to calculate the real time quantum correlation functions at finite temperature, the centroid molecular dynamics (CMD) method [7] and the effective potential analytic continuation (EPAC) method [8] have recently been proposed. Both the methods use effective potentials, which can be numerically calculated by means of the PIMC or PIMD technique.…”

A quantitative assessment of the accuracy of centroid molecular dynamics for the calculation of the infrared spectrum of liquid water

“…9 All these methods have been applied with variable degrees of success to the study of several quantum dynamical properties of different condensed phase systems. Besides quantum fluids such as parahydrogen, 10 liquid water is certainly the system that has been most extensively studied through quantum simulations ͑see Ref.…”

Effective potential analytic continuation approach for real time quantum correlation functions involving nonlinear operators

“…At the same time, we should note an important problem arising in the standard effective potential approach when it is applied to quantum systems that include the dissociation limit lim |q|→∞ V (q) = 0 [18,29]; for example, the systems represented in terms of the Morse potential V (r) (r = |q 1 − q 2 |) are classified into this category. For such systems with the dissociation limit, the minimum should disappear in the standard effective potential V β (R) because it is always convex for 0 < R < ∞ according to its definition [11,14,15]. Then the frequency ω β cannot be defined; this would lead to some unphysical flaw.…”