Dynamic spectral aspects of interparticle correlation

TL;DR

This paper investigates the spectral and correlation dynamics of a one-dimensional correlated atom under a time-dependent quadrupolar field, deriving exact decompositions and exploring effective potential models.

Contribution

It introduces an exact spectral decomposition of the time-dependent one-matrix and constructs an independent-particle model from it, providing new insights into correlation dynamics.

Findings

Exact spectral decomposition of the time-dependent one-matrix.

Construction of an independent-particle model capturing correlation effects.

Analysis of Rényi's entropy in the context of time-dependent correlation.

Abstract

Time-dependent quantities are calculated in the linear response limit for a correlated one dimensional model atom driven by an external quadrupolar time-dependent field. Besides the analysis of the time-evolving energy change in the correlated two-particle system, and orthogonality of initial and final states, Mehler's formula is applied in order to derive a point-wise decomposition of the time-dependent one-matrix in terms of time-dependent occupation numbers and time-dependent orthonormal, natural orbitals. Based on such exact spectral decomposition on the time domain, R\'enyi's entropy is also investigated. Considering the structure of the exact time-dependent one-matrix, an independent-particle model is defined from it which contains exact information on the single-particle probability density and probability current. The resulting noninteracting auxiliary state is used to construct an effective potential and discuss its applicability.