Microscopic realization of cross-correlated noise processes

TL;DR

This paper develops a microscopic Hamiltonian-based model to describe cross-correlated noise processes, deriving a Langevin equation that captures their key features from a system-reservoir perspective.

Contribution

It introduces a novel microscopic framework for cross-correlated noise, incorporating external driving and nonlinear system-reservoir coupling.

Findings

Derived Langevin equation includes cross-correlation features.

Model captures effects of external modulation on noise.

Provides a foundation for analyzing cross-correlated stochastic processes.

Abstract

We present a microscopic theory of cross-correlated noise processes, starting from a Hamiltonian system-reservoir description. In the proposed model, the system is nonlinearly coupled to a reservoir composed of harmonic oscillators, which in turn is driven by an external fluctuating force. We show that the resultant Langevin equation derived from the composite system (system+reservoir+external modulation) contains the essential features of cross-correlated noise processes.