# Effective description of the short-time dynamics in open quantum systems

## TL;DR

This paper investigates short-time dynamics of open quantum systems, demonstrating that under certain conditions, their evolution can be effectively described by classical noise, especially when global symmetries are present in large environments.

## Contribution

It provides a set of sufficient conditions for representing open quantum system dynamics with classical fields and offers an algebraic framework linking symmetries to classical descriptions.

## Key findings

- Short-time dynamics are described by Gaussian noise maps.
- Global symmetries enable classical field descriptions of environments.
- Constructive demonstration for bosonic environments confirms the theoretical conditions.

## Abstract

We address the dynamics of a bosonic system coupled to either a bosonic or a magnetic environment, and derive a set of sufficient conditions that allow one to describe the dynamics in terms of the effective interaction with a classical fluctuating field. We find that for short interaction times the dynamics of the open system is described by a Gaussian noise map for several different interaction models and independently on the temperature of the environment. In order to go beyond a qualitative understanding of the origin and physical meaning of the above short-time constraint, we take a general viewpoint and, based on an algebraic approach, suggest that any quantum environment can be described by classical fields whenever global symmetries lead to the definition of environmental operators that remain well defined when increasing the size, i.e. the number of dynamical variables, of the environment. In the case of the bosonic environment this statement is exactly demonstrated via a constructive procedure that explicitly shows why a large number of environmental dynamical variables and, necessarily, global symmetries, entail the set of conditions derived in the first part of the work.