Quantum Stochastic Differential Equations in View of Non-Equlibrium Thermo Field Dynamics

TL;DR

This paper challenges the assumption that quantum Langevin equations inherently preserve quantum commutation relations due to non-commutative noise, using a unified formalism within Non-Equilibrium Thermo Field Dynamics.

Contribution

It demonstrates that the preservation of commutation relations is not guaranteed in quantum stochastic differential equations, questioning the quantum origin of dissipation.

Findings

Non-commutative noise operators do not always preserve commutation relations.

The quantum mechanical origin of dissipation is not universally valid.

Unified formalism clarifies the conditions for preserving quantum relations.

Abstract

Most of the mathematical approaches for quantum Langevin equation are based on the non-commutativity of the random force operators. Non-commutative random force operators are introduced in order to guarantee that the equal-time commutation relation for the stochastic annihilation and creation operators preserves in time. If it is true, it means that the origin of dissipation is of quantum mechanical. However, physically, it is hard to believe it. By making use of the unified canonical operator formalism for the system of the quantum stochastic differential equations within Non-Equilibrium Thermo Field Dynamics, it is shown that it is not true in general.