Open Quantum Systems from Dynamical Constraints

TL;DR

This paper introduces a novel framework for open quantum systems where the environment emerges from dynamical constraints rather than being an external sector, offering a new perspective rooted in constrained quantization.

Contribution

It proposes a constraint-based approach to model environments in open quantum systems, replacing traditional interaction Hamiltonians with dynamical constraints.

Findings

Demonstrates how environment influence can be formulated via constraints in a quantum particle model.

Shows the equivalence of the constraint-based approach to traditional open system descriptions.

Provides a new perspective on the origin and modeling of quantum environments.

Abstract

Open quantum systems are traditionally described by decomposing the total Hilbert space into a system and an external environment, linked by an explicit interaction Hamiltonian. We propose an alternative framework in which the environment is not introduced as an independent sector a priori, but instead emerges from the dynamical activation of constraints in an initially constrained quantum system. Within Dirac quantization, the physical degrees of freedom define the system, whereas the constraint sector, once promoted to carry its own dynamics, functions as an environment. In this picture, the system-environment coupling is not added through a separate interaction term, but is encoded directly in the constraint structure. As an example, we study a quantum particle coupled to a Brownian-oscillator environment and show how the resulting environmental influence can be formulated in this constraint-based setting. Our results provide a new perspective on the origin of quantum environments and point toward a general framework for open quantum systems rooted in constrained quantization.