Hyperbolic ring based formulation for thermo field dynamics, quantum dissipation, entanglement, and holography

TL;DR

This paper introduces a hyperbolic ring framework for modeling dissipative quantum systems, revealing internal symmetries, constructing a grand partition function, and exploring entanglement and holography without unitarity issues.

Contribution

It develops a novel hyperbolic ring formulation for open quantum systems, addressing unitarity problems and linking dissipation, entanglement, and holography in a unified approach.

Findings

Hyperbolic rotations serve as an internal symmetry for dissipative dynamics.

A grand partition function is constructed with a chemical potential as conjugate to charge.

Entanglement entropy operators are formulated to analyze dissipation-induced entanglement.

Abstract

The classical and quantum formulations for open systems related to dissipative dynamics are constructed on a complex hyperbolic ring, following universal symmetry principles, and considering the double thermal fields approach for modeling the system of interest, and the environment. The hyperbolic rotations are revealed as an underlying internal symmetry for the dissipative dynamics, and a chemical potential is identified as conjugate variable to the charge operator, and thus a grand partition function is constructed. As opposed to the standard scheme, there are not patologies associated with the existence of many unitarity inequivalent representations on the hyperbolic ring, since the whole of the dissipative quantum dynamics is realized by choosing only one representation of the field commutation relations. Entanglement entropy operators for the subsystem of interest and the environment, are constructed as a tool for study the entanglement generated from the dissipation. The holographic perspectives of our results are discussed.