A phase-space approach to non-stationary nonlinear systems

TL;DR

This paper introduces a phase-space approach to analyze non-stationary nonlinear systems, bridging different physics domains and enabling direct calculation of statistical properties without extensive simulations.

Contribution

It presents a novel phase-space formulation applicable to both Hamiltonian and dissipative systems, revealing new insights into non-stationary dynamics and quantum states.

Findings

Distinction between vacuum and squeezed states clarified

Phase-space method allows direct statistical property calculations

Potential applications in laser physics and quantum computing

Abstract

A phase-space formulation of non-stationary nonlinear dynamics including both Hamiltonian (e.g., quantum-cosmological) and dissipative (e.g., dissipative laser) systems reveals an unexpected affinity between seemly different branches of physics such as nonlinear dynamics far from equilibrium, statistical mechanics, thermodynamics, and quantum physics. One of the key insights is a clear distinction between the "vacuum" and "squeezed" states of a non-stationary system. For a dissipative system, the "squeezed state" (or the coherent "concentrate") mimics vacuum one and can be very attractable in praxis, in particular, for energy harvesting at the ultrashort time scales in a laser or "material laser" physics including quantum computing. The promising advantage of the phase-space formulation of the dissipative soliton dynamics is the possibility of direct calculation of statistical (including quantum) properties of coherent, partially-coherent, and non-coherent dissipative structure without numerically consuming statistic harvesting.