Dynamical chaotic phases and constrained quantum dynamics

TL;DR

This paper introduces a novel framework for implementing quantum constraints through work protocols, demonstrating how such constraints can induce nonlinear and chaotic dynamics in quantum systems while preserving Gaussian states.

Contribution

It proposes a new method for quantum constraints using work protocols and applies it to a quantum spherical model, revealing complex dynamical behavior including chaos.

Findings

Constraints induce nonlinear and chaotic dynamics.

Gaussian states are preserved throughout evolution.

Framework is robust against experimental errors.

Abstract

In classical mechanics, external constraints on the dynamical variables can be easily implemented within the Lagrangian formulation. Conversely, the extension of this idea to the quantum realm, which dates back to Dirac, has proven notoriously difficult due to the noncommutativity of observables. Motivated by recent progress in the experimental control of quantum systems, we propose a framework for the implementation of quantum constraints based on the idea of work protocols, which are dynamically engineered to enforce the constraints. As a proof of principle, we consider the dynamical mean-field approach of the many-body quantum spherical model, which takes the form of a quantum harmonic oscillator plus constraints on the first and second moments of one of its quadratures. The constraints of the model are implemented by the combination of two work protocols, coupling together the first and second moments of the quadrature operators. We find that such constraints affect the equations of motion in a highly nontrivial way, inducing nonlinear behavior and even classical chaos. Interestingly, Gaussianity is preserved at all times. A discussion concerning the robustness of this approach to possible experimental errors is also presented.