Disorder-averaged Qudit Dynamics

TL;DR

This paper derives exact solutions for disorder-averaged quantum dynamics in systems with periodic Hamiltonians, applicable to both Hermitian and non-Hermitian cases, revealing insights into decoherence and non-Markovian behavior.

Contribution

It introduces a novel analytical framework for disorder-averaged dynamics in quantum systems with ($p,q$)-potent Hamiltonians, independent of initial states and applicable to various system types.

Findings

Disorder-averaged dynamics resemble open quantum system behavior.

Dynamics depend on disorder distribution and Hamiltonian periodicity.

Framework applies to qubit and qudit systems with spin and clock operators.

Abstract

Understanding how physical systems are influenced by disorder is a fundamental challenge in quantum science. Addressing its effects often involves numerical averaging over a large number of samples, and it is not always easy to gain an analytical handle on exploring the effect of disorder. In this work, we derive exact solutions for disorder-averaged dynamics generated by any Hamiltonian that is a periodic matrix (potentially with non-trivial base, a property also called ($p,q$)-potency). Notably, this approach is independent of the initial state, exact for arbitrary evolution times, and it holds for Hermitian as well as non-Hermitian systems. The ensemble behavior resembles that of an open quantum system, whose decoherence function or rates are determined by the disorder distribution and the periodicity of the Hamiltonian. Depending on the underlying distribution, the dynamics can display non-Markovian characteristics detectable through non-Markovian witnesses. We illustrate the scheme for qubit and qudit systems described by (products of) spin $1/2$, spin $1$, and clock operators. Our methodology offers a framework to leverage disorder-averaged exact dynamics for a range of applications in quantum-information processing and beyond.