Equivalence of dynamics of disordered quantum ensembles and semi-infinite lattices

Abstract

We develop a formalism for mapping the exact dynamics of an ensemble of disordered quantum systems onto the dynamics of a single particle propagating along a semi-infinite lattice, with parameters determined by the probability distribution of disorder realizations of the original heterogeneous quantum ensemble. This mapping provides a geometric interpretation on the loss of coherence when averaging over the ensemble and allows computation of the exact dynamics of the entire disordered ensemble in a single simulation. Alternatively, by exploiting the reverse map, one can obtain lattice dynamics by averaging over realisations of disorder. The potential of this equivalence is showcased with examples of the map in both directions: obtaining dephasing of a qubit via mapping to a lattice model, and solving a simple lattice model via taking an average over realizations of disorder of a unit cell.

11 pages, 5 figures

References in corpus (12)

• The numerical renormalization group method for quantum impurity systems
• Efficiency of energy transfer in a light-harvesting system under quantum coherence
• Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
• Chaos, Complexity, and Random Matrices
• The fundamental role of quantized vibrations in coherent light harvesting by cryptophyte algae
• Operator growth and Krylov construction in dissipative open quantum systems
• Krylov Complexity in Open Quantum Systems
• Krylov complexity and orthogonal polynomials
• Localization of phonons in ion traps with controlled quantum disorder
• Dynamical Anderson transition in one-dimensional periodically kicked incommensurate lattices
• Bunching and anti-bunching of localised particles in disordered media
• Localization of matter waves in lattice systems with moving disorder