Quantum Mechanics of Disordered Systems

Massimiliano Giona

Geoffrey L. Sewell

Part I. The Algebraic Quantum Mechanical Framework and the Description of Order, Disorder and Irreversibility in Macroscopic Systems: Prospect was published in Quantum Mechanics and Its Emergent Macrophysics on page 1.

François Huveneers

We review possible mechanisms for energy transfer based on ‘rare’ or ‘non‐perturbative’ effects, in physical systems that present a many‐body localized phenomenology. The main focus is on classical systems, with or without quenched disorder. For non‐quantum systems, the breakdown of localization is usually not regarded as an issue, and we thus aim at identifying the fastest channels for transport. Next, we contemplate the possibility of applying the same mechanisms in quantum systems, including disorder free systems (e.g. Bose‐Hubbard chain), disordered many‐body localized systems with mobility edges at energies below the edge, and strongly disordered lattice systems in . For quantum mechanical systems, the relevance of these considerations for transport is currently a matter of debate.

V. Dobrosavljević

Reiner Kree

François Huveneers

We review possible mechanisms for energy transfer based on 'rare' or 'non-perturbative' effects, in physical systems that present a many-body localized phenomenology. The main focus is on classical systems, with or without quenched disorder. For non-quantum systems, the breakdown of localization is usually not regarded as an issue, and we thus aim at identifying the fastest channels for transport. Next, we contemplate the possibility of applying the same mechanisms in quantum systems, including disorder free systems (e.g. Bose-Hubbard chain), disordered many-body localized systems with mobility edges at energies below the edge, and strongly disordered lattice systems in d>1. For quantum mechanical systems, the relevance of these considerations for transport is currently a matter of debate.