A remark on charge transfer processes in multi-particle systems

Abstract

We assess the probability of resonances between sufficiently distant states in a combinatorial graph serving as the configuration space of an N-particle disordered quantum system. This includes the cases where the transition "shuffles" the particles in the configurations. In presence of a random external potential V, such pairs of configurations give rise to local (random) Hamiltonians which are strongly coupled, so that eigenvalue (or eigenfunction) correlator bounds are difficult to obtain. This difficulty, which occurs for three or more particles, results in eigenfunction decay bounds weaker than expected. We show that more efficient bounds, obtained so far only for 2-particle systems, extend to any number of particles.

References in corpus (6)

• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• Multi-Particle Anderson Localisation: Induction on the Number of Particles
• Wegner bounds for a two-particle tight binding model
• A Wegner estimate for multi-particle random Hamiltonians
• Anderson localisation for an interacting two-particle quantum system on $\mathbb{Z}$
• The integrated density of states for an interacting multielectron homogeneous model

Cited by in corpus (9)

• On the regularity of the conditional distribution of the sample mean
• Direct Scaling Analysis of localization in disordered systems. II. Multi-particle lattice systems
• Fixed-energy multi-particle MSA implies dynamical localization
• Optimized estimates of the regularity of the conditional distribution of the sample mean
• Comprehensive proofs of localization in Anderson models with interaction. I. Two-particle localization estimates
• Resonances and localization in multi-particle disordered systems
• Efficient Anderson localization bounds for large multi-particle systems
• Uniform N-particle Anderson localization and unimodal eigenstates in deterministic disordered media without induction on the number of particles
• Efficient localization bounds in a continuous multi-particle Anderson model with long-range interaction