Dynamics and steady states of tight-binding chains in presence of isolated defects

Abstract

Reduced transport and localization in isolated quantum systems are typically attributed to spatially-extended disorder, but may also emerge from the influence of a few controllable defects. We show here how a single defect profoundly reshapes wave-function spreading on a finite and periodic tight-binding lattice. Adapting the defect technique from classical random-walk studies, we obtain exact time-resolved site-occupation probabilities and several observables of interest. Even a single defect induces remarkable nonlinear effects, including non-monotonic suppression of transport, enhanced localization at distant sites, and strong sensitivity to the initial particle position at long times. These results demonstrate that minimal perturbations can generate nontrivial long-time transport signatures, giving rise to a microscopic defect-driven mechanism of quantum localization. Although the main results presented pertain to a single isolated defect, we show that the developed formalism may naturally extend to multiple as well as to a wider class of defects.

Version 2; Accepted for publication in J. Stat

References in corpus (17)

• Many body localization and thermalization in quantum statistical mechanics
• Realization of quantum walks with negligible decoherence in waveguide lattices
• Experimental demonstration of single-site addressability in a two-dimensional optical lattice
• Hierarchy of linear light cones with long-range interactions
• Detection of a quantum particle on a lattice under repeated projective measurements
• First detected arrival of a quantum walker on an infinite line
• Wavepacket dynamics of the nonlinear Harper model
• Non-Hermitian scattering on a tight-binding lattice
• Quantum unitary evolution interspersed with repeated non-unitary interactions at random times: The method of stochastic Liouville equation, and two examples of interactions in the context of a tight-binding chain
• Diffusion through permeable interfaces: Fundamental equations and their application to first-passage and local time statistics
• Dynamics of Disordered Quantum Systems Using Flow Equations
• Universal non-Hermitian transport in disordered systems
• Quantum random walk and tight-binding model subject to projective measurements at random times
• Entanglement evolution after a global quench across a conformal defect
• Evolution of the magnetization after a local quench in the critical transverse-field Ising chain
• Causality, localization, and universality of monitored quantum walks with long-range hopping
• Universal stability of coherently diffusive 1D systems with respect to decoherence