Controlling transport with structured long-range hopping

Boris Gurevich; Michael H. Kolodrubetz

Home/Archive/arXiv

arXiv · 2610.33393

Controlling transport with structured long-range hopping

Boris Gurevich·Michael H. Kolodrubetz

View original source ↗Read source document ↗Export metadata ↓

Abstract

The combined effects of disorder and long-range hopping play an important role in determining localization and transport in low-dimensional quantum systems. We study transport in a one-dimensional disordered chain with nearest-neighbor hopping supplemented by a long-range hopping term. The long-range coupling is characterized by site-dependent amplitudes that may be either uniform or random. We investigate the interplay between diagonal disorder and long-range hopping, characterizing the resulting transport efficiency. We find that nearest-neighbor hopping in the presence of uniform long-range hopping amplitudes strongly suppresses delocalization over a range of weak disorder. The disorder-enhanced transport regime, established in previous studies, can be understood here as the recovery of delocalization from this strongly suppressed regime. An analytical solution in the Anderson eigenstate basis reveals the microscopic origin of this behavior. In particular, we show that the low-disorder regime of strongly suppressed delocalization can be eliminated by introducing randomness into the long-range hopping amplitudes, providing an additional mechanism for enhancing transport and qualitatively changing the response of the system to disorder.

Explore related subjects

cond-mat.dis-nn quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Boris Gurevich, Michael H. Kolodrubetz. 2026-10-24. Controlling transport with structured long-range hopping. https://arxiv.org/abs/2610.33393

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Optimality and annealing path planning of dynamical analog solvers

Recently proposed analog solvers based on dynamical systems, such as Ising machines, are promising platforms for large-scale combinatorial optimization. Yet, given the heuristic nature of the field, there is very limited insight on optimality guarantees of the solvers, as well as how parameter schedules shape dynamics and outcomes. Here, we develop a dynamical mean-field framework to analyze Ising-machine dynamics for finding the ground state energy of the Sherrington-Kirkpatrick(SK) model of spin glasses and identify mechanisms that enable rapid convergence to provenly near-optimal energies. For a fixed target energy density Ec, we show that solutions are typically reached within O(1) matrix vector multiplications, indicating constant time complexity. We further delineate theoretical limitations arising from different parameter-scheduling trajectories and demonstrate a pronounced benefit of temperature-only annealing for the Coherent Ising Machine. Building on these insights, we propose a general framework for designing optimized parameter schedules, thereby improving the practical effectiveness of Ising machines for complex optimization tasks. The superior performance of the dynamical solvers is illustrated by the attainment of the ground state energy of the SK model.

cond-mat.dis-nn↗

arXiv2026

Matter that learns what matters

Can a material learn what deserves its attention? We show that it can in a model optical network, in which action outcomes train a persistent record in each link. The record biases whether a source is consulted and sets how strongly it changes a stored answer, so useful sources gain attention and influence without being identified in advance. The network's experience thus shapes the information available for its future learning. Resonant readouts make this learning fragile: reinforcement can carry a record past resonance, where it persists but its influence weakens. We derive bounds within which relevant signals guide the answer, irrelevant signals are rejected and stored answers remain open to revision. These bounds guide a learning rule that limits reinforcement as records form; in simulations, it acquires useful records and keeps them functional. When relevance changes, an obsolete record can block its own replacement. A local state that strengthens negative writing after unsuccessful actions releases obsolete records and completes the learning sequence more often. How a memory is read should decide how it is written.

cond-mat.dis-nn↗

arXiv2026

Symmetry-driven in-situ physical adjoint computing beyond reciprocity

Nonreciprocity enriches wave control and information processing through directional transport, yet challenges conventional in-situ physical adjoint optimization, which relies on reciprocity to acquire adjoint responses. Here we demonstrate symmetry-driven in-situ physical adjoint computing (Sym-iPAC) in nonreciprocal systems, which enables access to adjoint responses on the original hardware through three classes of transpose symmetry: local geometric permutations, complex gauge reweighting, and latent symmetry in effective port dynamics revealed by Schur reduction. Experiments with programmable nonreciprocal microwave networks validate these transpose relations and yield adjoint gradients, enabling closed-loop optimization. These results establish experimentally accessible transpose symmetry as a route to in-situ physical adjoint computing beyond reciprocity.

cond-mat.dis-nn↗