Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1003.3002

Accuracy of the coherent potential approximation for a one-dimensional array with a Gaussian distribution of fluctuations in the on-site potential

I. Avgin·D. L. Huber
View original source ↗Read source document ↗Export metadata ↓

Abstract

We investigate the accuracy of the coherent potential approximation (CPA) for a one-dimensional array with nearest-neighbor interactions and a Gaussian distribution of fluctuations in the on-site potential. The CPA values of the integrated density of states and the inverse localization length are compared with the results of mode-counting studies carried out on arrays of 107 - 108 sites. Good agreement is obtained suggesting that the CPA may be exact for this model. We also consider the asymptotic behavior of the inverse localization length and show that it can be approximated by the reciprocal of the decay length of a state localized about a single, strongly perturbed site in an otherwise perfect lattice.

Explore related subjects

cond-mat.dis-nn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

I. Avgin, D. L. Huber. 2010-03-15. Accuracy of the coherent potential approximation for a one-dimensional array with a Gaussian distribution of fluctuations in the on-site potential. https://doi.org/10.1016/j.physe.2010.05.011

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

KEEP EXPLORING

Related papers

arXiv2026

Analytical quantification of strongly disordered discrete time crystals

Discrete time crystals (DTCs) have emerged as a novel non-equilibrium phenomenon. Nevertheless, analytical quantification for disordered DTCs remains challenging, leaving uncertainties about their behaviors in large scale systems amid current debates on the stability of (Floquet-)many-body localization. In this work, we introduce an analytical framework to calculate the values of key observables in a strongly disordered DTC without fitting parameter. The perturbatively obtained closed-form formulae show quantitative agreement with numerical simulations for inverse participation ratios for eigenstate localization in Fock space, Edwards-Anderson parameters for spin-glass orders, mutual information for long-range entanglement, and the steady-state amplitudes of autocorrelators for period-doubled oscillations. Meanwhile, we demonstrate that eigenstate resonances render the scaling for the deviation of physical observables from their unperturbed values as $O(λ)$, in contrast to non-resonant situations with suppressed deviation $O(λ^2)$. Our newly developed scheme adopts resolvent perturbation formalism, which can directly prescribe arbitrarily higher-order corrections without iterations. With such advantages, we analytically prove that quasienergy corrections for pairwise cat eigenstates are identical up to order $O(λ^{(L/n_{\text{op}})-1})$, where perturbations of strength $λ$ involve at most $n_{\text{op}}$-spin terms. Such spectral pairing deviations quantify the DTC lifetime as $τ_* \sim (1/λ)^{L/n_{\text{op}}}$. We further show that the analytical framework applies to generic DTC models with dominant Ising interaction and a given number of qubits, offering a unified scheme to quantify physical observables for systems beyond numerically accessible sizes, with or without disorders.

cond-mat.dis-nn↗
arXiv2026

Nonlocal Magic across the Many-Body Localization Crossover

Nonlocal magic quantifies the minimum nonstabilizerness attainable under independent local unitary transformations on the two subsystems. Here, we use min-relative nonlocal magic (NLM) to characterize the crossover from ergodicity to many-body localization (MBL) in the random-field XXZ chain. Unlike entanglement entropy, NLM probes how entanglement is organized through the distance of the Schmidt spectrum from dyadic-flat stabilizer spectra. From weak to intermediate disorder, NLM evolves from an $O(1)$ Haar-like value into a size-enhanced dome, while entanglement remains volume-law, revealing a spectral reorganization not visible in the entropy. Deep in the MBL regime, a two-level cut-hybridization model captures the nearly binary Schmidt spectrum and explains why the mean and median NLM decay approximately as $W^{-1}$ and $W^{-2}$, respectively. Following a product-state quench, NLM overshoots and relaxes in the ergodic regime, whereas at strong disorder it grows slowly and approximately logarithmically. These results show that NLM resolves Schmidt-spectrum structure not visible in the entanglement entropy and provides a complementary probe of ergodicity breaking.

cond-mat.dis-nn↗
arXiv2026

Latent kinetic Ising models of neural spike trains

Inferring directed effective interactions from neuronal spike trains is a central inverse problem in statistical physics and computational neuroscience. Kinetic Ising models provide a tractable framework for this task, but their application to neural data typically requires binning spike trains into binary activity variables, discarding within-bin timing and conflating collective network dynamics with single-neuron history effects. We introduce SpiKIsing, a latent-variable model that separates these two levels of description. A discrete-time asymmetric kinetic Ising model describes collective network activity, while continuous-time, history-dependent point processes generate the observed spikes conditional on the latent states, accounting explicitly for refractoriness and post-spike recovery. We derive a variational mean-field expectation-maximization scheme in which the point-process likelihood enters as an effective observation field, enabling joint inference of latent activity, network couplings, and emission parameters. The framework extends naturally to maximum-a-posteriori inference with structured priors, including sparsity and a hierarchical extension favouring Dale-consistent outgoing interactions. We validate parameter recovery on matched synthetic data and test the method on spike trains generated by a recurrent conductance-based leaky integrate-and-fire network. In this setting, SpiKIsing recovers sparse connection structure and correctly classifies all excitatory and inhibitory neurons despite the substantial mismatch between the data-generating dynamics and the SpiKIsing model.

cond-mat.dis-nn↗