Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9701122

History-Dependence and Ageing in a Periodic Long-Range Josephson Array

P. Chandra·M. V. Feigelman·L. B. Ioffe·D. M. Kagan
View original source ↗Read source document ↗Export metadata ↓

Abstract

History-dependence and ageing are studied in the low-temperature glass phase of a long-range periodic Josephson array. This model is characterized by two parameters, the number of wires ($2N$) and the flux per unit strip ($α$); in the limit $N \to \infty$ and fixed $α\ll 1$ the dynamics of the model are described by the set of coupled integral equations, which coincide with those for the $p=4$ disordered spherical model. Below the glass transition we have solved these equations numerically in a number of different regimes. We observe power-law ageing after a fast quench with an exponent that decreases rapidly with temperature. After slow cooling to a not-too-low temperature, we see ageing characterized by the appearance of a new time scale which has a power law dependence on the cooling rate. By contrast if the array is cooled slowly to very low temperatures the ageing disappears. The physical consequences of these results in different cooling regimes are discussed for future experiment. We also study the structure of the phase space in the low temperature glassy regime. Analytically we expect an exponential number of metastable states just below the glass transition temperature with vanishing mutual overlap, and numerical results indicate that this scenario remains valid down to zero temperature. Thus in this array there is no further subdivision of metastable states. We also investigate the probability to evolve to different states given a starting overlap, and our results suggest a broad distribution of barriers.

Explore related subjects

cond-mat.dis-nn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

P. Chandra, M. V. Feigelman, L. B. Ioffe, D. M. Kagan. 1997-01-17. History-Dependence and Ageing in a Periodic Long-Range Josephson Array. https://doi.org/10.1103/physrevb.56.11553

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

KEEP EXPLORING

Related papers

arXiv2026

R-transforms for non-Hermitian matrices: a spherical integral approach

In this paper, we establish a connection between the formalism of $\mathcal{R}$-transforms for non-Hermitian random matrices and the framework of spherical integrals, using the replica method. This connection was previously proved in the Hermitian setting and in the case of bi-invariant random matrices. We show that the $\mathcal{R}$-transforms used in the non-Hermitian context in fact originate from a single scalar function of two variables. This provides a new and transparent way to compute $\mathcal{R}$-transforms, which until now had been known only in restricted cases such as bi-invariant, Hermitian, or elliptic ensembles.

cond-mat.dis-nn↗
arXiv2026

Spectral boundaries of deterministic matrices deformed by rotationally invariant random non-Hermitian ensembles

One of the great miracles of random matrix theory is that, in the $N \to \infty$ limit, many otherwise intractable matrix problems with horrendously complicated finite-$N$ expressions admit remarkably simple and elegant asymptotic solutions. In this paper, we illustrate this phenomenon in the context of spectral boundaries (or spectral edges) for deformed random matrices. Specifically, we consider matrices of the form $\mathbf{A} + \mathbf{B}$, where $\mathbf{A}$ is a deterministic $N\times N$ matrix (not necessarily Hermitian) and $\mathbf{B}$ is a rotationally invariant random matrix. In the large-$N$ limit, we show that the complex eigenvalue distribution of $\mathbf{A} + \mathbf{B}$ satisfies remarkably simple boundary equations that depend on the $\mathcal{R}_1$ and $\mathcal{R}_2$ transforms of $\mathbf{B}$. We illustrate our results on several explicit random matrix ensembles and support them with numerical simulations.

cond-mat.dis-nn↗
arXiv2026

Electrical conductivity of crack-template-based transparent conducting films: mean-field approximation, effective-medium theory, and simulation

In this work, crack-template-based transparent conducting films were modeled as networks corresponding to the edges of a two-dimensional Poisson--Voronoi diagram. Two types of networks were considered: the original one, in which the conductance of each edge was inversely proportional to its length, and the effective one, in which all edges had the same conductance obtained from the effective-medium theory. The mean-field approximation was used for analytical evaluation of the electrical conductivity. Direct numerical calculations for the Poisson--Voronoi diagram showed that the mean-field approximation overestimated the effective conductivity of the original network by approximately 13\%, and of the effective network by 79\%. In addition, a honeycomb network with an edge conductance distribution corresponding to the Poisson--Voronoi diagram was studied: for it, the predictions of the effective-medium theory turned out to be more accurate than for the Poisson--Voronoi diagram, which was explained by the greater structural homogeneity of the periodic honeycomb lattice. The results indicate that, when modeling crack-template-based transparent conducting films, the application of the mean-field approximation may lead to significant errors if the resistance of individual conductors is not simply proportional to their length. This possibility is discussed as a motivation for future studies of hierarchical cracks with variable width, which are not directly investigated here.

cond-mat.dis-nn↗