Related papers: Spectral properties of the trap model on sparse ne…
We study the transport and spectral properties of a non-Hermitian one-dimensional disordered lattice, the diagonal matrix elements of which are random complex variables taking both positive (loss) and negative (gain) imaginary values: Their…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
We analyze a trapping reaction with a single penetrable trap, in a one dimensional lattice, where both species (particles and trap) are mobile and have a drift velocity. We obtain the density as seen from a reference system attached to the…
Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by…
In a recent computer study, we have shown that the combination of spatially heterogeneous dynamics and kinetic facilitation provides a microscopic explanation for the emergence of excess wings in deeply supercooled liquids. Motivated by…
We propose a novel way to detect the fractal energy spectrum of the Hofstadter model from the density distributions of ultracold fermions in an external trap. At low temperature, the local compressibility is proportional to the density of…
We propose Sparse Neural Network architectures that are based on random or structured bipartite graph topologies. Sparse architectures provide compression of the models learned and speed-ups of computations, they can also surpass their…
We investigate the memory effect in a simple model for glassy relaxation, a trap model with a Gaussian density of states. In this model thermal equilibrium is reached at all finite temperatures and therefore we can consider jumps from low…
Exact method of analytical solution of flat, non-dispersive eigenstates in a class of quasi-one dimensional structures is reported within the tight-binding framework. The states are localized over certain sublattice sites. One such finite…
Transformer networks are able to capture patterns in data coming from many domains (text, images, videos, proteins, etc.) with little or no change to architecture components. We perform a theoretical analysis of the core component…
We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration,…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
This paper investigates a distinctive spectral pattern exhibited by transmission eigenfunctions in wave scattering theory. Building upon the discovery in [7, 8] that these eigenfunctions localize near the domain boundary, we derive sharp…
We analyze dynamic random network models where younger vertices connect to older ones with probabilities proportional to their degrees as well as a propensity kernel governed by their attribute types. Using stochastic approximation…
We derive the spectral properties of adjacency matrix of complex networks and of their Laplacian by the replica method combined with a dynamical population algorithm. By assuming the order parameter to be a product of Gaussian…
Aging has become the paradigm to describe dynamical behavior of glassy systems, and in particular spin glasses. Trap models have been introduced as simple caricatures of effective dynamics of such systems. In this Letter we show that in a…
We consider quantum quenches of harmonically trapped one-dimensional bosons from repulsive to attractive interactions, and the resulting breathing dynamics of the so-called `super-Tonks-Girardeau' (sTG) state. This state is highly excited…
In the context of unitary evolution of a generic quantum system interrupted at random times with non-unitary evolution due to interactions with either the external environment or a measuring apparatus, we adduce a general theoretical…
The concept of metastability has caused a lot of interest in recent years. The spectral decomposition of the generator matrix of a stochastic network exposes all of the transition processes in the system. The assumption of the existence of…
Quantum many-body systems are expected to relax to a thermal state over time, with some exceptions such as systems with atypical eigenstates. In this study, we investigate the effect of the existence of spatially localized eigenstates on…