Related papers: A path integral approach to sparse non-Hermitian r…
We present the non-Markovian generalization of the widely used stochastic Schrodinger equation. Our result allows to describe open quantum systems in terms of stochastic state vectors rather than density operators, without approximation.…
Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
A non-Hermitean random matrix model proposed a few years ago has a remarkably intricate spectrum. Various attempts have been made to understand the spectrum, but even its dimension is not known. Using the Dyson-Schmidt equation, we show…
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…
We consider a generic time-reversal invariant model of fermions hopping randomly on a square lattice. By means of the conventional replica-trick within the fermionic path-integral formalism, the model is mapped onto a non-linear sigma-model…
We investigate one-dimensional harmonically trapped two-component systems for repulsive interaction strengths ranging from the non-interacting to the strongly interacting regime for Fermi-Fermi mixtures. A new and powerful mapping between…
We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical…
We introduce a response-theoretic framework that recasts parameter calibration of ergodic stochastic differential equations as a fluctuation-dissipation problem. Our central result is that the full Jacobian of any stationary observable with…
We introduce a new approach to highly correlated systems which generalizes the Fermi Hypernetted Chain and Correlated Basis Function techniques. While the latter approaches can only be applied to systems for which a nonrelativistic wave…
Most biochemical reactions in living cells are open systems interacting with environment through chemostats to exchange both energy and materials. At a mesoscopic scale, the number of each species in those biochemical reactions can be…
In this study we consider the Hamiltonian approach for the construction of a map for a system with nonlinear resonant interaction, including phase trapping and phase bunching effects. We derive basic equations for a single resonant…
We present the path integral formulation of a broad class of generalized diffusion processes. Employing the path integral we derive exact expressions for the path probability densities and joint probability distributions for the class of…
We study macroscopic observables of large random matrices introduced by Pennington and Worah, defined by applying entry wise a non linear function on a product of matrices with independent entries. We allow the variance of the entries of…
Statistical properties of cross sections are studied for an open system of interacting fermions. The description is based on the effective non-Hermitian Hamiltonian that accounts for the existence of open decay channels preserving the…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…
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…
I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees…
Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…