Related papers: q-Random Matrix Ensembles
We introduce structured random matrix ensembles, constructed to model many-body quantum systems with local interactions. These ensembles are employed to study equilibration of isolated many-body quantum systems, showing that rather complex…
Two quantum systems, each described as a random-matrix ensemble. are coupled to each other via a number of transition states. Each system is strongly coupled to a large number of channels. The average transmission probability is the product…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
As a hybrid of artificial intelligence and quantum computing, quantum neural networks (QNNs) have gained significant attention as a promising application on near-term, noisy intermediate-scale quantum (NISQ) devices. Conventional QNNs are…
We present an overview of our studies on the nonequilibrium dynamics of quantum systems that have many interacting particles. Our emphasis is on systems that show strong level repulsion, referred to as chaotic systems. We discuss how full…
We establish a general framework to explore parametric statistics of individual energy levels in disordered and chaotic quantum systems of unitary symmetry. The method is applied to the calculation of the universal intra-level parametric…
Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the…
We use multi-time correlation functions of quantum systems to construct random variables with statistical properties that reflect the degree of complexity of the underlying quantum dynamics.
The extended Gaussian ensemble introduced recently as a generalization of the canonical ensemble, which allows to treat energy fluctuations present in the system, is used to analyze the inelasticity distributions in high energy…
The application of random matrix theory to scattering requires introduction of system-specific information. This paper shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically…
In the paper is discussed complete probabilistic description of quantum systems with application to multiqubit quantum computations. In simplest case it is a set of probabilities of transitions to some fixed set of states. The probabilities…
Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
Investigation on foundational aspects of quantum statistical mechanics recently entered a renaissance period due to novel intuitions from quantum information theory and to increasing attention on the dynamical aspects of single quantum…
The random matrix ensembles (RME) of quantum statistical Hamiltonians, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied in literature to following quantum statistical systems:…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…
Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…
A simple model for open quantum systems is analyzed with Random Matrix Theory. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the…