Related papers: Dynamical and Quenched Random Matrices and Homolum…
We discuss a dynamical matrix model by which probability distribution is associated with Gaussian ensembles from random matrix theory. We interpret the matrix M as a Hamiltonian representing interaction of a bosonic system with a single…
We introduce a dynamical matrix model where the matrix $X$ is interpreted as a Hamiltonian representing interaction of a bosonic system with a single fermion. We show how a system of second-quantized fermions influences the ground state of…
We review the properties of reduced density matrices for free fermionic or bosonic many-particle systems in their ground state. Their basic feature is that they have a thermal form and thus lead to a quasi-thermodynamic problem with a…
Effects of randomness on interacting fermionic systems in one dimension are investigated by quantum Monte-Carlo techniques. At first, interacting spinless fermions are studied whose ground state shows charge ordering. Quantum phase…
Understanding how the dynamics of a given quantum system with many degrees of freedom is altered by the presence of a generic perturbation is a notoriously difficult question. Recent works predict that, in the overwhelming majority of…
We numerically investigate the momentum-space entanglement entropy and entanglement spectrum of the random-dimer model and its generalizations, which circumvent Anderson localization, after a quench in the Hamiltonian parameters. The type…
We study matrix element fluctuations of the two-body screened Coulomb interaction and of the one-body surface charge potential in ballistic quantum dots. For chaotic dots, we use a normalized random wave model to obtain analytic expansions…
This contribution describes a statistical model for decaying quantum systems (e.g. photo-dissociation or -ionization). It takes the interference between direct and indirect decay processes explicitely into account. The resulting expressions…
We introduce a random interaction matrix model (RIMM) for finite-size strongly interacting fermionic systems whose single-particle dynamics is chaotic. The model is applied to Coulomb blockade quantum dots with irregular shape to describe…
We study the ground state properties of the one-dimensional extended Hubbard model at half-filling from the perspective of its particle reduced density matrix. We focus on the reduced density matrix of $2$ fermions and perform an analysis…
We investigate the dynamics of the $\nu=1$ Quantum Symmetric Simple Exclusion Process starting from spatially inhomogeneous initial states. This one-dimensional system of free fermions has time-dependent stochastic hopping amplitudes that…
Following a recent work (briefly reviewed below) we consider temporal fluctuations in the reduced density matrix elements for a coupled system involving a pair of kicked rotors as also one made up of a pair of Harper Hamiltonians. These…
We study the non-equilibrium dynamics of the Luttinger model after suddenly turning on and off the bare Coulomb interaction between the fermions. We analyze several correlation functions such as the one particle density matrix and vertex…
Fermionic Hamiltonians play a critical role in quantum chemistry, one of the most promising use cases for near-term quantum computers. However, since encoding nonlocal fermionic statistics using conventional qubits results in significant…
We study the out-of-equilibrium dynamics of entanglement fluctuations in the $\nu=1$ Quantum Symmetric Simple Exclusion Process, a free-fermion chain with hopping amplitudes that are stochastic in time but homogeneous in space. Previous…
A consistent local approach to the study of interacting relativistic fermion systems with a condensation of bare particles in its ground or vacuum state, which may has a finite matter density, is developed. The attention is payed to some of…
Given a specific interacting quantum Hamiltonian in a general spatial dimension, can one access its entanglement properties, such as, the entanglement entropy corresponding to the ground state wavefunction? Even though progress has been…
Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix…
In many physical situations the behavior of a quantum system is affected by interaction with a larger environment. We develop, using the method of influence functional, how to deduce the density matrix of the quantum system incorporating…
We study the non equilibrium dynamics in the fermionic Hubbard model after a sudden change of the interaction strength. To this scope, we introduce a time dependent variational approach in the spirit of the Gutzwiller ansatz. At the…