Related papers: Higher-order gap ratios of singular values in open…
We calculate eigenvector statistics in an ensemble of non-Hermitian matrices describing open quantum systems [F. Haake et al., Z. Phys. B 88, 359 (1992)] in the limit of large matrix size. We show that ensemble-averaged eigenvector…
We study the problem of the basis of an open quantum system, under a quantum chaotic environment, which is preferred in view of its stationary reduced density matrix (RDM), that is, the basis in which the stationary RDM is diagonal. It is…
For a general class of large non-Hermitian random block matrices $\mathbf{X}$ we prove that there are no eigenvalues away from a deterministic set with very high probability. This set is obtained from the Dyson equation of the Hermitization…
We investigate the presence of off-diagonal long-range order in a harmonically confined two-dimensional Bose gas. In the noninteracting case, an analytical calculation of the the finite-temperature one-particle density martix provides an…
We show that a composite quantum system described by the tensor product of multiple systems each with a leading-order exceptional point (a non-Hermitian degeneracy at which not only eigenvalues but also eigenstates coalesce) exhibits a…
Many experimental systems exist that possess charge-density-wave order in their ground state. While this order should be able to be described with models similar to those used for superconductivity, nearly all systems have a ratio of the…
In this paper, we present a gradient algorithm for identifying unknown parameters in an open quantum system from the measurements of time traces of local observables. The open system dynamics is described by a general Markovian master…
In this letter, we introduce a novel method for investigating dissipation (gain) and thermalization in an open quantum system. In this method, the quantum system is coupled linearly with a copy of itself or with another system described by…
We derive the effective Hamiltonian $H - \mu N$ for open quantum systems with varying particle number from first principles within the framework of non-relativistic quantum statistical mechanics. We prove that under physically motivated…
We study the temporal evolution of quantum mechanical fermionic particles exhibiting one bound state within a one-dimensional attractive square-well potential in a heat bath of bosonic particles. For this open quantum system we formulate…
. We study the statistical properties of the eigenvalues of non-Hermitian operators assoicated with the dissipative complex systems. By considering the Gaussian ensembles of such operators, a hierarchical relation between the correlators is…
In the present paper we show that the Hamiltonian describing the resonant interaction of $N$ two-level systems with a single-mode electromagnetic quantum field in the Coulomb gauge can be diagonalized with a high degree of accuracy using a…
Long-range quantum systems, in which the interactions decay as $1/r^{\alpha}$, are of increasing interest due to the variety of experimental set-ups in which they naturally appear. Motivated by this, we study fundamental properties of…
Quantum phase transitions have been the subject of intense investigations in the last two decades [1]. Among other problems, these phase transitions are relevant in the study of heavy fermion systems, high temperature superconductors and…
The statistics of gap ratios between consecutive energy levels is a widely used tool, in particular in the context of many-body physics, to distinguish between chaotic and integrable systems, described respectively by Gaussian ensembles of…
We show that the density-matrix states of noncomposite qudit systems satisfy entropic and information relations like the subadditivity condition, strong subadditivity condition, and Araki--Lieb inequality, which characterize hidden quantum…
The main focus of this thesis is the theoretical study of strongly interacting quantum mixtures confined in one dimension and subjected to a harmonic external potential. Such strongly correlated systems can be realized and tested in…
We consider a problem of description of quantum correlations and dispersions of subsystems of complex open systems. Based on our previous results we proposed a method to evaluate pure quantum contributions from total statistical…
The influence of wave function symmetry on statistical correlation is studied for the case of three non-interacting spin-free quantum particles in a unidimensional box, in position and in momentum space. Higher-order statistical…
In this paper, we extend the method of Kadanoff-Baym equations for open quantum systems to arbitrary kinds of systems and heat baths, either fermionic or bosonic. This includes three spacial dimensions and different potentials for the…