Related papers: Spectroscopic studies in open quantum systems
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…
The creation of artificial gauge fields in neutral ultracold atom systems has opened the possibility to study the effects of spin-orbit coupling terms in clean environments. This work considers the multi-channel scattering properties of two…
In the spectrum of many-body quantum systems, the low-energy eigenstates were the traditional focus of research. The interest in the statistical properties of the full eigenspectrum has grown more recently, in particular in the context of…
We analyze a system of two-component fermions which interact via a Feshbach resonance in the presence of a three-dimensional lattice potential. By expressing a two-channel model of the resonance in the basis of Bloch states appropriate for…
The eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior. In particular, the spectral density $\rho(\lambda)$ of this matrix reveals important network…
The spectral form factor (SFF) can probe the eigenvalue statistic at different energy scales as its time variable varies. In closed quantum chaotic systems, the SFF exhibits a universal dip-ramp-plateau behavior, which reflects the spectrum…
The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take…
We show that a polynomial H(N) of degree N of a harmonic oscillator hamiltonian allows us to devise a fully solvable continuous quantum system for which the first N discrete energy eigenvalues can be chosen at will. In general such a choice…
We study complex eigenvalues of large $N\times N$ symmetric random matrices of the form ${\cal H}=\hat{H}-i\hat{\Gamma}$, where both $\hat{H}$ and $\hat{\Gamma}$ are real symmetric, $\hat{H}$ is random Gaussian and $\hat{\Gamma}$ is such…
We consider two ultracold particles confined in spherically symmetric harmonic trap and interacting via isotropic potential with absorbing boundary conditions at short range that models reactive scattering. First, we apply the contact…
The resonator is one of the main building blocks of a plethora of photonic and microwave devices from nanolasers to compact biosensors and magnetic resonance scanners. The symmetry of the resonators is tightly related to their mode…
The eigenvector-eigenvalue identity relates the eigenvectors of a Hermitian matrix to its eigenvalues and the eigenvalues of its principal submatrices in which the jth row and column have been removed. We show that one-dimensional arrays of…
We investigate the super and sub-radiance characteristics of the radiation emitted from a system of three two-level atoms, in the GHZ and W-states. The dipolar coupling between atoms leads to two distinct configurations, one in which the…
In this paper we study an interacting two-particle system on the positive half-line. We focus on spectral properties of the Hamiltonian for a large class of two-particle potentials. We characterize the essential spectrum and prove, as a…
The spectral problem $(A + V(z))\psi=z\psi$ is considered where the main Hamiltonian $A$ is a self-adjoint operator of sufficiently arbitrary nature. The perturbation $V(z)=-B(A'-z)^{-1}B^{*}$ depends on the energy $z$ as resolvent of…
The phenomenon of super-radiance (Dicke effect, coherent spontaneous radiation by a gas of atoms coupled through the common radiation field) is well known in quantum optics. The review discusses similar physics that emerges in open and…
In part I, the formalism for the description of open quantum systems (that are embedded into a common well-defined environment) by means of a non-Hermitian Hamilton operator $\ch$ is sketched. Eigenvalues and eigenfunctions are…
In dimension $d=1,2,3$ we define a family of two-channel Hamiltonians obtained as point perturbations of the generator of the free decoupled dynamics. Within the family we choose two Hamiltonians, $\hat H_0$ and $\hat H_\ve$, giving rise…
We consider an open (scattering) quantum system under the action of a perturbation of its closed counterpart. It is demonstrated that the resulting shift of resonance widths is a sensitive indicator of the non-orthogonality of resonance…
Information on quantum systems can be obtained only when they are open (or opened) in relation to a certain environment. As a matter of fact, realistic open quantum systems appear in very different shape. We sketch the theoretical…