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The case of quantum-mechanical system (including electronic molecules) is considered where Hamiltonian allows a separation, in particular by the Faddeev method, of a weakly coupled channel. Width (i.e. the imaginary part) of the resonance…
The density matrix formalism and the equation of motion approach are two semi-analytical methods that can be used to compute the non-equilibrium dynamics of correlated systems. While for a bilinear Hamiltonian both formalisms yield the…
The behaviour of a system of two two-level atoms, both identical as well as non-identical, under the influence of a continuously varying dipole-dipole coupling parameter for a wide range of other parameters such as the atomic level…
We discuss the Jaynes-Cummings model in different representations of the algebra of canonical commutation relations. The first conclusion is that all the irreducible representations lead to equivalent physical predictions. However, the…
Certain Hamiltonians based on two coupled quantum mechanical spins exhibit degenerate eigenvalues despite having no obvious non-abelian symmetries. Operators acting to permute the degenerate states do not have a simple form when expressed…
We consider a generalization of the non-Hermitian ${\mathcal PT}$ symmetric Jaynes-Cummings {Hamiltonian, recently introduced for studying optical phenomena with time-dependent physical parameters, that includes environment-induced decay}.…
The eigenvalue absorption for a many-particle Hamiltonian depending on a parameter is analyzed in the framework of non--relativistic quantum mechanics. The long--range part of pair potentials is assumed to be pure Coulomb and no restriction…
Interaction of a two-level atom with a single mode of electromagnetic field including Kerr nonlinearity for the field and intensity-dependent atom-field coupling is discussed. The Hamiltonian for the atom-field system is written in terms of…
We analyze two-particle binding factors of H2, LiH, and HeH+ molecules/ions with the help of our original exact diagonalization ab intio (EDABI) approach. The interelectronic correlations are taken into account rigorously within the second…
We introduce the anisotropic two-photon Rabi model in which the rotating and counter rotating terms enters along with two different coupling constants. Eigenvalues and eigenvectors are studied with exact means. We employ a variation of the…
The goal of this chapter is to compare the predictions of the semiclassical Rabi model (SRM), which describes the interaction between a two-level system (qubit) and a classical monochromatic wave, and the quantum Rabi model (QRM), under the…
A cavity QED system is analyzed which duplicates the dynamics of a two-level atom in free space interacting exclusively with broadband squeezed light. We consider atoms in a three or four-level Lambda-configuration coupled to a high-finesse…
The entanglement dynamics of two remote qubits is examined analytically. The qubits interact arbitrarily strongly with separate harmonic oscillators in the idealized degenerate limit of the Jaynes-Cummings Hamiltonian. In contrast to well…
We develop a method to find analytical solutions for the eigenstates of the quantum Rabi model. These include symmetric, anti-symmetric and asymmetric analytic solutions given in terms of the confluent Heun functions. Both regular and…
We study theoretically the quantum dynamics of an electron in the symmetric four-level double-dot structure under the influence of the monochromatic resonant pulse. The probability amplitudes of the eigenstates relevant for the quantum…
We discuss the elementary errors in D.G. Zhang's [New. J. Phys. 23, 093014 (2021)] claimed exact solution of the quantum Rabi model. The erroneous solution is seen to be nothing more than the combined solution of the simpler Jaynes-Cummings…
The paper deals with a suitable transformation related to the metric scalar of the hyper-surface so that the Raychaudhuri Equation (RE) can be written as a second order nonlinear differential equation. A first integral of this second order…
Quantum coherence and quantum correlations are studied in the strongly interacting system composed of two qubits and an oscillator with the presence of a parametric medium. To analytically solve the system, we employ the adiabatic…
We construct a double degenerate supersymmetry in one dimensional quantum mechanics. Here the energy levels satisfy the conditions $E_{0,1}^{((-)}=0$ and $E_{n,n+1}^{(+)}=E_{n+2,n+3}^{(-)}$.The corresponding SUSY Hamiltonians$(H^{(\pm)}$)…
The quantum to classical transition (QCT) is one of the central mysteries in quantum physics. This process is generally interpreted as state collapse from measurement or decoherence from interacting with the environment. Here we define the…