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We introduce a quantum generalization of classical kinetic Ising models, described by a certain class of quantum many body master equations. Similarly to kinetic Ising models with detailed balance that are equivalent to certain Hamiltonian…
In this paper, the 2+1 Dirac-Moshinsky oscillator (2+1 DMO) coupled to an external isospin field is mapped onto the Jaynes-Cummings model (JCM), which describes the interaction between two two-level systems and a quantum single-mode field.…
Analytical solution for the stationary density matrix is derived, by using the Morris-Shore transformation, for an open Jaynes-Cummings system of a two-level atom with Zeeman sublevel degeneracy coupled to an arbitrary-polarized cavity…
We present a theory of resonances for a class of non-autonomous Hamiltonians to treat the structural instability of spatially localized and time-periodic solutions associated with an unperturbed autonomous Hamiltonian. The mechanism of…
The Jaynes-Cummings-Hubbard (JCH) system describes a network of single-mode photonic cavities connected via evanescent coupling. Each cavity contains a single two level system which can be tuned in resonance with the cavity. Here we explore…
The use of the hyperspherical harmonic (HH) basis in the description of bound states in an $A$-body system composed by identical particles is normally preceded by a symmetrization procedure in which the statistic of the system is taken into…
We derive a novel two-component generalization of the nonlinear variational wave equation as a model for the director field of a nematic liquid crystal with a variable order parameter. The two-component nonlinear variational wave equation…
We introduce a class of PT-symmetric systems which include mutually matched nonlinear loss and gain (inother words, a class of PT-invariant Hamiltonians in which both the harmonic and anharmonic parts are non-Hermitian). For a basic system…
In this paper, we develop the notion of the linear atomic quantum coupler. This device consists of two modes propagating into two waveguides, each of them includes a localized and/or a trapped atom. These waveguides are placed close enough…
We treat control of several two-level atoms interacting with one mode of the electromagnetic field in a cavity. This provides a useful model to study pertinent aspects of quantum control in infinite dimensions via the emergence of…
For an anyon model in two spatial dimensions described by a modular tensor category, the topological S-matrix encodes the mutual braiding statistics, the quantum dimensions, and the fusion rules of anyons. It is nontrivial whether one can…
Recent studies have established and rigorously validated a modified Langevin noise formalism that enables first-principles quantization of electromagnetic fields in open and dissipative environments [1,2,3]. Building on this foundation, a…
In this study we consider the Hamiltonian approach for the construction of a map for a system with nonlinear resonant interaction, including phase trapping and phase bunching effects. We derive basic equations for a single resonant…
In quantum interaction problems with explicitly time-dependent interaction Hamiltonians, the time ordering plays a crucial role for describing the quantum evolution of the system under consideration. In such complex scenarios, exact…
This work presents a pedagogical and self-contained derivation of the first-order effective Hamiltonian for the two-mode Jaynes-Cummings model in the dispersive regime. A perturbative unitary transformation removes nonresonant atom-field…
The simplified models of interaction of charged matter with resonance modes of radiation generalizing the well-known Jaynes-Cummings and Dicke models are considered. It is found that these new models are integrable for arbitrary numbers of…
A general non-local point transformation for position-dependent mass Lagrangians and their mapping into a "constant unit-mass" Lagrangians in the generalized coordinates is introduced. The conditions on the invariance of the related…
An exact solution of the problem of two-atom one- and two-mode Jaynes-Cummings model with intensity-dependent coupling is presented. Asymptotic solutions for system state vectors are obtained in the approximation of large initial coherent…
Different ways to incorporate two-dimensional systems, which are not amenable to separation of variables, into the framework of Supersymmetrical Quantum Mechanics (SUSY QM) are analyzed. In particular, the direct generalization of…
With the Jaynes-Cummings model, we have studied the atom and light field quantum entanglement of multiphoton transition, and researched the effect of initial state superposition coefficient $C_{1}$, the transition photon number $N$, the…