Full Analytic Spectrum of Generalized Jaynes-Cummings Hamiltonians

Theoretical and Mathematical Physics - We develop an analytic formalism using basic quantum mechanics techniques to successfully solve the multiphoton Jaynes–Cummings and the generalized...     

Deformed ladder operators for the generalized one- and two-mode squeezed harmonic oscillator in the presence of a minimal length

Theoretical and Mathematical Physics - We construct the deformed ladder operators in the presence of a minimal length to study the one- and two-mode squeezed harmonic oscillator. The generalized...     

Biorthogonal quantum mechanics for non-Hermitian multimode and multiphoton Jaynes–Cummings models

We develop a biorthogonal formalism for non-Hermitian multimode and multiphoton Jaynes–Cummings models. For these models, we define supersymmetric generators, which are especially convenient for diagonalizing the Hamiltonians. The Hamiltonian and its adjoint are expressed in terms of supersymmetric generators having the Lie superalgebra properties. The method consists in using a similarity dressing operator that maps onto spaces suitable for diagonalizing Hamiltonians even in an infinite-dimensional Hilbert space. We then successfully solve the eigenproblems related to the Hamiltonian and its adjoint. For each model, the eigenvalues are real, while the eigenstates do not form a set of orthogonal vectors. We then introduce the biorthogonality formalism to construct a consistent theory.     

The mixed spin-1/2 and spin-1 Ising system on a two-layer Bethe lattice

Two layered magnetic Bethe lattice with varying coordination number q is introduced and numerically studied via exact recursion relations within a pairwise approach. The system is influenced by competing interlayer and intralayer nearest-neighbour (NN) coupling interactions and also by the crystal and external magnetic fields. Cases where both layers are ferromagnetic or one is ferro and the other antiferromagnetic are considered. System configurations’ energy calculations are used to devise some ground state phase diagrams that have proven useful for the investigation of the very low temperature behaviour of the model. Analysis of the thermal behaviours of the total magnetization within the model parameters’ space yield interesting phase diagrams which display fascinating properties, in particular the presence of tricritical points. Increasing negative values of the crystal field strength stabilizes the disordered paramagnetic phase and sometimes gives rise to wavy transition lines.     

Quantization of Some Generalized Jaynes-Cummings Models in a Kerr-Like Medium

Theoretical and Mathematical Physics - Based on fundamental principles of quantum mechanics, we present a method for a rigorous analytic construction of the spectra of the one- and two-photon...