Related papers: Inverse square root level-crossing quantum two-sta…
We formulate a universal method for solving an arbitrary quantum system which, in the Bargmann representation, is described by a system of linear equations with one independent variable, such as one- and multi-photon Rabi models, or $N$…
A class of shape-invariant bound-state problems which represent transitions in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels. We show that the coupled-channel…
We present a simple systematic algorithm for construction of expansions of the solutions of ordinary differential equations with rational coefficients in terms of mathematical functions having indefinite integral representation. The…
We introduce creation and annihilation operators of pseudo-Hermitian fermions for two-level systems described by pseudo-Hermitian Hamiltonian with real eigenvalues. This allows the generalization of the fermionic coherent states approach to…
We present exact solutions for the non-equilibrium steady states of a class of dissipative spinless fermionic systems with arbitrary Hamiltonian pairing terms, global charging energy interactions, and uniform single particle loss on every…
The purpose of this paper is to generalize fermionic coherent states for two-level systems described by pseudo-Hermitian Hamiltonian \cite{Trifonov}, to n-level systems. Central to this task is the expression of the coherent states in terms…
We review the series solutions of the general and single-confluent Heun equations in terms of powers, ordinary-hypergeometric and confluent-hypergeometric functions. The conditions under which the expansions reduce to finite sums as well as…
We construct large classes of exactly solvable pseudo-Hermitian 2D spin Hamiltonians. The ground states of these systems depend only on the spatial topology of the system. We identify the ground state system on a surface with the value…
The decoherent histories approach to quantum theory is applied to a class of reparametrization invariant models, which includes systems described by the Klein-Gordon equation, and by a minisuperspace Wheeler-DeWitt equation. A key step in…
The non-Hermitian models, which are symmetric under parity (P) and time-reversal (T) operators, are the cornerstone for the fabrication of new ultra-sensitive optoelectronic devices. However, providing the gain in such systems usually…
It is shown that the two-axis countertwisting Hamiltonian is exactly solvable when the quantum number of the total angular momentum of the system is an integer after the Jordan-Schwinger (differential) boson realization of the SU(2)…
We discuss how a q-mutation relation can be deformed replacing a pair of conjugate operators with two other and unrelated operators, as it is done in the construction of pseudo-fermions, pseudo-bosons and truncated pseudo-bosons. This…
We establish an intriguing connection between quantum phase transitions and bifurcations in the ground-state fidelity per lattice site, and construct the universal order parameter for quantum Ising model in a transverse magnetic field on an…
We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative…
We show that and how point interactions offer one of the most suitable guides towards a quantitative analysis of properties of certain specific non-Hermitian (usually called PT-symmetric) quantum-mechanical systems. A double-well model is…
In this article we study the retrospective inverse problem. The retrospective inverse problem consists of in the reconstruction of a priori unknown initial condition of the dynamic system from its known final condition. Existence and…
We study quantum corrections for a family of 24 non-supersymmetric heterotic strings in two dimensions. We compute their genus two cosmological constant using the hyperelliptic formalism and the genus one two-point functions for the…
We have briefly analyzed the existence of the pseudofermionic structure of multilevel pseudo-Hermitian systems with odd time-reversal and higher order involutive symmetries. We have shown that 2N-level Hamiltonians with N-order eigenvalue…
We study a large-N deformation of the S=1/2 pyrochlore Heisenberg antiferromagnet which leads to a soluble quantum dimer model at leading non-trivial order. In this limit, the ground state manifold -- while extensively degenerate -- breaks…
The first order nonlinear ODE \dot \phi(t) + \sin\phi(t)=q(t),q(t)=B+A\cos\omega t, where A,B,\omega are real constants, is considered, the transformation converting it to a second order linear homogeneous ODE with polynoimial coefficients…