Related papers: Analytical eigenstates for the quantum Rabi model
By mapping the Hamiltonians of the two-mode and 2-photon Rabi models to differential operators in suitable Hilbert spaces of entire functions, we prove that the two models possess entire and normalizable wavefunctions in the…
The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with N sites have solutions containing i/2, -i/2 that are singular: both the corresponding energy and the algebraic Bethe ansatz vector are divergent. Such solutions…
A procedure for constructing bound state potentials is given. We show that, under the natural conditions imposed on a radial eigenvalue problem, the only special cases of the general central potential, which are exactly solvable and have…
The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex model with fixed open boundary conditions and the corresponding $SU_{q}(n)$ invariant…
A new bi-parametric $su(1,1)$ algebraization of the Heun class of equations is explored. This yields additional quasi-polynomial solutions of the form $\{z^{\alpha}P_N(z): \ \alpha \in \mathbb{C}, \ N \in \mathbb{N}_0\}$ to the General Heun…
We define the anisotropic Rabi model as the generalization of the spin-boson Rabi model: The Hamiltonian system breaks the parity symmetry; the rotating and counter-rotating interactions are governed by two different coupling constants; a…
We consider the eigenstate problem for a Hamiltonian operator of the field theory. Methods of construction the effective field theoretical Hamiltonians for which the eigenstate problem may be solved are discussed. In particular, we discuss…
We show that the Heun confluent equation admits infinitely many solutions in terms of the confluent generalized hypergeometric functions. For each of these solutions a characteristic exponent of a regular singularity of the Heun confluent…
We study the two-qubit Rabi model in the most general case where the qubits are different from each other. The spectrum of the system in the ultrastrong-coupling regime is shown to converge to two forced oscillator chains by perturbation…
We study two models describing the interaction of a two-level system with two quantum field modes. The first one is equivalent to a dissipative two-state system with just two boson fields in the absence of tunneling. The second describes…
Several examples of Jacobi matrices with an explicitly solvable spectral problem are worked out in detail. In all discussed cases the spectrum is discrete and coincides with the set of zeros of a special function. Moreover, the components…
We consider the problem of a qubit driven by a harmonically oscillating external field while it is coupled to a quantum two-level system. We perform a systematic numerical analysis of the problem by varying the relevant parameters. The…
The anisotropic two-photon quantum Rabi model is studied using the Bogoliubov operator approach. The doubly degenerate exceptional states are identified through analytical methods. By adjusting the position of the last exceptional point…
We examine the bound state solutions of the Dirac equation under the spin and pseudospin symmetries for a new suggested combined potential, Hulten plus a class of Yukawa potential including a Coulomb-like tensor interaction. An improved…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…
Starting with the Gaudin-like Bethe ansatz equations associated with the quasi-exactly solved (QES) exceptional points of the asymmetric quantum Rabi model (AQRM) a spectral equivalence is established with QES hyperbolic Schr\"odinger…
A stationary physical system satisfies peculiar balance conditions involving mean values of appropriate observables. In this paper we show how to deduce such quantitative links, named balance equations, demonstrating as well their…
We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in ref. [20] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic…
We study Heun's differential equation in the case that one of the singularities is apparent. In particular we conjecture a relationship with generalized hypergeometric differential equation and establish it in some cases. We apply our…
We studied the two-qubit quantum Rabi model and found its dark state solutions with at most N photons. One peculiar case presents when $N=3$, which has constant eigenenergy in the whole coupling regime and leads to level crossings within…