Related papers: Analytically solvable Hamiltonians for quantum sys…
A coinless quantisation procedure of general reversible Markov chains on graphs is presented. A quantum Hamiltonian H is obtained by a similarity transformation of the fundamental transition probability matrix K in terms of the square root…
Analytical solutions of the Bohr Hamiltonian are obtained in the $\gamma$-unstable case, as well as in an exactly separable rotational case with $\gamma\approx 0$, called the exactly separable Morse (ES-M) solution. Closed expressions for…
The problem of one pair of identical nucleons sitting in ${\cal N}$ single particle levels of a potential well and interacting through the pairing force is treated introducing, in the Hamiltonian formalism, even Grassmann variables. The…
In this article, we study and settle several structural questions concerning the exact solvability of the Olshanetsky-Perelomov quantum Hamiltonians corresponding to an arbitrary root system. We show that these operators can be written as…
Recently, Feh\'er and Kluck discovered, at the level of classical mechanics, new compactified trigonometric Ruijsenaars-Schneider $n$-particle systems, with phase space symplectomorphic to the $(n-1)$-dimensional complex projective space.…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
Quantum harmonic oscillators linearly coupled through coordinates and momenta, represented by the Hamiltonian $ {\hat H}=\sum^2_{i=1}\left( \frac{ {\hat p}^{2}_i}{2 m_i } + \frac{m_i \omega^2_i}{2} x^2_i\right) +{\hat H}_{int} $, where the…
An array of N subsequent Laguerre polynomials is interpreted as an eigenvector of a non-Hermitian tridiagonal Hamiltonian $H$ with real spectrum or, better said, of an exactly solvable N-site-lattice cryptohermitian Hamiltonian whose…
We present in this article all Hamiltonian systems in E(2) that are separable in cartesian coordinates and that admit a third-order integral, both in quantum and in classical mechanics. Many of these superintegrable systems are new, and it…
Within the framework of quantum mechanics working with one-dimensional, manifestly non-Hermitian Hamiltonians $H=T+V$ the traditional class of the exactly solvable models with local point interactions $V=V(x)$ is generalized. The…
We present a new exactly solvable Hamiltonian with a separable pairing interaction and non-degenerate single-particle energies. It is derived from the hyperbolic family of Richardson-Gaudin models and possesses two free parameters, one…
We describe an algorithm that computes the ground state energy and correlation functions for 2-local Hamiltonians in which interactions between qubits are weak compared to single-qubit terms. The running time of the algorithm is polynomial…
Rydberg-atom quantum simulators are of keen interest because of their possibilities towards high-dimensional qubit architectures. Here we report three-dimensional conformation spectra of quantum-Ising Hamiltonian systems with programmed…
Using a complete basis set we have obtained an analytic expression for the matrix elements of the Coulomb interaction. These matrix elements are written in a closed form. We have used the basis set of the three-dimensional isotropic quantum…
The pure-quantum self-consistent harmonic approximation (PQSCHA) permits to study a quantum system by means of an effective classical Hamiltonian. In this work the PQSCHA is reformulated in terms of the holomorphic variables connected to a…
This paper derives master equations for an atomic two-level system for a large set of unitarily equivalent Hamiltonians without employing the rotating wave and certain Markovian approximations. Each Hamiltonian refers to physically…
In an innovative inverse-problem construction the measured, experimental energies $E_1$, $E_2$, ...$E_N$ of a quantum bound-state system are assumed fitted by an N-plet of zeros of a classical orthogonal polynomial $f_N(E)$. We reconstruct…
It is known that a linear system with a system matrix A constitutes a Hamiltonian system with a quadratic Hamiltonian if and only if A is a Hamiltonian matrix. This provides a straightforward method to verify whether a linear system is…
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential…
We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension…