相关论文: Singular factorizations, self-adjoint extensions, …
We consider the exact solution of a many-body problem of spin-$s$ particles interacting through an arbitrary U(1) invariant factorizable $S$-matrix. The solution is based on a unified formulation of the quantum inverse scattering method for…
The variational quantum eigensolver has been proposed as a low-depth quantum circuit that can be employed to examine strongly correlated systems on today's noisy intermediate-scale quantum computers. We examine details associated with the…
Based on the fact that the Hamiltonians of the Coulomb many-particle systems are always factorized we develop the two different approaches for analytical solution of the Schr\"{o}dinger equation written for arbitrary few- and many-particle…
We recognize quantum circuit model of computation as factorisable scattering model and propose that a quantum computer is associated with a quantum many-body system solved by the Bethe ansatz. As an typical example to support our…
A practical method is developed to deal with the second quantization of the many-body system containing the composite particles. In our treatment, the modes associated with composite particles are regarded approximately as independent ones…
We construct certain eigenfunctions of the Calogero-Sutherland hamiltonian for particles on a circle, with mixed boundary conditions. That is, the behavior of the eigenfunction, as neighbouring particles collide, depend on the pair of…
We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this…
The main characteristics of the quantum oscillator coherent states including the two-particle Calogero interaction are investigated. We show that these Calogero coherent states are the eigenstates of the second-order differential…
We discuss self-adjoint operators given formally by expressions quadratic in bosonic creation and annihilation operators. We give conditions when they can be defined as self-adjoint operators, possibly after an infinite renormalization. We…
Gamow solutions are used to transform self-adjoint energy operators by means of factorization (supersymmetric) techniques. The transformed non-hermitian operators admit a discrete real spectrum which is occasionally extended by a single…
We construct in this article a class of closed semi-bounded quadratic forms on the space of square integrable functions over a smooth Riemannian manifold with smooth boundary. Each of these quadratic forms specifies a semi-bounded…
In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Newmann for symmetric operators in order to determine whether the…
Maximally entangled bipartite unitary operators or gates find various applications from quantum information to being building blocks of minimal models of many-body quantum chaos, and have been referred to as "dual unitaries". Dual unitary…
The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-body Hamiltonian via a radial differential operator and…
We solve the N-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form $\half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i - x_j)^2}]$, by constructing annihilation and creation operators of the form $…
We prove that some perturbation of a J-selfadjoint second order differential operator admits factorization and use this new representation of the operator to prove compactness of its resolvent and to find its domain.
We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determine correlation functions in an efficient way. We…
The Calogero-Sutherland model represents a paradigmatic example of an integrable quantum system with applications ranging from cold atoms to random matrix theory. Combining sum rules with the Monte Carlo technique, we introduce a stochastic…
We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A…
We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows to determine rigorously existence, location, and exact form of separable ground…