Related papers: Some invariant biorthogonal sets with an applicati…

We study the structure of stationary non equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non…

Motivated by the existence of bi-Hamiltonian classical systems and the correspondence principle, in this paper we analyze the problem of finding Hermitian scalar products which turn a given flow on a Hilbert space into a unitary one. We…

A weighted composition operator on a reproducing kernel Hilbert space is given by a composition, followed by a multiplication. We study unitary and co-isometric weighted composition operators on unitarily invariant spaces on the Euclidean…

We introduce a set of coherent states which are associated with quantum systems governed by a trilinear boson Hamiltonian. These states are produced by the action of a nonunitary displacement operator on a reference state and can be…

We construct a new class of multipartite states possessing orthogonal symmetry. This new class defines a convex hull of multipartite states which are invariant under the action of local unitary operations introduced in our previous paper…

A general procedure for constructing coherent states, which are eigenstates of annihilation operators, related to quantum mechanical potential problems, is presented. These coherent states, by construction are not potential specific and…

Coherent states are required to form a complete set of vectors in the Hilbert space by providing the resolution of identity. We study the completeness of coherent states for two different models in a noncommutative space associated with the…

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…

The state spaces of generalised coherent states associated with special unitary groups are shown to form rational curves and surfaces in the space of pure states. These curves and surfaces are generated by the various Veronese embeddings of…

In the setting of operators on Hilbert spaces, we prove that every quasinilpotent operator has a non-trivial closed invariant subspace if and only if every pair of idempotents with a quasinilpotent commutator has a non-trivial common closed…

Using the {\it nonlinear coherent states method}, a formalism for the construction of the coherent states associated to {\it "inverse bosonic operators"} and their dual family has been proposed. Generalizing the approach, the "inverse of…

This paper defines coherent manifolds and discusses their properties and their application in quantum mechanics. Every coherent manifold with a large group of symmetries gives rise to a Hilbert space, the completed quantum space of $Z$,…

For many years coherent states have been a useful tool for understanding fundamental questions in quantum mechanics. Recently, there has been work on developing a consistent way of including constraints into the phase space path integral…

In biorthogonal quantum mechanics, the eigenvectors of a quasi-Hermitian operator and those of its adjoint are biorthogonal and complete and the probability for a transition from a quantum state to any one of these eigenvectors is positive…

The problem of building coherent states from non-normalizable fiducial states is considered. We propose a way of constructing such coherent states by regularizing the divergence of the fiducial state norm. Then, we successfully apply the…

It is well-known that any two pure quantum states (in the same Hilbert space) can be mapped to any other using unitary transformations. However, previous approaches to this problem required two explicit bases for the Hilbert space, one each…

In a recent series of papers we have analyzed a certain deformation of the canonical commutation relations producing an interesting functional structure which has been proved to have some connections with physics, and in particular with…

We present a set of necessary conditions for the existence of a biorthonormal basis composed of eigenvectors of non-Hermitian operators. As an illustration, we examine these conditions in the case of normal operators. We also provide a…

We review the construction and applications of exactly Poincar\'e invariant quantum mechanical models of few-degree of freedom systems. We discuss the construction of dynamical representations of the Poincar\'e group on few-particle Hilbert…

We provide a simple construction of bipartite entangled states that are positive under partial transposition, and hence undistillable. The construction makes use of the properties of the projectors onto the symmetric and antisymmetric…