We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product H = H ⊗ · · ·⊗H is separable or entangled. We show that the tensor convolution ( φ . . . φ ) : G → H defined for mappings φ : G → H μ on an almost arbitrary locally compact abelian group G, give rise to formulation of an equivalent problem to the separability one.

Generalised observables (POM observables) are necessary for representing all possible measurements on a quantum system. Useful algebraic operations such as addition and multiplication are defined for these observables, recovering many advantages of the more restrictive Hermitian operator formalism. Examples include new uncertainty relations and metrics, and optical phase applications.

The generally deformed oscillator (GDO) and its multiphoton realization as well as the coherent and squeezed vacuum states are studied. We discuss, in particular, the GDO depending on a complex parameter q (therefore we call it q-GDO) together with the finite dimensional cyclic representations. As a realistic physical system of GDO the isospectral oscillator system is studied and it is found th...

We examine the properties and consequences of pseudo-supersymmetry for quantum systems admitting a pseudo-Hermitian Hamiltonian. We explore the Witten index of pseudo-supersymmetry and show that every pair of diagonalizable (not necessarily Hermitian) Hamiltonians with discrete spectra and real or complex-conjugate pairs of eigenvalues are isospectral and have identical degeneracy structure exc...

In infinite-dimensional Hilbert spaces, the application of the concept of quasiHermiticity to the description of non-Hermitian Hamiltonians with real spectra may lead to problems related to the definition of the metric operator. We discuss these problems by examining some examples taken from the recent literature and propose a formulation that is free of these difficulties.

We describe all almost contact metric, almost hermitian and G 2-structures admitting a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the ∇-parallel spinors. In particular, we obtain solutions of the type II string equations in dimension n = 5, 6 and 7.

This note provides a completeness result on the compressed modes introduced in [7, 8]. We prove the fact that for an unbounded Hermitian operator, the sub-eigenspace of spanned by the first M eigenfunctions can be approximated by first N compressed modes with improvable accuracy as N increases, for any fixed regularization parameter μ.

Excited bound states are often understood within scattering based theories as resulting from the collision of a particle on a target via a short-range potential. We show that the resulting formalism is non-Hermitian and describe the Hilbert spaces and metric operator relevant to a correct formulation of such theories. The structure and tools employed are the same that have been introduced in cu...

The Lee model was introduced in the 1950s as an elementary quantum field theory in which mass, wave function, and charge renormalization could be carried out exactly. In early studies of this model it was found that there is a critical value of g2, the square of the renormalized coupling constant, above which g2 0 , the square of the unrenormalized coupling constant, is negative. Thus, for g2 l...

In infinite-dimensional Hilbert spaces, the application of the concept of pseudo-Hermiticity to the description of non-Hermitian Hamiltonians with real spectra may lead to difficulties related to the definition of the metric operator. These difficulties are illustrated by examining some examples taken from the recent literature. We present a formulation that avoids such problems. PACS numbers: ...