Related papers: Some invariant biorthogonal sets with an applicati…
It is shown that second variations of the causal action can be decomposed into a sum of three terms, two of which being positive and one being small. This gives rise to an approximate decoupling of the linearized field equations into the…
We formulate a relation between quantum-mechanical coherent states and complex-differentiable structures on the classical phase space ${\cal C}$ of a finite number of degrees of freedom. Locally-defined coherent states parametrised by the…
Universal properties of many-body systems in conformal quantum mechanics in arbitrary dimensions are presented. Specially, a general structure of discrete energy spectra and eigenstates is found. Finally, a simple construction of a…
This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an…
In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new definition of fusion dual sequence associated with a fusion…
At finite $N$ the ring of gauge invariant operators is not freely generated. For problems of interest in physics, these rings are Cohen--Macaulay and admit a Hironaka decomposition, in which the full invariant ring is a free module over a…
Previous $\lambda$-deformed {\it non-Hermitian} Hamiltonians with respect to the usual scalar product of Hilbert spaces dealing with harmonic oscillator-like developments are (re)considered with respect to a new scalar product in order to…
We investigate the superposition of coherent states, emphasizing quantum states with distinct Wigner phase-space features relevant to quantum information applications. In this study, we introduce generalized versions of the compass state,…
We introduce an extended version of the Swanson model, defined on a two-dimensional non commutative space, which can be diagonalized exactly by making use of pseudo-bosonic operators. Its eigenvalues are explicitly computed and the…
While dealing with a class of generalized Bergman spaces on the unit ball, we construct for each of these spaces a set of coherent states to apply a coherent states quantization method. This provides us with another way to recover the…
A fractional Chern insulator is thought to emerge from the competition between one-particle band topology and strong repulsive interactions. As an attempt to study lattice models of fractional Chern insulators, we introduce a biorthogonal…
The uncertainty principle of SE(2) allows to construct a coherent states transform that is strictly related to the Bargmann transform for the second Heisenberg group H2. The corresponding target space is characterized constructively and…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
We present a unified approach to (bi-)orthogonal basis sets for gravitating systems. Central to our discussion is the notion of mutual gravitational energy, which gives rise to the self-energy inner product on mass densities. We consider a…
We propose an extension of {\em supersymmetric quantum mechanics} which produces a family of isospectral hamiltonians. Our procedure slightly extends the idea of intertwining operators. Several examples of the construction are given.…
In the second part of our review (for the first part see quant-ph/0108080), we discuss a physical model for generation of "truncated" coherent and squeezed states in finite-dimensional Hibert spaces.
It has been shown that a positive semi-definite Hamiltonian H, that has a tridiagonal matrix representation in a given basis, can be represented in the form H = A{\dag}A, where A is a forward shift operator playing the role of an…
In~this paper, we construct noncommutative coherent states using various families of unitary irreducible representations (UIRs) of $\g$, a connected, simply connected nilpotent Lie group, that was identified as the kinematical symmetry…
The supersymmetric structure of a generalized non-Hermitian driven two-level system is demonstrated. A unitary rotation turns the Hamiltonian into a more convenient form. After decoupling a set of differential equations, the supersymmetric…
We consider the 2-generated free metabelian associative and Lie algebras over the complex field and the invariants of the dihedral groups of finite order acting on these algebras. In the associative case we find a finite set of generators…