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We review some aspects of the relation between ordinary coherent states and q-deformed generalized coherent states with some of the simplest cases of quantum Lie algebras. In particular, new properties of (q-)coherent states are utilized to…
The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a…
We derive a formula expanding the bracket with respect to a natural deformation parameter. The expansion is in terms of a two-variable polynomial algebra of diagram resolutions generated by basic operations involving the Goldman bracket. A…
A covariant functor from the category of generic complex algebraic curves to a category of the AF-algebras is constructed. The construction is based on a representation of the Teichmueller space of a curve by the measured foliations due to…
Among the mutation finite cluster algebras the tubular ones are a particularly interesting class. We show that all tubular (simply laced) cluster algebras are of exponential growth by two different methods: first by studying the…
A class of state models, called Kronecker-Weierstrass models (or, simply, KW-models), is introduced, and the state representation problem for linear differential systems is studied in the context of these models. It is shown, in particular,…
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here…
We investigate some particular completely positive maps which admit a stable commutative Von Neumann subalgebra. The restriction of such maps to the stable algebra is then a Markov operator. In the first part of this article, we propose a…
The linearity of quantum mechanics leads, under the assumption that the wave function offers a complete description of reality, to grotesque situations famously known as Schroedinger's cat. Ways out are either adding elements of reality or…
For linear nonautonomous differential equations we introduce a new family of spectrums defined with general nonuniform dichotomies: for a given growth rate $\mu$ in a large family of growth rates, we consider a notion of spectrum, named…
We analyze the time evolution describing a quantum source for noninteracting particles, either bosons or fermions. The growth behaviour of the particle number (trace of the density matrix) is investigated, leading to spectral criteria for…
Within the so-called scaled quantum theory, the standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. In this framework, the quantum-classical transition of the density matrix is…
An n-particle 3-dimensional Wigner quantum oscillator model is constructed explicitly. It is non-canonical in that the usual coordinate and linear momentum commutation relations are abandoned in favour of Wigner's suggestion that Hamilton's…
As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we…
A class of well-behaved *-representations of a q-deformed Heisenberg algebra is studied and classified.
A number of ideas and questions related to the construction of quantum processes are discussed. Quantum state extension, entanglement and asymptotic behaviour of the entropy are some of the issues explored. These topics are studied in more…
This paper studies the Kalman decomposition for linear quantum systems. Contrary to the classical case, the coordinate transformation used for the decomposition must belong to a specific class of transformations as a consequence of the laws…
This is a noncommutative version of the previous work entitled "Deformation Expression for Elements of Algebras (I)." In general in a noncommutative algebra, there is no canonical way to express elements in univalent way, which is often…
`Hypergeometric states', which are a one-parameter generalization of binomial states of the single-mode quantized radiation field, are introduced and their nonclassical properties are investigated. Their limits to the binomial states and to…
The quantum statistical treatment of the Rutherford model, considering matter as a system of point charges (electrons and nuclei) is analyzed. First, in the historical context, the solutions of different fundamental problems, such as the…