Related papers: On relations between vertex operators, quasiclassi…
Quantum baker`s map is a model of chaotic system. We study quantum dynamics for the quantum baker's map. We use the Schack and Caves symbolic description of the quantum baker`s map. We find an exact expression for the expectation value of…
Discrepancy between periodic orbit theory and numerical calculation of a modified Kepler problem is cleared by a quantum mechanical calculation. The diagonal approximation already gives a good fit for the numerical calculation. A better…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
Formal structure of phase-space path integrals based on different types of operator orderings is analysed.
Geometrical structures of quantum mechanics provide us with new insightful results about the nature of quantum theory. In this work we consider mixed quantum states represented by finite rank density operators. We review our geometrical…
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
Starting from a real scalar quantum field theory with quartic self-interactions and non-minimal coupling to classical gravity, we define four equal-time, spatially covariant phase-space operators through a Wigner transformation of spatially…
Do the partial order and ortholattice operations of a quantum logic correspond to the logical implication and connectives of classical logic? Re-phrased, how far might a classical understanding of quantum mechanics be, in principle,…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…
In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states…
The ``problem of time'' has been a pressing issue in quantum gravity for some time. To help understand this problem, Rovelli proposed a model of a two harmonic oscillators system where one of the oscillators can be thought of as a ``clock''…
Homoclinic and heteroclinic orbits provide a skeleton of the full dynamics of a chaotic dynamical system and are the foundation of semiclassical sums for quantum wave packet, coherent state, and transport quantities. Here, the homoclinic…
The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications…
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…
Quasi-classical quantization of crystal dislocations field is considered in terms of functional integral. The generalized zeta-function is used to evaluate the functional integral and quantum corrections to mass in quasi-classical…
Parallel to the quantization of the complex plane, using the canonical coherent states of a right quaternionic Hilbert space, quaternion field of quaternionic quantum mechanics is quantized. Associated upper symbols, lower symbols and…
We present the characterizations of symbol correspondences for mechanical systems that are symmetric by $SU(3)$, which we refer to as \emph{quark systems}. The quantum quark systems are the unitary irreducible representations of $SU(3)$ of…
The Gromov-Witten invariants of a smooth, projective variety $V$, when twisted by the tautological classes on the moduli space of stable maps, give rise to a family of cohomological field theories and endow the base of the family with…
In this paper we construct quantum analogs of strata of coadjoint orbits and describe their representations. This kind objects play an important role in describing quantum groups as repeated extensions of quantum strata.
A general notion of a quasi-finite algebra is introduced as an algebra graded by the set of all integers equipped with topologies on the homogeneous subspaces satisfying certain properties. An analogue of the regular bimodule is introduced…