22 research outputs found
Why must we work in the phase space?
We are going to prove that the phase-space description is fundamental both in
the classical and quantum physics. It is shown that many problems in
statistical mechanics, quantum mechanics, quasi-classical theory and in the
theory of integrable systems may be well-formulated only in the phase-space
language.Comment: 130 page
Coherent States Measurement Entropy
Coherent states (CS) quantum entropy can be split into two components. The
dynamical entropy is linked with the dynamical properties of a quantum system.
The measurement entropy, which tends to zero in the semiclassical limit,
describes the unpredictability induced by the process of a quantum approximate
measurement. We study the CS--measurement entropy for spin coherent states
defined on the sphere discussing different methods dealing with the time limit
. In particular we propose an effective technique of computing
the entropy by iterated function systems. The dependence of CS--measurement
entropy on the character of the partition of the phase space is analysed.Comment: revtex, 22 pages, 14 figures available upon request (e-mail:
[email protected]). Submitted to J.Phys.
Perspectives: Quantum Mechanics on Phase Space
The basic ideas in the theory of quantum mechanics on phase space are
illustrated through an introduction of generalities, which seem to underlie
most if not all such formulations and follow with examples taken primarily from
kinematical particle model descriptions exhibiting either Galileian or
Lorentzian symmetry. The structures of fundamental importance are the relevant
(Lie) groups of symmetries and their homogeneous (and associated) spaces that,
in the situations of interest, also possess Hamiltonian structures. Comments
are made on the relation between the theory outlined and a recent paper by
Carmeli, Cassinelli, Toigo, and Vacchini.Comment: "Quantum Structures 2004" - Meeting of the International Quantum
Structures Association; Denver, Colorado; 17-22 July, 200
On Locality in Quantum General Relativity and Quantum Gravity
The physical concept of locality is first analyzed in the special
relativistic quantum regime, and compared with that of microcausality and the
local commutativity of quantum fields. Its extrapolation to quantum general
relativity on quantum bundles over curved spacetime is then described. It is
shown that the resulting formulation of quantum-geometric locality based on the
concept of local quantum frame incorporating a fundamental length embodies the
key geometric and topological aspects of this concept. Taken in conjunction
with the strong equivalence principle and the path-integral formulation of
quantum propagation, quantum-geometric locality leads in a natural manner to
the formulation of quantum-geometric propagation in curved spacetime. Its
extrapolation to geometric quantum gravity formulated over quantum spacetime is
described and analyzed.Comment: Mac-Word file translated to postscript for submission. The author may
be reached at: [email protected] To appear in Found. Phys. vol. 27,
199
Wigner function for twisted photons
A comprehensive theory of the Weyl-Wigner formalism for the canonical pair
angle-angular momentum is presented, with special emphasis in the implications
of rotational periodicity and angular-momentum discreteness.Comment: 6 pages, 4 figure
On central atoms of Archimedean atomic lattice effect algebras
summary:If element of a lattice effect algebra is central, then the interval is a lattice effect algebra with the new top element and with inherited partial binary operation . It is a known fact that if the set of central elements of is an atomic Boolean algebra and the supremum of all atoms of in equals to the top element of , then is isomorphic to a direct product of irreducible effect algebras ([16]). In [10] Paseka and Riečanová published as open problem whether is a bifull sublattice of an Archimedean atomic lattice effect algebra . We show that there exists a lattice effect algebra with atomic which is not a bifull sublattice of . Moreover, we show that also , the center of compatibility, may not be a bifull sublattice of