239 research outputs found
Quantization with Action-Angle Coherent States
For a single degree of freedom confined mechanical system with given energy,
we know that the motion is always periodic and action-angle variables are
convenient choice as conjugate phase-space variables. We construct action-angle
coherent states in view to provide a quantization scheme that yields precisely
a given observed energy spectrum for such a system. This construction
is based on a Bayesian approach: each family corresponds to a choice of
probability distributions such that the classical energy averaged with respect
to this probability distribution is precisely up to a constant shift. The
formalism is viewed as a natural extension of the Bohr-Sommerfeld rule and an
alternative to the canonical quantization. In particular, it also yields a
satisfactory angle operator as a bounded self-adjoint operator
A discrete nonetheless remarkable brick in de Sitter: the "massless minimally coupled field"
Over the last ten years interest in the physics of de Sitter spacetime has
been growing very fast. Besides the supposed existence of a "de sitterian
period" in inflation theories, the observational evidence of an acceleration of
the universe expansion (interpreted as a positive cosmological constant or a
"dark energy" or some form of "quintessence") has triggered a lot of attention
in the physics community. A specific de sitterian field called "massless
minimally coupled field" (mmc) plays a fundamental role in inflation models and
in the construction of the de sitterian gravitational field. A covariant
quantization of the mmc field, `a la Krein-Gupta-Bleuler was proposed in [1].
In this talk, we will review this construction and explain the relevance of
such a field in the construction of a massless spin 2 field in de Sitter
space-time.Comment: Proceedings of the XXVII Colloquium on Group Theoretical Methods in
Physics, Yerevan, August 200
Coherent States and Bayesian Duality
We demonstrate how large classes of discrete and continuous statistical
distributions can be incorporated into coherent states, using the concept of a
reproducing kernel Hilbert space. Each family of coherent states is shown to
contain, in a sort of duality, which resembles an analogous duality in Bayesian
statistics, a discrete probability distribution and a discretely parametrized
family of continuous distributions. It turns out that nonlinear coherent
states, of the type widely studied in quantum optics, are a particularly useful
class of coherent states from this point of view, in that they contain many of
the standard statistical distributions. We also look at vector coherent states
and multidimensional coherent states as carriers of mixtures of probability
distributions and joint probability distributions
Coherent-State Approach to Two-dimensional Electron Magnetism
We study in this paper the possible occurrence of orbital magnetim for
two-dimensional electrons confined by a harmonic potential in various regimes
of temperature and magnetic field. Standard coherent state families are used
for calculating symbols of various involved observables like thermodynamical
potential, magnetic moment, or spatialdistribution of current. Their
expressions are given in a closed form and the resulting Berezin-Lieb
inequalities provide a straightforward way to study magnetism in various limit
regimes. In particular, we predict a paramagnetic behaviour in the
thermodynamical limit as well as in the quasiclassical limit under a weak
field. Eventually, we obtain an exact expression for the magnetic moment which
yields a full description of the phase diagram of the magnetization.Comment: 21 pages, 6 figures, submitted to PR
"Massless" vector field in de Sitter Universe
In the present work the massless vector field in the de Sitter (dS) space has
been quantized. "Massless" is used here by reference to conformal invariance
and propagation on the dS light-cone whereas "massive" refers to those dS
fields which contract at zero curvature unambiguously to massive fields in
Minkowski space. Due to the gauge invariance of the massless vector field, its
covariant quantization requires an indecomposable representation of the de
Sitter group and an indefinite metric quantization. We will work with a
specific gauge fixing which leads to the simplest one among all possible
related Gupta-Bleuler structures. The field operator will be defined with the
help of coordinate independent de Sitter waves (the modes) which are simple to
manipulate and most adapted to group theoretical matters. The physical states
characterized by the divergencelessness condition will for instance be easy to
identify. The whole construction is based on analyticity requirements in the
complexified pseudo-Riemanian manifold for the modes and the two-point
function.Comment: 33 pages, 3 figure
Delocalization and the semiclassical description of molecular rotation
We discuss phase-space delocalization for the rigid rotator within a
semiclassical context by recourse to the Husimi distributions of both the
linear and the anisotropic instances. Our treatment is based upon the
concomitant Fisher information measures. The pertinent Wehrl entropy is also
investigated in the linear case.Comment: 6 pages, 3 figure
Temporally stable coherent states for infinite well and P\"oschl-Teller potentials
This paper is a direct illustration of a construction of coherent states
which has been recently proposed by two of us (JPG and JK). We have chosen the
example of a particle trapped in an infinite square-well and also in
P\"oschl-Teller potentials of the trigonometric type. In the construction of
the corresponding coherent states, we take advantage of the simplicity of the
solutions, which ultimately stems from the fact they share a common SU(1,1)
symmetry \`a la Barut--Girardello. Many properties of these states are then
studied, both from mathematical and from physical points of view.Comment: 48 pages, 21 figure
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