294 research outputs found
Coherent State Approach to Time Reparameterization Invariant Systems
For many years coherent states have been a useful tool for understanding
fundamental questions in quantum mechanics. Recently, there has been work on
developing a consistent way of including constraints into the phase space path
integral that naturally arises in coherent state quantization. This new
approach has many advantages over other approaches, including the lack of any
Gribov problems, the independence of gauge fixing, and the ability to handle
second-class constraints without any ambiguous determinants. In this paper, I
use this new approach to study some examples of time reparameterization
invariant systems, which are of special interest in the field of quantum
gravity
Fisher information, Wehrl entropy, and Landau Diamagnetism
Using information theoretic quantities like the Wehrl entropy and Fisher's
information measure we study the thermodynamics of the problem leading to
Landau's diamagnetism, namely, a free spinless electron in a uniform magnetic
field. It is shown that such a problem can be "translated" into that of the
thermal harmonic oscillator. We discover a new Fisher-uncertainty relation,
derived via the Cramer-Rao inequality, that involves phase space localization
and energy fluctuations.Comment: no figures. Physical Review B (2005) in pres
Reply on `comment on our paper `Single two-level ion in an anharmonic-oscillator trap: Time evolution of the Q function and population inversion ''
We show here that the model Hamiltonian used in our paper for ion vibrating
in a q-analog harmonic oscillator trap and interacting with a classical
single-mode light field is indeed obtained by replacing the usual bosonic
creation and annihilation operators of the harmonic trap model by their
q-deformed counterparts. The approximations made in our paper amount to using
for the ion-laser interaction in a q-analog harmonic oscillator trap, the
operator F_{q}=exp{-(|\epsilon|^2}/2)}exp{i\epsilon A^{\dagger}}exp{i\epsilon
A}, which is analogous to the corresponding operator for ion in a harmonic
oscillator trap that is . In our article we do not claim to have diagonalized the
operator, , for which the basis states
|g,m> and |e,m> are not analytic vectors.Comment: Revtex, 4pages. To be Published in Physical Review A59, NO.4(April
99
GazeauKlauder squeezed states associated with solvable quantum systems
A formalism for the construction of some classes of GazeauKlauder squeezed
states, corresponding to arbitrary solvable quantum systems with a known
discrete spectrum, are introduced. As some physical applications, the proposed
structure is applied to a few known quantum systems and then statistical
properties as well as squeezing of the obtained squeezed states are studied.
Finally, numerical results are presented.Comment: 18 pages, 12 figure
Phase space spinor amplitudes for spin 1/2 systems
The concept of phase space amplitudes for systems with continuous degrees of
freedom is generalized to finite-dimensional spin systems. Complex amplitudes
are obtained on both a sphere and a finite lattice, in each case enabling a
more fundamental description of pure spin states than that previously given by
Wigner functions. In each case the Wigner function can be expressed as the star
product of the amplitude and its conjugate, so providing a generalized Born
interpretation of amplitudes that emphasizes their more fundamental status. The
ordinary product of the amplitude and its conjugate produces a (generalized)
spin Husimi function. The case of spin-\half is treated in detail, and it is
shown that phase space amplitudes on the sphere transform correctly as spinors
under under rotations, despite their expression in terms of spherical
harmonics. Spin amplitudes on a lattice are also found to transform as spinors.
Applications are given to the phase space description of state superposition,
and to the evolution in phase space of the state of a spin-\half magnetic
dipole in a time-dependent magnetic field.Comment: 19 pages, added new results, fixed typo
Generalized Phase Space Representation of Operators
Introducing asymmetry into the Weyl representation of operators leads to a
variety of phase space representations and new symbols. Specific
generalizations of the Husimi and the Glauber-Sudarshan symbols are explicitly
derivedComment: latex, 8 pages, expanded version accepted by J. Phys.
Coherent states of P{\"o}schl-Teller potential and their revival dynamics
A recently developed algebraic approach for constructing coherent states for
solvable potentials is used to obtain the displacement operator coherent state
of the P\"{o}schl-Teller potential. We establish the connection between this
and the annihilation operator coherent state and compare their properties. We
study the details of the revival structure arising from different time scales
underlying the quadratic energy spectrum of this system.Comment: 13 pages, 6 figure
Coherent states associated to the wavefunctions and the spectrum of the isotonic oscillator
Classes of coherent states are presented by replacing the labeling parameter
of Klauder-Perelomov type coherent states by confluent hypergeometric
functions with specific parameters. Temporally stable coherent states for the
isotonic oscillator Hamiltonian are presented and these states are identified
as a particular case of the so-called Mittag-Leffler coherent states.Comment: 12 page
Complex Langevin Equation and the Many-Fermion Problem
We study the utility of a complex Langevin (CL) equation as an alternative
for the Monte Carlo (MC) procedure in the evaluation of expectation values
occurring in fermionic many-body problems. We find that a CL approach is
natural in cases where non-positive definite probability measures occur, and
remains accurate even when the corresponding MC calculation develops a severe
``sign problem''. While the convergence of CL averages cannot be guaranteed in
principle, we show how convergent results can be obtained in three examples
ranging from simple one-dimensional integrals over quantum mechanical models to
a schematic shell model path integral.Comment: 19 pages, 10 PS figures embedded in tex
Consistent thermodynamics for spin echoes
Spin-echo experiments are often said to constitute an instant of
anti-thermodynamic behavior in a concrete physical system that violates the
second law of thermodynamics. We argue that a proper thermodynamic treatment of
the effect should take into account the correlations between the spin and
translational degrees of freedom of the molecules. To this end, we construct an
entropy functional using Boltzmann macrostates that incorporates both spin and
translational degrees of freedom. With this definition there is nothing special
in the thermodynamics of spin echoes: dephasing corresponds to Hamiltonian
evolution and leaves the entropy unchanged; dissipation increases the entropy.
In particular, there is no phase of entropy decrease in the echo. We also
discuss the definition of macrostates from the underlying quantum theory and we
show that the decay of net magnetization provides a faithful measure of entropy
change.Comment: 15 pages, 2 figs. Changed figures, version to appear in PR
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