426 research outputs found
Enhanced quantization on the circle
We apply the quantization scheme introduced in [arXiv:1204.2870] to a
particle on a circle. We find that the quantum action functional restricted to
appropriate coherent states can be expressed as the classical action plus
-corrections. This result extends the examples presented in the cited
paper.Comment: 7 page
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
Extended coherent states and modified perturbation theory
An extended coherent state for describing a system of two interacting quanum
objects is considered. A modified perturbation theory based on using the
extended coherent states is formulated.Comment: LaTex, 7 pages, no figures, minor correction
Coherent states for a particle on a sphere
The coherent states for a particle on a sphere are introduced. These states
are labelled by points of the classical phase space, that is the position on
the sphere and the angular momentum of a particle. As with the coherent states
for a particle on a circle discussed in Kowalski K {\em et al} 1996 {\em J.
Phys. A} {\bf 29} 4149, we deal with a deformation of the classical phase space
related with quantum fluctuations. The expectation values of the position and
the angular momentum in the coherent states are regarded as the best possible
approximation of the classical phase space. The correctness of the introduced
coherent states is illustrated by an example of the rotator.Comment: LaTeX, 16 pages, 2 figure
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
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.
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
Simulating nonequilibrium quantum fields with stochastic quantization techniques
We present lattice simulations of nonequilibrium quantum fields in
Minkowskian space-time. Starting from a non-thermal initial state, the
real-time quantum ensemble in 3+1 dimensions is constructed by a stochastic
process in an additional (5th) ``Langevin-time''. For the example of a
self-interacting scalar field we show how to resolve apparent unstable Langevin
dynamics, and compare our quantum results with those obtained in classical
field theory. Such a direct simulation method is crucial for our understanding
of collision experiments of heavy nuclei or other nonequilibrium phenomena in
strongly coupled quantum many-body systems.Comment: 4 pages, 4 figures, PRL version, minor change
Lattice simulations of real-time quantum fields
We investigate lattice simulations of scalar and nonabelian gauge fields in
Minkowski space-time. For SU(2) gauge-theory expectation values of link
variables in 3+1 dimensions are constructed by a stochastic process in an
additional (5th) ``Langevin-time''. A sufficiently small Langevin step size and
the use of a tilted real-time contour leads to converging results in general.
All fixed point solutions are shown to fulfil the infinite hierarchy of
Dyson-Schwinger identities, however, they are not unique without further
constraints. For the nonabelian gauge theory the thermal equilibrium fixed
point is only approached at intermediate Langevin-times. It becomes more stable
if the complex time path is deformed towards Euclidean space-time. We analyze
this behavior further using the real-time evolution of a quantum anharmonic
oscillator, which is alternatively solved by diagonalizing its Hamiltonian.
Without further optimization stochastic quantization can give accurate
descriptions if the real-time extend of the lattice is small on the scale of
the inverse temperature.Comment: 36 pages, 15 figures, Late
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
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