310 research outputs found
On calculating the mean values of quantum observables in the optical tomography representation
Given a density operator the optical tomography map defines a
one-parameter set of probability distributions on the real line allowing to reconstruct . We
introduce a dual map from the special class of quantum observables
to a special class of generalized functions such that the
mean value is given by the formula
. The class
includes all the symmetrized polynomials of canonical variables
and .Comment: 8 page
How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?
The chemical Fokker-Planck equation and the corresponding chemical Langevin
equation are commonly used approximations of the chemical master equation.
These equations are derived from an uncontrolled, second-order truncation of
the Kramers-Moyal expansion of the chemical master equation and hence their
accuracy remains to be clarified. We use the system-size expansion to show that
chemical Fokker-Planck estimates of the mean concentrations and of the variance
of the concentration fluctuations about the mean are accurate to order
for reaction systems which do not obey detailed balance and at
least accurate to order for systems obeying detailed balance,
where is the characteristic size of the system. Hence the chemical
Fokker-Planck equation turns out to be more accurate than the linear-noise
approximation of the chemical master equation (the linear Fokker-Planck
equation) which leads to mean concentration estimates accurate to order
and variance estimates accurate to order . This
higher accuracy is particularly conspicuous for chemical systems realized in
small volumes such as biochemical reactions inside cells. A formula is also
obtained for the approximate size of the relative errors in the concentration
and variance predictions of the chemical Fokker-Planck equation, where the
relative error is defined as the difference between the predictions of the
chemical Fokker-Planck equation and the master equation divided by the
prediction of the master equation. For dimerization and enzyme-catalyzed
reactions, the errors are typically less than few percent even when the
steady-state is characterized by merely few tens of molecules.Comment: 39 pages, 3 figures, accepted for publication in J. Chem. Phy
Phenomenology of Noncommutative Field Theories
Experimental limits on the violation of four-dimensional Lorentz invariance
imply that noncommutativity among ordinary spacetime dimensions must be small.
In this talk, I review the most stringent bounds on noncommutative field
theories and suggest a possible means of evading them: noncommutativity may be
restricted to extra, compactified spatial dimensions. Such theories have a
number of interesting features, including Abelian gauge fields whose
Kaluza-Klein excitations have self couplings. We consider six-dimensional QED
in a noncommutative bulk, and discuss the collider signatures of the model.Comment: 7 pages RevTeX, 4 eps figures, Invited plenary talk, IX Mexican
Workshop on Particles and Fields, November 17-22, 2003, Universidad de
Colima, Mexic
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.
On the concepts of radial and angular kinetic energies
We consider a general central-field system in D dimensions and show that the
division of the kinetic energy into radial and angular parts proceeds
differently in the wavefunction picture and the Weyl-Wigner phase-space
picture. Thus, the radial and angular kinetic energies are different quantities
in the two pictures, containing different physical information, but the
relation between them is well defined. We discuss this relation and illustrate
its nature by examples referring to a free particle and to a ground-state
hydrogen atom.Comment: 10 pages, 2 figures, accepted by Phys. Rev.
Probability Distributions and Hilbert Spaces: Quantum and Classical Systems
We use the fact that some linear Hamiltonian systems can be considered as
``finite level'' quantum systems, and the description of quantum mechanics in
terms of probabilities, to associate probability distributions with this
particular class of linear Hamiltonian systems.Comment: LATEX,13pages,accepted by Physica Scripta (1999
Coherent States and N Dimensional Coordinate Noncommutativity
Considering coordinates as operators whose measured values are expectations
between generalized coherent states based on the group SO(N,1) leads to
coordinate noncommutativity together with full dimensional rotation
invariance. Through the introduction of a gauge potential this theory can
additionally be made invariant under dimensional translations. Fluctuations
in coordinate measurements are determined by two scales. For small distances
these fluctuations are fixed at the noncommutativity parameter while for larger
distances they are proportional to the distance itself divided by a {\em very}
large number. Limits on this number will lbe available from LIGO measurements.Comment: 16 pqges. LaTeX with JHEP.cl
Quantum theory of successive projective measurements
We show that a quantum state may be represented as the sum of a joint
probability and a complex quantum modification term. The joint probability and
the modification term can both be observed in successive projective
measurements. The complex modification term is a measure of measurement
disturbance. A selective phase rotation is needed to obtain the imaginary part.
This leads to a complex quasiprobability, the Kirkwood distribution. We show
that the Kirkwood distribution contains full information about the state if the
two observables are maximal and complementary. The Kirkwood distribution gives
a new picture of state reduction. In a nonselective measurement, the
modification term vanishes. A selective measurement leads to a quantum state as
a nonnegative conditional probability. We demonstrate the special significance
of the Schwinger basis.Comment: 6 page
Feynman Path Integral on the Noncommutative Plane
We formulate Feynman path integral on a non commutative plane using coherent
states. The propagator for a free particle exhibits UV cut-off induced by the
parameter of non commutativity.Comment: 7pages, latex 2e, no figures. Accepted for publication on J.Phys.
Diagonalization of multicomponent wave equations with a Born-Oppenheimer example
A general method to decouple multicomponent linear wave equations is presented. First, the Weyl calculus is used to transform operator relations into relations between c-number valued matrices. Then it is shown that the symbol representing the wave operator can be diagonalized systematically up to arbitrary order in an appropriate expansion parameter. After transforming the symbols back to operators, the original problem is reduced to solving a set of linear uncoupled scalar wave equations. The procedure is exemplified for a particle with a Born-Oppenheimer-type Hamiltonian valid through second order in h. The resulting effective scalar Hamiltonians are seen to contain an additional velocity-dependent potential. This contribution has not been reported in recent studies investigating the adiabatic motion of a neutral particle moving in an inhomogeneous magnetic field. Finally, the relation of the general method to standard quantum-mechanical perturbation theory is discussed
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