2,066 research outputs found
Parametric statistics of zeros of Husimi representations of quantum chaotic eigenstates and random polynomials
Local parametric statistics of zeros of Husimi representations of quantum
eigenstates are introduced. It is conjectured that for a classically fully
chaotic systems one should use the model of parametric statistics of complex
roots of Gaussian random polynomials which is exactly solvable as demonstrated
below. For example, the velocities (derivatives of zeros of Husimi function
with respect to an external parameter) are predicted to obey a universal
(non-Maxwellian) distribution where is the mean square velocity. The
conjecture is demonstrated numerically in a generic chaotic system with two
degrees of freedom. Dynamical formulation of the ``zero-flow'' in terms of an
integrable many-body dynamical system is given as well.Comment: 13 pages in plain Latex (1 figure available upon request
Quasiprobability methods for multimode conditional optical gates
We present a method for computing the action of conditional linear optical
transformations, conditioned on photon counting, for arbitrary signal states.
The method is based on the Q-function, a quasi probability distribution for
anti normally ordered moments. We treat an arbitrary number of signal and
ancilla modes. The ancilla modes are prepared in an arbitrary product number
state. We construct the conditional, non unitary, signal transformations for an
arbitrary photon number count on each of the ancilla modes.Comment: 6 pages, 2 figures. JOSA B Special Issue "Optical Quantum Information
Science
g = 2 as a Gauge Condition
Charged matter spin-1 fields enjoy a nonelectromagnetic gauge symmetry when
interacting with vacuum electromagnetism, provided their gyromagnetic ratio is
2.Comment: 5 pages, REVTeX, submitted to Phys Rev D Brief Report
Simple trace criterion for classification of multilayers
The action of any lossless multilayer is described by a transfer matrix that
can be factorized in terms of three basic matrices. We introduce a simple trace
criterion that classifies multilayers in three classes with properties closely
related with one (and only one) of these three basic matrices.Comment: To be published in Optics Letter
Wedge Local Deformations of Charged Fields leading to Anyonic Commutation Relations
The method of deforming free fields by using multiplication operators on Fock
space, introduced by G. Lechner in [11], is generalized to a charged free field
on two- and three-dimensional Minkowski space. In this case the deformation
function can be chosen in such a way that the deformed fields satisfy
generalized commutation relations, i.e. they behave like Anyons instead of
Bosons. The fields are "polarization free" in the sense that they create only
one-particle states from the vacuum and they are localized in wedges (or "paths
of wedges"), which makes it possible to circumvent a No-Go theorem by J. Mund
[12], stating that there are no free Anyons localized in spacelike cones. The
two-particle scattering matrix, however, can be defined and is different from
unity
Standard-model particles and interactions from field equations on spin 9+1 dimensional space
We consider a Dirac equation set on an extended spin space that contains
fermion and boson solutions. At given dimension, it determines the scalar
symmetries. The standard field equations can be equivalently written in terms
of such degrees of freedom, and are similarly constrained. At 9+1 dimensions,
the SU(3) X SU(2)_L X U(1) gauge groups emerge, as well as solution
representations with quantum numbers of related gauge bosons, leptons, quarks,
Higgs-like particles and others as lepto-quarks. Information on the coupling
constants is also provided; e. g., for the hypercharge g'=(1/2) sqrt(3/5) ~
>.387, at tree level.Comment: 13 pages, Fig. 1(a)-(d
Galilean Lee Model of the Delta Function Potential
The scattering cross section associated with a two dimensional delta function
has recently been the object of considerable study. It is shown here that this
problem can be put into a field theoretical framework by the construction of an
appropriate Galilean covariant theory. The Lee model with a standard Yukawa
interaction is shown to provide such a realization. The usual results for delta
function scattering are then obtained in the case that a stable particle exists
in the scattering channel provided that a certain limit is taken in the
relevant parameter space. In the more general case in which no such limit is
taken finite corrections to the cross section are obtained which (unlike the
pure delta function case) depend on the coupling constant of the model.Comment: 7 pages, latex, no figure
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
Discrete Accidental Symmetry for a Particle in a Constant Magnetic Field on a Torus
A classical particle in a constant magnetic field undergoes cyclotron motion
on a circular orbit. At the quantum level, the fact that all classical orbits
are closed gives rise to degeneracies in the spectrum. It is well-known that
the spectrum of a charged particle in a constant magnetic field consists of
infinitely degenerate Landau levels. Just as for the and
potentials, one thus expects some hidden accidental symmetry, in this case with
infinite-dimensional representations. Indeed, the position of the center of the
cyclotron circle plays the role of a Runge-Lenz vector. After identifying the
corresponding accidental symmetry algebra, we re-analyze the system in a finite
periodic volume. Interestingly, similar to the quantum mechanical breaking of
CP invariance due to the -vacuum angle in non-Abelian gauge theories,
quantum effects due to two self-adjoint extension parameters and
explicitly break the continuous translation invariance of the
classical theory. This reduces the symmetry to a discrete magnetic translation
group and leads to finite degeneracy. Similar to a particle moving on a cone, a
particle in a constant magnetic field shows a very peculiar realization of
accidental symmetry in quantum mechanics.Comment: 25 pages, 2 figure
New methods in conformal partial wave analysis
We report on progress concerning the partial wave analysis of higher
correlation functions in conformal quantum field theory.Comment: 16 page
- …