4,991 research outputs found
Traces on Infinite-Dimensional Brauer Algebras
We describe the central measures for the random walk on graded graphs. Using
this description, we obtain the list of all finite traces on three
infinite-dimensional algebras: on the Brauer algebra, on the partition algebra,
and on the walled Brauer algebra. For the first two algebras, these lists
coincide with the list of all finite traces of the infinite symmetric group.
For the walled Brauer algebra, the list of finite traces coincide with the list
of finite traces of the square of the latter group. We introduce the operation
which corresponds to the graph another graph which called "Pasclization" of the
initial graph and then give the general criteria for coinsidness of the sets of
traces on both graphs.Comment: 9 pages, 20 Re
Limitations on squeezing and formation of the superposition of two macroscopically distinguishable states at fundamental frequency in the process of second harmonic generation
The results of numerical simulations of quantum state evolution in the process of second harmonic generation (SHG) are discussed. It is shown that at a particular moment of time in the fundamental mode initially coherent state turns into a superposition of two macroscopically distinguished states. The question of whether this superposition exhibits quantum interference is analyzed
Exotic solutions in string theory
Solutions of classical string theory, correspondent to the world sheets,
mapped in Minkowsky space with a fold, are considered. Typical processes for
them are creation of strings from vacuum, their recombination and annihilation.
These solutions violate positiveness of square of mass and Regge condition. In
quantum string theory these solutions correspond to physical states |DDF>+|sp>
with non-zero spurious component.Comment: accepted in Il Nuovo Cimento A for publication in 199
Superintegrable systems with spin and second-order integrals of motion
We investigate a quantum nonrelativistic system describing the interaction of
two particles with spin 1/2 and spin 0, respectively. We assume that the
Hamiltonian is rotationally invariant and parity conserving and identify all
such systems which allow additional integrals of motion that are second order
matrix polynomials in the momenta. These integrals are assumed to be scalars,
pseudoscalars, vectors or axial vectors. Among the superintegrable systems
obtained, we mention a generalization of the Coulomb potential with scalar
potential and spin orbital one
.Comment: 32 page
Relativistic Coulomb problem for particles with arbitrary half-integer spin
Using relativistic tensor-bispinorial equations proposed in hep-th/0412213 we
solve the Kepler problem for a charged particle with arbitrary half-integer
spin interacting with the Coulomb potential.Comment: Misprints are correcte
New exactly solvable systems with Fock symmetry
New superintegrable systems are presented which, like the Hydrogen atom,
possess a dynamical symmetry w.r.t. algebra o(4). One of them simulates a
neutral fermion with non-trivial dipole moment, interacting with the external
e.m. field. This system is presented in both non-relativistic and relativistic
formulations. Another recently discovered system (see arXiv:1208.2886v1) is
non-relativistic and includes the minimal and spin-orbit interaction with the
external electric field. It is shown that all the considered systems are shape
invariant. Applying this quality, these systems are integrated using the tools
of SUSY quantum mechanics.Comment: Section 6 and some new references are adde
Phase locking below rate threshold in noisy model neurons
The property of a neuron to phase-lock to an oscillatory stimulus before adapting its spike rate to the stimulus frequency plays an important role for the auditory system. We investigate under which conditions neurons exhibit this phase locking below rate threshold. To this end, we simulate neurons employing the widely used leaky integrate-and-fire (LIF) model. Tuning parameters, we can arrange either an irregular spontaneous or a tonic spiking mode. When the neuron is stimulated in both modes, a significant rise of vector strength prior to a noticeable change of the spike rate can be observed. Combining analytic reasoning with numerical simulations, we trace this observation back to a modulation of interspike intervals, which itself requires spikes to be only loosely coupled. We test the limits of this conception by simulating an LIF model with threshold fatigue, which generates pronounced anticorrelations between subsequent interspike intervals. In addition we evaluate the LIF response for harmonic stimuli of various frequencies and discuss the extension to more complex stimuli. It seems that phase locking below rate threshold occurs generically for all zero mean stimuli. Finally, we discuss our findings in the context of stimulus detection
Hamiltonian Formulation of Two Body Problem in Wheeler-Feynman electrodynamics
A Hamiltonian formulation for the classical problem of electromagnetic
interaction of two charged relativistic particles is found.Comment: 22 pages, 8 Uuencoded Postscript figure
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