76 research outputs found
Multivariate hypergeometric functions as tau functions of Toda lattice and Kadomtsev-Petviashvili equation
We present the q-deformed multivariate hypergeometric functions related to
Schur polynomials as tau-functions of the KP and of the two-dimensional Toda
lattice hierarchies. The variables of the hypergeometric functions are the
higher times of those hierarchies. The discrete Toda lattice variable shifts
parameters of hypergeometric functions. The role of additional symmetries in
generating hypergeometric tau-functions is explained
Dynamics of molecular motors in reversible burnt-bridge models
Dynamic properties of molecular motors whose motion is powered by interactions with specific lattice bonds are studied theoretically with the help of discrete-state stochastic "burnt-bridge" models. Molecular motors are depicted as random walkers that can destroy or rebuild periodically distributed weak connections ("bridges") when crossing them, with probabilities p1 and p2 correspondingly. Dynamic properties, such as velocities and dispersions, are obtained in exact and explicit form for arbitrary values of parameters p1 and p2. For the unbiased random walker, reversible burning of the bridges results in a biased directed motion with a dynamic transition observed at very small concentrations of bridges. In the case of backward biased molecular motor its backward velocity is reduced and a reversal of the direction of motion is observed for some range of parameters. It is also found that the dispersion demonstrates a complex, non-monotonic behavior with large fluctuations for some set of parameters. Complex dynamics of the system is discussed by analyzing the behavior of the molecular motors near burned bridges
Two electrons in an external oscillator potential: hidden algebraic structure
It is shown that the Coulomb correlation problem for a system of two
electrons (two charged particles) in an external oscillator potential possesses
a hidden -algebraic structure being one of recently-discovered
quasi-exactly-solvable problems. The origin of existing exact solutions to this
problem, recently discovered by several authors, is explained. A degeneracy of
energies in electron-electron and electron-positron correlation problems is
found. It manifests the first appearence of hidden -algebraic structure
in atomic physics.Comment: 7 pages (plus one figure avaliable via direct request), LaTeX,
Preprint IFUNAM FT 94-4
Derivation of Index Theorems by Localization of Path Integrals
We review the derivation of the Atiyah-Singer and Callias index theorems
using the recently developed localization method to calculate exactly the
relevant supersymmetric path integrals. (Talk given at the III International
Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta,
Ukraine, June 13-24, 1993)Comment: 11 pages in LaTeX, HU-TFT-93-3
An hbar-expansion of the Toda hierarchy: a recursive construction of solutions
A construction of general solutions of the \hbar-dependent Toda hierarchy is
presented. The construction is based on a Riemann-Hilbert problem for the pairs
(L,M) and (\bar L,\bar M) of Lax and Orlov-Schulman operators. This
Riemann-Hilbert problem is translated to the language of the dressing operators
W and \bar W. The dressing operators are set in an exponential form as W =
e^{X/\hbar} and \bar W = e^{\phi/\hbar}e^{\bar X/\hbar}, and the auxiliary
operators X,\bar X and the function \phi are assumed to have \hbar-expansions X
= X_0 + \hbar X_1 + ..., \bar X = \bar X_0 + \hbar\bar X_1 + ... and \phi =
\phi_0 + \hbar\phi_1 + .... The coefficients of these expansions turn out to
satisfy a set of recursion relations. X,\bar X and \phi are recursively
determined by these relations. Moreover, the associated wave functions are
shown to have the WKB form \Psi = e^{S/\hbar} and \bar\Psi = e^{\bar S/\hbar},
which leads to an \hbar-expansion of the logarithm of the tau function.Comment: 37 pages, no figures. arXiv admin note: substantial text overlap with
arXiv:0912.486
Towards a correct description of zooplankton feeding in models: Taking into account food-mediated unsynchronized vertical migration
On the CP-odd Nucleon Potential
The CP-odd nucleon potential for different models of CP violation in the one
meson exchange approximation is studied. It is shown that the main contribution
is due to the -meson exchange which leads to a simple one parameter CP-odd
nucleon potential.Comment: 12 pages, RevTex, UM-P-92/114, OZ-92/3
Quantum Mechanics of the Vacuum State in Two-Dimensional QCD with Adjoint Fermions
A study of two-dimensional QCD on a spatial circle with Majorana fermions in
the adjoint representation of the gauge groups SU(2) and SU(3) has been
performed. The main emphasis is put on the symmetry properties related to the
homotopically non-trivial gauge transformations and the discrete axial symmetry
of this model. Within a gauge fixed canonical framework, the delicate interplay
of topology on the one hand and Jacobians and boundary conditions arising in
the course of resolving Gauss's law on the other hand is exhibited. As a
result, a consistent description of the residual gauge symmetry (for
SU(N)) and the ``axial anomaly" emerges. For illustrative purposes, the vacuum
of the model is determined analytically in the limit of a small circle. There,
the Born-Oppenheimer approximation is justified and reduces the vacuum problem
to simple quantum mechanics. The issue of fermion condensates is addressed and
residual discrepancies with other approaches are pointed out.Comment: 44 pages; for hardcopies of figures, contact
[email protected]
Measurement of and between 3.12 and 3.72 GeV at the KEDR detector
Using the KEDR detector at the VEPP-4M collider, we have measured
the values of and at seven points of the center-of-mass
energy between 3.12 and 3.72 GeV. The total achieved accuracy is about or
better than at most of energy points with a systematic uncertainty of
about . At the moment it is the most accurate measurement of in
this energy range
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