2,459 research outputs found
A direct proof of Kim's identities
As a by-product of a finite-size Bethe Ansatz calculation in statistical
mechanics, Doochul Kim has established, by an indirect route, three
mathematical identities rather similar to the conjugate modulus relations
satisfied by the elliptic theta constants. However, they contain factors like
and , instead of . We show here that
there is a fourth relation that naturally completes the set, in much the same
way that there are four relations for the four elliptic theta functions. We
derive all of them directly by proving and using a specialization of
Weierstrass' factorization theorem in complex variable theory.Comment: Latex, 6 pages, accepted by J. Physics
Sub-Kolmogorov-Scale Fluctuations in Fluid Turbulence
We relate the intermittent fluctuations of velocity gradients in turbulence
to a whole range of local dissipation scales generalizing the picture of a
single mean dissipation length. The statistical distribution of these local
dissipation scales as a function of Reynolds number is determined in numerical
simulations of forced homogeneous isotropic turbulence with a spectral
resolution never applied before which exceeds the standard one by at least a
factor of eight. The core of the scale distribution agrees well with a
theoretical prediction. Increasing Reynolds number causes the generation of
ever finer local dissipation scales. This is in line with a less steep decay of
the large-wavenumber energy spectra in the dissipation range. The energy
spectrum for the highest accessible Taylor microscale Reynolds number
R_lambda=107 does not show a bottleneck.Comment: 8 pages, 5 figures (Figs. 1 and 3 in reduced quality
The Exotic Statistics of Leapfrogging Smoke Rings
The leapfrogging motion of smoke rings is a three dimensional version of the
motion that in two dimensions leads to exotic exchange statistics. The
statistical phase factor can be computed using the hydrodynamical Euler
equation, which is a universal law for describing the properties of a large
class of fluids. This suggests that three dimensional exotic exchange
statistics is a common property of closed vortex loops in a variety of quantum
liquids and gases, from helium superfluids to Bose-Einstein condensed alkali
gases, metallic hydrogen in its liquid phases and maybe even nuclear matter in
extreme conditions.Comment: 9 pages 1 figur
Linear and multiplicative 2-forms
We study the relationship between multiplicative 2-forms on Lie groupoids and
linear 2-forms on Lie algebroids, which leads to a new approach to the
infinitesimal description of multiplicative 2-forms and to the integration of
twisted Dirac manifolds.Comment: to appear in Letters in Mathematical Physic
Potential for a new muon g-2 experiment
A new experiment to measure the muon g-2 factor is proposed. We suppose the
sensitivity of this experiment to be about 0.03 ppm. The developed experiment
can be performed on an ordinary storage ring with a noncontinuous field created
by usual magnets. When the total length of straight sections of the ring is
appropriate, the spin rotation frequency becomes almost independent of the
particle momentum. In this case, a high-precision measurement of an average
magnetic field can be carried out with polarized proton beams. A muon beam
energy can be arbitrary. Possibilities to avoid a betatron resonance are
analyzed and corrections to the g-2 frequency are considered.Comment: 5 pages, 1 figur
Exact Solutions of a Model for Granular Avalanches
We present exact solutions of the non-linear {\sc bcre} model for granular
avalanches without diffusion. We assume a generic sandpile profile consisting
of two regions of constant but different slope. Our solution is constructed in
terms of characteristic curves from which several novel predictions for
experiments on avalanches are deduced: Analytical results are given for the
shock condition, shock coordinates, universal quantities at the shock, slope
relaxation at large times, velocities of the active region and of the sandpile
profile.Comment: 7 pages, 2 figure
Electromagnetic Oscillations in a Driven Nonlinear Resonator: A New Description of Complex Nonlinear Dynamics
Many intriguing properties of driven nonlinear resonators, including the
appearance of chaos, are very important for understanding the universal
features of nonlinear dynamical systems and can have great practical
significance. We consider a cylindrical cavity resonator driven by an
alternating voltage and filled with a nonlinear nondispersive medium. It is
assumed that the medium lacks a center of inversion and the dependence of the
electric displacement on the electric field can be approximated by an
exponential function. We show that the Maxwell equations are integrated exactly
in this case and the field components in the cavity are represented in terms of
implicit functions of special form. The driven electromagnetic oscillations in
the cavity are found to display very interesting temporal behavior and their
Fourier spectra contain singular continuous components. To the best of our
knowledge, this is the first demonstration of the existence of a singular
continuous (fractal) spectrum in an exactly integrable system.Comment: 5 pages, 3 figure
Fredholm's Minors of Arbitrary Order: Their Representations as a Determinant of Resolvents and in Terms of Free Fermions and an Explicit Formula for Their Functional Derivative
We study the Fredholm minors associated with a Fredholm equation of the
second type. We present a couple of new linear recursion relations involving
the th and th minors, whose solution is a representation of the th
minor as an determinant of resolvents. The latter is given a simple
interpretation in terms of a path integral over non-interacting fermions. We
also provide an explicit formula for the functional derivative of a Fredholm
minor of order with respect to the kernel. Our formula is a linear
combination of the th and the th minors.Comment: 17 pages, Latex, no figures connection to supplementary compound
matrices mentioned, references added, typos correcte
On the Green-Functions of the classical offshell electrodynamics under the manifestly covariant relativistic dynamics of Stueckelberg
In previous paper derivations of the Green function have been given for 5D
off-shell electrodynamics in the framework of the manifestly covariant
relativistic dynamics of Stueckelberg (with invariant evolution parameter
). In this paper, we reconcile these derivations resulting in different
explicit forms, and relate our results to the conventional fundamental
solutions of linear 5D wave equations published in the mathematical literature.
We give physical arguments for the choice of the Green function retarded in the
fifth variable .Comment: 16 pages, 1 figur
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