365 research outputs found
Separation of variables for the classical and quantum Neumann model
The method of separation of variables is shown to apply to both the classical
and quantum Neumann model. In the classical case this nicely yields the
linearization of the flow on the Jacobian of the spectral curve. In the quantum
case the Schr\"odinger equation separates into one--dimensional equations
belonging to the class of generalized Lam\'e differential equations.Comment: 16 page
Derivative corrections to the Born-Infeld action through beta-function calculations in N=2 boundary superspace
We calculate the beta-functions for an open string sigma-model in the
presence of a U(1) background. Passing to N=2 boundary superspace, in which the
background is fully characterized by a scalar potential, significantly
facilitates the calculation. Performing the calculation through three loops
yields the equations of motion up to five derivatives on the fieldstrengths,
which upon integration gives the bosonic sector of the effective action for a
single D-brane in trivial bulk background fields through four derivatives and
to all orders in alpha'. Finally, the present calculation shows that demanding
ultra-violet finiteness of the non-linear sigma-model can be reformulated as
the requirement that the background is a deformed stable holomorphic U(1)
bundle.Comment: 25 pages, numerous figure
Scattering of Noncommutative Waves and Solitons in a Supersymmetric Chiral Model in 2+1 Dimensions
Interactions of noncommutative waves and solitons in 2+1 dimensions can be
analyzed exactly for a supersymmetric and integrable U(n) chiral model
extending the Ward model. Using the Moyal-deformed dressing method in an
antichiral superspace, we construct explicit time-dependent solutions of its
noncommutative field equations by iteratively solving linear equations. The
approach is illustrated by presenting scattering configurations for two
noncommutative U(2) plane waves and for two noncommutative U(2) solitons as
well as by producing a noncommutative U(1) two-soliton bound state.Comment: 1+13 pages; v2: reference added, version published in JHE
Moduli-Space Dynamics of Noncommutative Abelian Sigma-Model Solitons
In the noncommutative (Moyal) plane, we relate exact U(1) sigma-model
solitons to generic scalar-field solitons for an infinitely stiff potential.
The static k-lump moduli space C^k/S_k features a natural K"ahler metric
induced from an embedding Grassmannian. The moduli-space dynamics is blind
against adding a WZW-like term to the sigma-model action and thus also applies
to the integrable U(1) Ward model. For the latter's two-soliton motion we
compare the exact field configurations with their supposed moduli-space
approximations. Surprisingly, the two do not match, which questions the
adiabatic method for noncommutative solitons.Comment: 1+15 pages, 2 figures; v2: reference added, to appear in JHE
Lax pair and Darboux transformation of noncommutative U(N) principal chiral model
We present a noncommutative generalization of Lax formalism of U(N) principal
chiral model in terms of a one-parameter family of flat connections. The Lax
formalism is further used to derive a set of parametric noncommutative
B\"{a}cklund transformation and an infinite set of conserved quantities. From
the Lax pair, we derive a noncommutative version of the Darboux transformation
of the model.Comment: 1+20 page
Observing Brownian motion in vibration-fluidized granular matter
At the beginning of last century, Gerlach and Lehrer observed the rotational
Brownian motion of a very fine wire immersed in an equilibrium environment, a
gas. This simple experiment eventually permitted the full development of one of
the most important ideas of equilibrium statistical mechanics: the very
complicated many-particle problem of a large number of molecules colliding with
the wire, can be represented by two macroscopic parameters only, namely
viscosity and the temperature. Can this idea, mathematically developed in the
so-called Langevin model and the fluctuation-dissipation theorem be used to
describe systems that are far from equilibrium? Here we address the question
and reproduce the Gerlach and Lehrer experiment in an archetype non-equilibrium
system, by immersing a sensitive torsion oscillator in a granular system of
millimetre-size grains, fluidized by strong external vibrations. The
vibro-fluidized granular medium is a driven environment, with continuous
injection and dissipation of energy, and the immersed oscillator can be seen as
analogous to an elastically bound Brownian particle. We show, by measuring the
noise and the susceptibility, that the experiment can be treated, in first
approximation, with the same formalism as in the equilibrium case, giving
experimental access to a ''granular viscosity'' and an ''effective
temperature'', however anisotropic and inhomogeneous, and yielding the
surprising result that the vibro-fluidized granular matter behaves as a
''thermal'' bath satisfying a fluctuation-dissipation relation
Instantons and Yang-Mills Flows on Coset Spaces
We consider the Yang-Mills flow equations on a reductive coset space G/H and
the Yang-Mills equations on the manifold R x G/H. On nonsymmetric coset spaces
G/H one can introduce geometric fluxes identified with the torsion of the spin
connection. The condition of G-equivariance imposed on the gauge fields reduces
the Yang-Mills equations to phi^4-kink equations on R. Depending on the
boundary conditions and torsion, we obtain solutions to the Yang-Mills
equations describing instantons, chains of instanton-anti-instanton pairs or
modifications of gauge bundles. For Lorentzian signature on R x G/H, dyon-type
configurations are constructed as well. We also present explicit solutions to
the Yang-Mills flow equations and compare them with the Yang-Mills solutions on
R x G/H.Comment: 1+12 page
Diffusion over a saddle with a Langevin equation
The diffusion problem over a saddle is studied using a multi-dimensional
Langevin equation. An analytical solution is derived for a quadratic potential
and the probability to pass over the barrier deduced. A very simple solution is
given for the one dimension problem and a general scheme is shown for higher
dimensions.Comment: 13 pages, use revTeX, to appear in Phys. Rev. E6
Chern-Simons Solitons, Chiral Model, and (affine) Toda Model on Noncommutative Space
We consider the Dunne-Jackiw-Pi-Trugenberger model of a U(N) Chern-Simons
gauge theory coupled to a nonrelativistic complex adjoint matter on
noncommutative space. Soliton configurations of this model are related the
solutions of the chiral model on noncommutative plane. A generalized
Uhlenbeck's uniton method for the chiral model on noncommutative space provides
explicit Chern-Simons solitons. Fundamental solitons in the U(1) gauge theory
are shaped as rings of charge `n' and spin `n' where the Chern-Simons level `n'
should be an integer upon quantization. Toda and Liouville models are
generalized to noncommutative plane and the solutions are provided by the
uniton method. We also define affine Toda and sine-Gordon models on
noncommutative plane. Finally the first order moduli space dynamics of
Chern-Simons solitons is shown to be trivial.Comment: latex, JHEP style, 23 pages, no figur
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