294 research outputs found
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
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
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
Hydrodynamic modes in a trapped Bose gas above the Bose-Einstein transition
We discuss the collective modes of a trapped Bose gas in the hydrodynamic
regime where atomic collisions ensure local thermal equilibrium for the
distribution function. Starting from the conservation laws, in the linearized
limit we derive a closed equation for the velocity fluctuations in a trapped
Bose gas above the Bose-Einstein transition temperature. Explicit solutions for
a parabolic trap are given. We find that the surface modes have the same
dispersion relation as the one recently obtained by Stringari for the
oscillations of the condensate at within the Thomas-Fermi approximation.
Results are also given for the monopole ``breathing'' mode as well as for the
excitations which result from the coupling of the monopole and quadrupole
modes in an anisotropic parabolic well.Comment: 4 pages, no figure, submitted to Phys. Rev. Let
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
Instantons and Killing spinors
We investigate instantons on manifolds with Killing spinors and their cones.
Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds,
nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and
3-Sasakian manifolds. We construct a connection on the tangent bundle over
these manifolds which solves the instanton equation, and also show that the
instanton equation implies the Yang-Mills equation, despite the presence of
torsion. We then construct instantons on the cones over these manifolds, and
lift them to solutions of heterotic supergravity. Amongst our solutions are new
instantons on even-dimensional Euclidean spaces, as well as the well-known
BPST, quaternionic and octonionic instantons.Comment: 40 pages, 2 figures v2: author email addresses and affiliations adde
Towards Rigorous Derivation of Quantum Kinetic Equations
We develop a rigorous formalism for the description of the evolution of
states of quantum many-particle systems in terms of a one-particle density
operator. For initial states which are specified in terms of a one-particle
density operator the equivalence of the description of the evolution of quantum
many-particle states by the Cauchy problem of the quantum BBGKY hierarchy and
by the Cauchy problem of the generalized quantum kinetic equation together with
a sequence of explicitly defined functionals of a solution of stated kinetic
equation is established in the space of trace class operators. The links of the
specific quantum kinetic equations with the generalized quantum kinetic
equation are discussed.Comment: 25 page
Yang-Mills instantons and dyons on homogeneous G_2-manifolds
We consider Lie G-valued Yang-Mills fields on the space R x G/H, where G/H is
a compact nearly K"ahler six-dimensional homogeneous space, and the manifold R
x G/H carries a G_2-structure. After imposing a general G-invariance condition,
Yang-Mills theory with torsion on R x G/H is reduced to Newtonian mechanics of
a particle moving in R^6, R^4 or R^2 under the influence of an inverted
double-well-type potential for the cases G/H = SU(3)/U(1)xU(1),
Sp(2)/Sp(1)xU(1) or G_2/SU(3), respectively. We analyze all critical points and
present analytical and numerical kink- and bounce-type solutions, which yield
G-invariant instanton configurations on those cosets. Periodic solutions on S^1
x G/H and dyons on iR x G/H are also given.Comment: 1+26 pages, 14 figures, 6 miniplot
Collective oscillations of a classical gas confined in harmonic traps
Starting from the Boltzmann equation we calculate the frequency and the
damping of the monopole and quadrupole oscillations of a classical gas confined
in an harmonic potential. The collisional term is treated in the relaxation
time approximation and a gaussian ansatz is used for its evaluation. Our
approach provides an explicit description of the transition between the
hydrodynamic and collisionless regimes in both spherical and deformed traps.
The predictions are compared with the results of a numerical simulation.Comment: 6 pages, revtex, 2 figures include
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