884 research outputs found
Long time stability of small amplitude Breathers in a mixed FPU-KG model
In the limit of small couplings in the nearest neighbor interaction, and
small total energy, we apply the resonant normal form result of a previous
paper of ours to a finite but arbitrarily large mixed Fermi-Pasta-Ulam
Klein-Gordon chain, i.e. with both linear and nonlinear terms in both the
on-site and interaction potential, with periodic boundary conditions. An
existence and orbital stability result for Breathers of such a normal form,
which turns out to be a generalized discrete Nonlinear Schr\"odinger model with
exponentially decaying all neighbor interactions, is first proved. Exploiting
such a result as an intermediate step, a long time stability theorem for the
true Breathers of the KG and FPU-KG models, in the anti-continuous limit, is
proven.Comment: Substantial revision in the presentation. Stability time scale
slightly modifie
Covariant quantization of N=1/2 SYM theories and supergauge invariance
So far, quantum properties of N=1/2 nonanticommutative (NAC) super
Yang--Mills theories have been investigated in the WZ gauge. The gauge
independence of the results requires assuming that at the quantum level
supergauge invariance is not broken by nonanticommutative geometry. In this
paper we use an alternative approach which allows studying these theories in a
manifestly gauge independent superspace setup. This is accomplished by
generalizing the background field method to the NAC case, by moving to a
momentum superspace where star products are treated as exponential factors and
by developing momentum supergraph techniques. We compute the one--loop gauge
effective action for NAC U(N) gauge theories with matter in the adjoint
representation. Despite the appearance of divergent contributions which break
(super)gauge invariance, we prove that the effective action at this order is
indeed invariant.Comment: 24 pages, 3 figures, some references adde
The nonminimal scalar multiplet coupled to supersymmetric Yang-Mills
We consider the coupling of nonminimal scalar multiplets to supersymmetric
Yang-Mills in four dimensions and compute the one-loop contribution to the
low-energy effective action in the abelian sector. We show that the resulting
theory realizes the dual version of the corresponding one from N=2
supersymmetric Yang-Mills.Comment: 10 pages, Latex, no figure
An extensive adiabatic invariant for the Klein-Gordon model in the thermodynamic limit
We construct an extensive adiabatic invariant for a Klein-Gordon chain in the
thermodynamic limit. In particular, given a fixed and sufficiently small value
of the coupling constant , the evolution of the adiabatic invariant is
controlled up to times scaling as for any large enough
value of the inverse temperature . The time scale becomes a stretched
exponential if the coupling constant is allowed to vanish jointly with the
specific energy. The adiabatic invariance is exhibited by showing that the
variance along the dynamics, i.e. calculated with respect to time averages, is
much smaller than the corresponding variance over the whole phase space, i.e.
calculated with the Gibbs measure, for a set of initial data of large measure.
All the perturbative constructions and the subsequent estimates are consistent
with the extensive nature of the system.Comment: 60 pages. Minor corrections with respect to the first version. To
appear in Annales Henri Poincar\'
Approximation of small-amplitude weakly coupled oscillators with discrete nonlinear Schrodinger equations
Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are
approximated by equations of the discrete nonlinear Schrodinger type. We show
how to justify this approximation by two methods, which have been very popular
in the recent literature. The first method relies on a priori energy estimates
and multi-scale decompositions. The second method is based on a resonant normal
form theorem. We show that although the two methods are different in the
implementation, they produce equivalent results as the end product. We also
discuss applications of the discrete nonlinear Schrodinger equation in the
context of existence and stability of breathers of the Klein--Gordon lattice
Exact anomalous dimensions of {\cal N}=4 Yang-Mills operators with large R charge
In a {\cal N}=1 superspace formulation of {\cal N}=4 Yang-Mills theory we
obtain the anomalous dimensions of chiral operators with large R charge J \to
\infty keeping g^2 N/J^2 finite, to all orders of perturbation theory in the
planar limit. Our result proves the conjecture that the anomalous dimensions
are indeed finite in the above limit. This amounts to an exact check of the
proposed duality between a sector of {\cal N}=4 Yang-Mills theory with large R
charge J and string theory in a pp-wave background.Comment: 6 pages, LaTex; v2: minor change
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