3,588 research outputs found
On the classification of discrete Hirota-type equations in 3D
In the series of recent publications we have proposed a novel approach to the
classification of integrable differential/difference equations in 3D based on
the requirement that hydrodynamic reductions of the corresponding
dispersionless limits are `inherited' by the dispersive equations. In this
paper we extend this to the fully discrete case. Our only constraint is that
the initial ansatz possesses a non-degenerate dispersionless limit (this is the
case for all known Hirota-type equations). Based on the method of deformations
of hydrodynamic reductions, we classify discrete 3D integrable Hirota-type
equations within various particularly interesting subclasses. Our method can be
viewed as an alternative to the conventional multi-dimensional consistency
approach.Comment: 29 page
Transport of the repulsive Bose-Einstein condensate in a double-well trap: interaction impact and relation to Josephson effect
Two aspects of the transport of the repulsive Bose-Einstein condensate (BEC)
in a double-well trap are inspected: impact of the interatomic interaction and
analogy to the Josephson effect. The analysis employs a numerical solution of
3D time-dependent Gross-Pitaevskii equation for a total order parameter
covering all the trap. The population transfer is driven by a time-dependent
shift of a barrier separating the left and right wells. Sharp and soft profiles
of the barrier velocity are tested. Evolution of the relevant characteristics,
involving phase differences and currents, is inspected. It is shown that the
repulsive interaction substantially supports the transfer making it possible i)
in a wide velocity interval and ii) three orders of magnitude faster than in
the ideal BEC. The transport can be approximately treated as the d.c. Josephson
effect. A dual origin of the critical barrier velocity (break of adiabatic
following and d.c.-a.c. transition) is discussed. Following the calculations,
robustness of the transport (d.c.) crucially depends on the interaction and
barrier velocity profile. Only soft profiles which minimize undesirable dipole
oscillations are acceptable.Comment: 10 pages, 8 figures, accepted by Laser Physis. arXiv admin note: text
overlap with arXiv:1312.2750 The replaced version has a few corrections and
additional reference
Once more on extra quark-lepton generations and precision measurements
Precision measurements of -boson parameters and -boson and -quark
masses put strong constraints on non singlet New Physics. We
demonstrate that one extra generation passes electroweak constraints even when
all new particle masses are well above their direct mass bounds.Comment: Dedicated to L.B. Okun's 80th birthda
On the classification of scalar evolutionary integrable equations in dimensions
We consider evolutionary equations of the form where
is the nonlocality, and the right hand side is polynomial
in the derivatives of and . The recent paper \cite{FMN} provides a
complete list of integrable third order equations of this kind. Here we extend
the classification to fifth order equations. Besides the known examples of
Kadomtsev-Petviashvili (KP), Veselov-Novikov (VN) and Harry Dym (HD) equations,
as well as fifth order analogues and modifications thereof, our list contains a
number of equations which are apparently new. We conjecture that our examples
exhaust the list of scalar polynomial integrable equations with the nonlocality
. The classification procedure consists of two steps. First, we classify
quasilinear systems which may (potentially) occur as dispersionless limits of
integrable scalar evolutionary equations. After that we reconstruct dispersive
terms based on the requirement of the inheritance of hydrodynamic reductions of
the dispersionless limit by the full dispersive equation
Anomalous scaling in two and three dimensions for a passive vector field advected by a turbulent flow
A model of the passive vector field advected by the uncorrelated in time
Gaussian velocity with power-like covariance is studied by means of the
renormalization group and the operator product expansion. The structure
functions of the admixture demonstrate essential power-like dependence on the
external scale in the inertial range (the case of an anomalous scaling). The
method of finding of independent tensor invariants in the cases of two and
three dimensions is proposed to eliminate linear dependencies between the
operators entering into the operator product expansions of the structure
functions. The constructed operator bases, which include the powers of the
dissipation operator and the enstrophy operator, provide the possibility to
calculate the exponents of the anomalous scaling.Comment: 9 pages, LaTeX2e(iopart.sty), submitted to J. Phys. A: Math. Ge
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