10,624 research outputs found
Baxter's Q-operator for the homogeneous XXX spin chain
Applying the Pasquier-Gaudin procedure we construct the Baxter's Q-operator
for the homogeneous XXX model as integral operator in standard representation
of SL(2). The connection between Q-operator and local Hamiltonians is
discussed. It is shown that operator of Lipatov's duality symmetry arises
naturally as leading term of the asymptotic expansion of Q-operator for large
values of spectral parameter.Comment: 23 pages, Late
Spectral properties of fractional Fokker-Plank operator for the L\'evy flight in a harmonic potential
We present a detailed analysis of the eigenfunctions of the Fokker-Planck
operator for the L\'evy-Ornstein-Uhlenbeck process, their asymptotic behavior
and recurrence relations, explicit expressions in coordinate space for the
special cases of the Ornstein-Uhlenbeck process with Gaussian and with Cauchy
white noise and for the transformation kernel, which maps the fractional
Fokker-Planck operator of the Cauchy-Ornstein-Uhlenbeck process to the
non-fractional Fokker-Planck operator of the usual Gaussian Ornstein-Uhlenbeck
process. We also describe how non-spectral relaxation can be observed in
bounded random variables of the L\'evy-Ornstein-Uhlenbeck process and their
correlation functions.Comment: 10 pages, 5 figures, submitted to Euro. Phys. J.
Spectral decomposition for the Dirac system associated to the DSII equation
A new (scalar) spectral decomposition is found for the Dirac system in two
dimensions associated to the focusing Davey--Stewartson II (DSII) equation.
Discrete spectrum in the spectral problem corresponds to eigenvalues embedded
into a two-dimensional essential spectrum. We show that these embedded
eigenvalues are structurally unstable under small variations of the initial
data. This instability leads to the decay of localized initial data into
continuous wave packets prescribed by the nonlinear dynamics of the DSII
equation
Lifshitz holography: The whole shebang
We provide a general algorithm for constructing the holographic dictionary
for any asymptotically locally Lifshitz background, with or without
hyperscaling violation, and for any values of the dynamical exponents and
, as well as the vector hyperscaling violating exponent, that are
compatible with the null energy condition. The analysis is carried out for a
very general bottom up model of gravity coupled to a massive vector field and a
dilaton with arbitrary scalar couplings. The solution of the radial
Hamilton-Jacobi equation is obtained recursively in the form of a graded
expansion in eigenfunctions of two commuting operators, which are the
appropriate generalization of the dilatation operator for non scale invariant
and Lorentz violating boundary conditions. The Fefferman-Graham expansions, the
sources and 1-point functions of the dual operators, the Ward identities, as
well as the local counterterms required for holographic renormalization all
follow from this asymptotic solution of the radial Hamilton-Jacobi equation. We
also find a family of exact backgrounds with and corresponding
to a marginal deformation shifting the vector hyperscaling violating parameter
and we present an example where the conformal anomaly contains the only
conformal invariant in with four spatial derivatives.Comment: 83 pages, 1 figur
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