17,936 research outputs found
Free field representation for the O(3) nonlinear sigma model and bootstrap fusion
The possibility of the application of the free field representation developed
by Lukyanov for massive integrable models is investigated in the context of the
O(3) sigma model. We use the bootstrap fusion procedure to construct a free
field representation for the O(3) Zamolodchikov- Faddeev algebra and to write
down a representation for the solutions of the form-factor equations which is
similar to the ones obtained previously for the sine-Gordon and SU(2) Thirring
models. We discuss also the possibility of developing further this
representation for the O(3) model and comment on the extension to other
integrable field theories.Comment: 14 pages, latex, revtex v3.0 macro package, no figures Accepted for
publication in Phys. Rev.
Energetic Consistency and Momentum Conservation in the Gyrokinetic Description of Tokamak Plasmas
Gyrokinetic field theory is addressed in the context of a general
Hamiltonian. The background magnetic geometry is static and axisymmetric, and
all dependence of the Lagrangian upon dynamical variables is in the Hamiltonian
or in free field terms. Equations for the fields are given by functional
derivatives. The symmetry through the Hamiltonian with time and toroidal angle
invariance of the geometry lead to energy and toroidal momentum conservation.
In various levels of ordering against fluctuation amplitude, energetic
consistency is exact. The role of this in underpinning of conservation laws is
emphasised. Local transport equations for the vorticity, toroidal momentum, and
energy are derived. In particular, the momentum equation is shown for any form
of Hamiltonian to be well behaved and to relax to its magnetohydrodynamic (MHD)
form when long wavelength approximations are taken in the Hamiltonian. Several
currently used forms, those which form the basis of most global simulations,
are shown to be well defined within the gyrokinetic field theory and energetic
consistency.Comment: RevTeX 4, 47 pages, no figures, revised version updated following
referee comments (discussion more strictly correct/consistent, 4 references
added, results unchanged as they depend on consistency of the theory),
resubmitted to Physics of Plasma
Quasi-exactly solvable problems and the dual (q-)Hahn polynomials
A second-order differential (q-difference) eigenvalue equation is constructed
whose solutions are generating functions of the dual (q-)Hahn polynomials. The
fact is noticed that these generating functions are reduced to the (little
q-)Jacobi polynomials, and implications of this for quasi-exactly solvable
problems are studied. A connection with the Azbel-Hofstadter problem is
indicated.Comment: 15 pages, LaTex; final version, presentation improved, title changed,
to appear in J.Math.Phy
Dirac equation in the magnetic-solenoid field
We consider the Dirac equation in the magnetic-solenoid field (the field of a
solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm
solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using
von Neumann's theory of deficiency indices. We find self-adjoint extensions of
the Dirac Hamiltonian in both above dimensions and boundary conditions at the
AB solenoid. Besides, for the first time, solutions of the Dirac equation in
the magnetic-solenoid field with a finite radius solenoid were found. We study
the structure of these solutions and their dependence on the behavior of the
magnetic field inside the solenoid. Then we exploit the latter solutions to
specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm
solenoid.Comment: 23 pages, 2 figures, LaTex fil
Sympathetic cooling route to Bose-Einstein condensate and Fermi-liquid mixtures
We discuss a sympathetic cooling strategy that can successfully mitigate
fermion-hole heating in a dilute atomic Fermi-Bose mixture and access the
temperature regime in which the fermions behave as a Fermi liquid. We introduce
an energy-based formalism to describe the temperature dynamics with which we
study a specific and promising mixture composed of 6Li and 87Rb. Analyzing the
harmonically trapped mixture, we find that the favourable features of this
mixture are further enhanced by using different trapping frequencies for the
two species.Comment: 4 pages, 2 figure
The Tails of the Crossing Probability
The scaling of the tails of the probability of a system to percolate only in
the horizontal direction was investigated numerically for correlated
site-bond percolation model for .We have to demonstrate that the
tails of the crossing probability far from the critical point have shape
where is the correlation
length index, is the probability of a bond to be closed. At
criticality we observe crossover to another scaling . Here is a scaling index describing the
central part of the crossing probability.Comment: 20 pages, 7 figures, v3:one fitting procedure is changed, grammatical
change
Exactly solvable model of the 2D electrical double layer
We consider equilibrium statistical mechanics of a simplified model for the
ideal conductor electrode in an interface contact with a classical
semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of
pointlike unit charges in the stability-against-collapse regime of
reduced inverse temperatures . If there is a potential difference
between the bulk interior of the electrolyte and the grounded interface, the
electrolyte region close to the interface (known as the electrical double
layer) carries some nonzero surface charge density. The model is mappable onto
an integrable semi-infinite sine-Gordon theory with Dirichlet boundary
conditions. The exact form-factor and boundary state information gained from
the mapping provide asymptotic forms of the charge and number density profiles
of electrolyte particles at large distances from the interface. The result for
the asymptotic behavior of the induced electric potential, related to the
charge density via the Poisson equation, confirms the validity of the concept
of renormalized charge and the corresponding saturation hypothesis. It is
documented on the non-perturbative result for the asymptotic density profile at
a strictly nonzero that the Debye-H\"uckel limit is a
delicate issue.Comment: 14 page
One-point functions in integrable quantum field theory at finite temperature
We determine the form factor expansion of the one-point functions in
integrable quantum field theory at finite temperature and find that it is
simpler than previously conjectured. We show that no singularities are left in
the final expression provided that the operator is local with respect to the
particles and argue that the divergences arising in the non-local case are
related to the absence of spontaneous symmetry breaking on the cylinder. As a
specific application, we give the first terms of the low temperature expansion
of the one-point functions for the Ising model in a magnetic field.Comment: 10 pages, late
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