6,305 research outputs found
On one-point functions for sinh-Gordon model at finite temperature
Using fermionic basis we conjecture the exact formulae for the expectation
values of local fields in sinh-Gordon model. The conjecture is checked against
previously known results.Comment: 21 pages, some explanation on relation to the lattice model is adde
Reflection relations and fermionic basis
There are two approaches to computing the one-point functions for sine-Gordon
model in infinite volume. One is a bootstrap type procedure based on the
reflection relations. Another uses the fermionic basis which was originally
found for the lattice six-vertex model. In this paper we show that the two
approaches are deeply interrelated.Comment: 17 pages; several typos are correcte
The Perlick system type I: from the algebra of symmetries to the geometry of the trajectories
In this paper, we investigate the main algebraic properties of the maximally
superintegrable system known as "Perlick system type I". All possible values of
the relevant parameters, and , are considered. In particular,
depending on the sign of the parameter entering in the metrics, the motion
will take place on compact or non compact Riemannian manifolds. To perform our
analysis we follow a classical variant of the so called factorization method.
Accordingly, we derive the full set of constants of motion and construct their
Poisson algebra. As it is expected for maximally superintegrable systems, the
algebraic structure will actually shed light also on the geometric features of
the trajectories, that will be depicted for different values of the initial
data and of the parameters. Especially, the crucial role played by the rational
parameter will be seen "in action".Comment: 16 pages, 7 figure
Integrability, Supersymmetry and Coherent States. A volume in honour of Professor VĂ©ronique Hussin
ISBN 978-3-030-20087-
Heisenberg-type higher order symmetries of superintegrable systems separable in cartesian coordinates
Heisenberg-type higher order symmetries are studied for both classical and
quantum mechanical systems separable in cartesian coordinates. A few particular
cases of this type of superintegrable systems were already considered in the
literature, but here they are characterized in full generality together with
their integrability properties. Some of these systems are defined only in a
region of , and in general they do not include bounded solutions.
The quantum symmetries and potentials are shown to reduce to their
superintegrable classical analogs in the limit.Comment: 23 Pages, 3 figures, To appear in Nonlinearit
Superintegrability of the Fock-Darwin system
The Fock-Darwin system is analysed from the point of view of its symmetry
properties in the quantum and classical frameworks. The quantum Fock-Darwin
system is known to have two sets of ladder operators, a fact which guarantees
its solvability. We show that for rational values of the quotient of two
relevant frequencies, this system is superintegrable, the quantum symmetries
being responsible for the degeneracy of the energy levels. These symmetries are
of higher order and close a polynomial algebra. In the classical case, the
ladder operators are replaced by ladder functions and the symmetries by
constants of motion. We also prove that the rational classical system is
superintegrable and its trajectories are closed. The constants of motion are
also generators of symmetry transformations in the phase space that have been
integrated for some special cases. These transformations connect different
trajectories with the same energy. The coherent states of the quantum
superintegrable system are found and they reproduce the closed trajectories of
the classical one.Comment: 21 pages,16 figure
Discrete derivatives and symmetries of difference equations
We show on the example of the discrete heat equation that for any given
discrete derivative we can construct a nontrivial Leibniz rule suitable to find
the symmetries of discrete equations. In this way we obtain a symmetry Lie
algebra, defined in terms of shift operators, isomorphic to that of the
continuous heat equation.Comment: submitted to J.Phys. A 10 Latex page
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