1,401 research outputs found
Quantum Transport in Molecular Rings and Chains
We study charge transport driven by deformations in molecular rings and
chains. Level crossings and the associated Longuet-Higgins phase play a central
role in this theory. In molecular rings a vanishing cycle of shears pinching a
gap closure leads, generically, to diverging charge transport around the ring.
We call such behavior homeopathic. In an infinite chain such a cycle leads to
integral charge transport which is independent of the strength of deformation.
In the Jahn-Teller model of a planar molecular ring there is a distinguished
cycle in the space of uniform shears which keeps the molecule in its manifold
of ground states and pinches level crossing. The charge transport in this cycle
gives information on the derivative of the hopping amplitudes.Comment: Final version. 26 pages, 8 fig
On the numerical evaluation of algebro-geometric solutions to integrable equations
Physically meaningful periodic solutions to certain integrable partial
differential equations are given in terms of multi-dimensional theta functions
associated to real Riemann surfaces. Typical analytical problems in the
numerical evaluation of these solutions are studied. In the case of
hyperelliptic surfaces efficient algorithms exist even for almost degenerate
surfaces. This allows the numerical study of solitonic limits. For general real
Riemann surfaces, the choice of a homology basis adapted to the
anti-holomorphic involution is important for a convenient formulation of the
solutions and smoothness conditions. Since existing algorithms for algebraic
curves produce a homology basis not related to automorphisms of the curve, we
study symplectic transformations to an adapted basis and give explicit formulae
for M-curves. As examples we discuss solutions of the Davey-Stewartson and the
multi-component nonlinear Schr\"odinger equations.Comment: 29 pages, 20 figure
On the water-bag model of dispersionless KP hierarchy
We investigate the bi-Hamiltonian structure of the waterbag model of dKP for
two component case. One can establish the third-order and first-order
Hamiltonian operator associated with the waterbag model. Also, the dispersive
corrections are discussed.Comment: 19 page
Solution of the dispersionless Hirota equations
The dispersionless differential Fay identity is shown to be equivalent to a
kernel expansion providing a universal algebraic characterization and solution
of the dispersionless Hirota equations. Some calculations based on D-bar data
of the action are also indicated.Comment: Late
Topological Phenomena in the Real Periodic Sine-Gordon Theory
The set of real finite-gap Sine-Gordon solutions corresponding to a fixed
spectral curve consists of several connected components. A simple explicit
description of these components obtained by the authors recently is used to
study the consequences of this property. In particular this description allows
to calculate the topological charge of solutions (the averaging of the
-derivative of the potential) and to show that the averaging of other
standard conservation laws is the same for all components.Comment: LaTeX, 18 pages, 3 figure
On a Conjecture of Givental
These brief notes record our puzzles and findings surrounding Givental's
recent conjecture which expresses higher genus Gromov-Witten invariants in
terms of the genus-0 data. We limit our considerations to the case of a
projective line, whose Gromov-Witten invariants are well-known and easy to
compute. We make some simple checks supporting his conjecture.Comment: 13 pages, no figures; v.2: new title, minor change
Symmetry reductions of a particular set of equations of associativity in twodimensional topological field theory
The WDVV equations of associativity arising in twodimensional topological
field theory can be represented, in the simplest nontrivial case, by a single
third order equation of the Monge-Ampe`re type. By investigating its Lie point
symmetries, we reduce it to various nonlinear ordinary differential equations,
and we obtain several new explicit solutions.Comment: 10 pages, Latex, to appear in J. Phys. A: Math. Gen. 200
On Darboux-Treibich-Verdier potentials
It is shown that the four-parameter family of elliptic functions
introduced
by Darboux and rediscovered a hundred years later by Treibich and Verdier, is
the most general meromorphic family containing infinitely many finite-gap
potentials.Comment: 8 page
Darboux-Egoroff Metrics, Rational Landau-Ginzburg Potentials and the Painleve VI Equation
We present a class of three-dimensional integrable structures associated with
the Darboux-Egoroff metric and classical Euler equations of free rotations of a
rigid body. They are obtained as canonical structures of rational
Landau-Ginzburg potentials and provide solutions to the Painleve VI equation.Comment: 20 page
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