135,455 research outputs found
Hydrodynamic type integrable equations on a segment and a half-line
The concept of integrable boundary conditions is applied to hydrodynamic type
systems. Examples of such boundary conditions for dispersionless Toda systems
are obtained. The close relation of integrable boundary conditions with
integrable reductions of multi-field systems is observed. The problem of
consistency of boundary conditions with the Hamiltonian formulation is
discussed. Examples of Hamiltonian integrable hydrodynamic type systems on a
segment and a semi-line are presented
Signatures of integrability in charge and thermal transport in 1D quantum systems
Integrable and non-integrable systems have very different transport
properties. In this work, we highlight these differences for specific one
dimensional models of interacting lattice fermions using numerical exact
diagonalization. We calculate the finite temperature adiabatic stiffness (or
Drude weight) and isothermal stiffness (or ``Meissner'' stiffness) in
electrical and thermal transport and also compute the complete momentum and
frequency dependent dynamical conductivities and
. The Meissner stiffness goes to zero rapidly with system
size for both integrable and non-integrable systems. The Drude weight shows
signs of diffusion in the non-integrable system and ballistic behavior in the
integrable system. The dynamical conductivities are also consistent with
ballistic and diffusive behavior in the integrable and non-integrable systems
respectively.Comment: 4 pages, 4 figure
Dispersionless integrable equations as coisotropic deformations. Extensions and reductions
Interpretation of dispersionless integrable hierarchies as equations of
coisotropic deformations for certain algebras and other algebraic structures
like Jordan triple systInterpretation of dispersionless integrable hierarchies
as equations of coisotropic deformations for certain algebras and other
algebraic structures like Jordan triple systems is discussed. Several
generalizations are considered. Stationary reductions of the dispersionless
integrable equations are shown to be connected with the dynamical systems on
the plane completely integrable on a fixed energy level. ems is discussed.
Several generalizations are considered. Stationary reductions of the
dispersionless integrable equations are shown to be connected with the
dynamical systems on the plane completely integrable on a fixed energy level.Comment: 21 pages, misprints correcte
Quaternionic integrable systems
Standard (Arnold-Liouville) integrable systems are intimately related to
complex rotations. One can define a generalization of these, sharing many of
their properties, where complex rotations are replaced by quaternionic ones.
Actually this extension is not limited to the integrable case: one can define a
generalization of Hamilton dynamics based on hyperKahler structures.Comment: 10 pages. To appear in the proceedings of the SPT2002 conference,
edited by S. Abenda, G. Gaeta and S. Walcher, World Scientifi
Coupling symmetries with Poisson structures
We study local normal forms for completely integrable systems on Poisson
manifolds in the presence of additional symmetries. The symmetries that we
consider are encoded in actions of compact Lie groups. The existence of
Weinstein's splitting theorem for the integrable system is also studied giving
some examples in which such a splitting does not exist, i.e. when the
integrable system is not, locally, a product of an integrable system on the
symplectic leaf and an integrable system on a transversal. The problem of
splitting for integrable systems with additional symmetries is also considered.Comment: 14 page
Integrable Hamiltonian systems with vector potentials
We investigate integrable 2-dimensional Hamiltonian systems with scalar and
vector potentials, admitting second invariants which are linear or quadratic in
the momenta. In the case of a linear second invariant, we provide some examples
of weakly-integrable systems. In the case of a quadratic second invariant, we
recover the classical strongly-integrable systems in Cartesian and polar
coordinates and provide some new examples of integrable systems in parabolic
and elliptical coordinates.Comment: 23 pages, Submitted to Journal of Mathematical Physic
Hypercomplex Integrable Systems
In this paper we study hypercomplex manifolds in four dimensions. Rather than
using an approach based on differential forms, we develop a dual approach using
vector fields. The condition on these vector fields may then be interpreted as
Lax equations, exhibiting the integrability properties of such manifolds. A
number of different field equations for such hypercomplex manifolds are
derived, one of which is in Cauchy-Kovaleskaya form which enables a formal
general solution to be given. Various other properties of the field equations
and their solutions are studied, such as their symmetry properties and the
associated hierarchy of conservation laws.Comment: Latex file, 19 page
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