24 research outputs found
Grassmanian and Bosonic Thirring Models with Jump Defects
In this paper we discuss the Lax formulation of the Grassmanian and Bosonic
Thirring models in the presence of jump defects. For the Grassmanian case, the
defect is described by B\"acklund transformation which is responsible for
preserving the integrability of the model.
We then propose an extension of the B\"acklund transformation for the Bosonic
Thirring model which is verified by some B\"acklund transitions like
Vacuum-One soliton, One soliton - One soliton, One soliton - Two solitons and
Two solitons - Two solitons. The Lax formulation within the space split by the
defect leads to the integrability of Bosonic Thirring model.Comment: Latex 21 page
Permutability of Backlund Transformation for N=1 Supersymmetric Sinh-Gordon
The permutability of two Backlund transformations is employed to construct a
non linear superposition formula to generate a class of solutions for the N=1
super sinh-Gordon model.Comment: 10 pages. to appear in Phys. Lett.
A Class of Soliton Solutions for the N=2 Super mKdV/Sinh-Gordon Hierarchy
Employing the Hirota's method, a class of soliton solutions for the N=2 super
mKdV equations is proposed in terms of a single Grassmann parameter. Such
solutions are shown to satisfy two copies of N=1 supersymmetric mKdV equations
connected by nontrivial algebraic identities. Using the super Miura
transformation, we obtain solutions of the N=2 super KdV equations. These are
shown to generalize solutions derived previously. By using the mKdV/sinh-Gordon
hierarchy properties we generate the solutions of the N=2 super sinh-Gordon as
well.Comment: 8 page
Classical Integrable N=1 and Super Sinh-Gordon Models with Jump Defects
The structure of integrable field theories in the presence of jump defects is
discussed in terms of boundary functions under the Lagrangian formalism.
Explicit examples of bosonic and fermionic theories are considered. In
particular, the boundary functions for the N=1 and N=2 super sinh-Gordon models
are constructed and shown to generate the Backlund transformations for its
soliton solutions. As a new and interesting example, a solution with an
incoming boson and an outgoing fermion for the N=1 case is presented. The
resulting integrable models are shown to be invariant under supersymmetric
transformation.Comment: talk presented at the V International Symposium on Quantum Theory and
Symmetries, Valladolid, Spain, July 22-28,200
Integrable Field Theories with Defects
The structure of integrable field theories in the presence of defects is
discussed in terms of boundary functions under the Lagrangian formalism.
Explicit examples of bosonic and fermionic theories are considered. In
particular, the boundary functions for the super sinh-Gordon model is
constructed and shown to generate the Backlund transformations for its soliton
solutions.Comment: talk presented at the XVth International Colloquium on Integrable
Systems and Quantum Symmetries, to appear in Czechoslovak Journal of Physics
(2006
Permutability of Backlund Transformations for N=2 Supersymmetric Sine-Gordon
The permutability of two Backlund transformations is employed to construct a
non linear superposition formula and to generate a class of solutions for the
N=2 super sine-Gordon model.Comment: two references adde
Integrable atomtronic interferometry
High sensitivity quantum interferometry requires more than just access to
entangled states. It is achieved through deep understanding of quantum
correlations in a system. Integrable models offer the framework to develop this
understanding. We communicate the design of interferometric protocols for an
integrable model that describes the interaction of bosons in a four-site
configuration. Analytic formulae for the quantum dynamics of certain
observables are computed. These expose the system's functionality as both an
interferometric identifier, and producer, of NOON states. Being equivalent to a
controlled-phase gate acting on two hybrid qudits, this system also highlights
an equivalence between Heisenberg-limited interferometry and quantum
information. These results are expected to open new avenues for
integrability-enhanced atomtronic technologies.Comment: 6 pages, 4 figures, 1 tabl
Deformations of N=2 super-conformal algebra and supersymmetric two-component Camassa-Holm equation
This paper is concerned with a link between central extensions of N=2
superconformal algebra and a supersymmetric two-component generalization of the
Camassa--Holm equation.
Deformations of superconformal algebra give rise to two compatible bracket
structures. One of the bracket structures is derived from the central extension
and admits a momentum operator which agrees with the Sobolev norm of a
coadjoint orbit element. The momentum operator induces via Lenard relations a
chain of conserved hamiltonians of the resulting supersymmetric Camassa-Holm
hierarchy.Comment: Latex, 21 pages, version to appear in J. Phys.