3,839 research outputs found
Construction and exact solution of a nonlinear quantum field model in quasi-higher dimension
Nonperturbative exact solutions are allowed for quantum integrable models in
one space-dimension. Going beyond this class we propose an alternative Lax
matrix approach, exploiting the hidden multi-time concept in integrable systems
and construct a novel quantum nonlinear Schroedinger model in quasi-two
dimensions. An intriguing field commutator is discovered, confirming the
integrability of the model and yielding its exact Bethe ansatz solution with
rich scattering and bound-state properties. The universality of the scheme is
expected to cover diverse models, opening up a new direction in the field.Comment: 12 pages, 1 figure, Latex (This version to be published in Nucl Phys
B as Frontiers Article
Nonlinearizing linear equations to integrable systems including new hierarchies with nonholonomic deformations
We propose a scheme for nonlinearizing linear equations to generate
integrable nonlinear systems of both the AKNS and the KN classes, based on the
simple idea of dimensional analysis and detecting the building blocks of the
Lax pair. Along with the well known equations we discover a novel integrable
hierarchy of higher order nonholonomic deformations for the AKNS family, e.g.
for the KdV, the mKdV, the NLS and the SG equation, showing thus a two-fold
universality of the recently found deformation for the KdV equation.Comment: 17 pages, 5 figures, Latex, Final version to be published in J. Math.
Phy
Exact asymmetric Skyrmion in anisotropic ferromagnet and its helimagnetic application
Topological Skyrmions as intricate spin textures were observed experimentally
in helimagnets on 2d plane. Theoretical foundation of such solitonic states to
appear in pure ferromagnetic model, as exact solutions expressed through any
analytic function, was made long ago by Belavin and Polyakov (BP). We propose
an innovative generalization of the BP solution for an anisotropic ferromagnet,
based on a physically motivated geometric (in-)equality, which takes the exact
Skyrmion to a new class of functions beyond analyticity. The possibility of
stabilizing such metastable states in helimagnets is discussed with the
construction of individual Skyrmion and Skyrmion crystal with asymmetry, likely
to be detected in precision experiments.Comment: 12 pages, latex, 3 figures, published in Nucl Phys B (As Frontiers
article
Unifying structures in quantum integrable systems
Basic concepts of quantum integrable systems (QIS) are presented stressing on
the unifying structures underlying such diverse models. Variety of ultralocal
and nonultralocal models is shown to be described by a few basic relations
defining novel algebraic entries. Such properties can generate and classify
integrable models systematically and also help to solve exactly their
eigenvalue problem in an almost model-independent way. The unifying thread
stretches also beyond the QIS to establish its deep connections with
statistical models, conformal field theory etc. as well as with abstract
mathematical objects like quantum group, braided or quadratic algebraComment: Latex, 18 pages, no figure (Invited review article by Indian J.Phys.
Ascent and descent of the Golod property along algebra retracts
We study ascent and descent of the Golod property along an algebra retract.
We characterise trivial extensions of modules, fibre products of rings to be
Golod rings. We present a criterion for a graded module over a graded affine
algebra of characteristic zero to be a Golod module.Comment: 16 page
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