arXiv subjects

J. -C. Yera

Publications and source records attributed to J. -C. Yera.

3 recordsLinked to original sources

arXiv2009

The non-linear Schrödinger equation and the conformal properties of non-relativistic space-time

The cubic non-linear Schrödinger equation where the coefficient of the nonlinear term is a function $F(t,x)$ only passes the Painlevé test of Weiss, Tabor, and Carnevale only for $F=(a+bt)^{-1}$, where $a$ and $b$ are constants. This is explained by transforming the time-dependent system into the constant-coefficient NLS by means of a time-dependent non-linear transformation, related to the conformal properties of non-relativistic space-time. A similar argument explains the integrability of the NLS in a uniform force field or in an oscillator background.

math-ph↗

arXiv2003

Vortices in the Landau--Ginzburg Model of the Quantized Hall Effect

The `Landau--Ginzburg' theory of Girvin and MacDonald, modified by adding the natural magnetic term, is shown to admit stable topological as well as non-topological vortex solutions. The system is the commun $λ\to0$ limit of two slightly different non-relativistic Maxwell--Chern--Simons models of the type introduced recently by Manton. The equivalence with the model of Zhang, Hansson and Kivelson is demonstrated.

hep-th↗

arXiv1997

Non-relativistic Maxwell-Chern-Simons Vortices

The non-relativistic Maxwell-Chern-Simons model recently introduced by Manton is shown to admit self-dual vortex solutions with non-zero electric field. The interrelated ``geometric'' and ``hidden'' symmetries are explained. The theory is also extended to (non-relativistic) spinors. A relativistic, self-dual model, whose non-relativistic limit is the Manton model is also presented. The relation to previous work is discussed.

hep-th↗