24-26 September 2020
Lima, Perú
America/Lima timezone
Share our event through the following link: https://indico.uni.edu.pe/e/Meeting-of-Physics-2020

Modified non-linear Schr\"odinger models, ${\cal C}{\cal P}_s{\cal T}_d$ symmetric $N-$bright solitons and towers of anomalous charges

26 Sep 2020, 14:40
20m
Lima, Perú

Lima, Perú

Centro de Investigación de la Facultad de Ciencias Universidad Nacional de Ingeniería
video conference General relativity and Field theory General relativity and Field theory

Speaker

Dr Harold Blas (Instituto de Fisica-UFMT)

Description

Modifications of the non-linear Schr\"odinger model (MNLS) $ i \partial_{t} \psi(x,t) + \partial^2_{x} \psi(x,t) - [\frac{\delta V}{\delta |\psi|^2} ] \psi(x,t) = 0,$ where $\psi \in C$ and $V: R_{+} \rightarrow R$, are considered. We show that the quasi-integrable MNLS models possess infinite towers of quasi-conservation laws for soliton-type configurations with a special complex conjugation, shifted parity and delayed time reversion (${\cal C}{\cal P}_s{\cal T}_d$) symmetry. Infinite towers of anomalous charges appear even in the standard NLS model for ${\cal C}{\cal P}_s{\cal T}_d$ invariant $N-$bright solitons. The true conserved charges emerge through some kind of anomaly cancellation mechanism, since a convenient linear combination of the relevant anomalies vanishes.

A Riccati-type pseudo-potential is introduced for a modified AKNS system (MAKNS), which reproduces the MNLS quantities upon a reduction process. Two infinite towers of exact non-local conservation laws are uncovered in this framework.

Our analytical results are supported by numerical simulations of $2-$bright-soliton scatterings with potential $ V = - \frac{ 2\eta}{2+ \epsilon} ( |\psi|^2 )^{2 + \epsilon}, \epsilon \in R, \eta>0$. Our numerical simulations show the elastic scattering of bright solitons for a wide range of values of the set $\{\eta, \epsilon\}$ and a variety of amplitudes and relative velocities. The AKNS-type system is quite ubiquitous, and so, our results may find potential applications in several areas of non-linear physics, such as Bose-Einstein condensation, superconductivity, soliton turbulence and the triality among gauge theories, integrable models and gravity theories.

Primary authors

Dr Harold Blas (Instituto de Fisica-UFMT) Dr Martin Cerna Dr Luis dos Santos

Presentation Materials

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