TITLE:

SOLITON AND VORTEX LATTICES IN NONLINEAR MEDIA: FROM ISOLATED STRUCTURES TO MOLECULAR CRYSTALS (No. 75)

DATE:

Friday, March 25th, 2005

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Ricardo Carretero, Nonlinear Dynamical Systems (NLDS) , Dept. of Mathematics, San Diego State University

ABSTRACT:

Nonlinear media host a wide variety of localized coherent structures
(waves, bright and dark solitons, vortices, aggregates, spirals, etc.)
with complex intrinsic properties and interactions. In many situations
such as optical communications, condensed matter waves and biochemical aggregates it is crucial to study the interaction dynamics of coherent structures arranged in periodic lattices. In this talk I will present results concerning chains and lattices of coherent structures in
Bose-Einstein condensates (BECs). BECs, the so-called fifth state of
matter, correspond to macroscopic (micron-size) drops of quantum matter that behave as a single quantum particle (ie. quantum mechanics at an observable macroscopic scale!). You can think of the BEC as a fluid with quantum properties. In fact, a BEC is to matter what laser is to light (think coherently about coherence…).

Our approach to study interactions of localized structures is to provide
a simple, yet realistic, approximation for the interaction of structures
by considering each structure as a (quasi-)particle that is coupled
to the remaining ones. Within this framework, one can considerably
reduce the complexity of the dynamic description of the BEC, a partial
differential equation, to a set of couple ordinary differential equations
on the quasi-particle’s parameters (position, width, mass, phase, etc…).
This reduction allows for a more straightforward (time- and complexity-wise) study of possible emergent patterns. In particular, by using this reduction, we are able to engineer and study exciting solutions such as a) global and localized oscillations in one-dimensional chains of bright and dark solitons and b) crystallization of vortex lattices and their structural transitions using a molecular dynamics approach on a two-dimensional soup (gas) of quantum vortices.

The talk will be aimed for the general audience with many pictures and
movies to illustrate the motivations, techniques and results involved
in this work.

HOST:

Peter Blomgren

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