Nonlinear Waves in Atomic and Optical Physics P.G. Kevrekidis http:www.math.umass.edukevrekid

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Nonlinear Waves in Atomic and Optical
PhysicsP.G. Kevrekidishttp//www.math.umass.edu
/kevrekid

• In Collaboration With
• D.J. Frantzeskakis, G. Theocharis (Athens), Z.
  Rapti (UIUC)
• B. Malomed (Tel Aviv), R. Carretero (San Diego
  State)
• T. Kapitula (UNM), Z. Chen (SFSU)
• D.E. Pelinovsky (McMaster)
• M. Porter, M. Centurion, D. Psaltis, Y. Pu
  (CalTech)
• V.V. Konotop, E.A. Alfimov (Lisbon), M. Salerno
  (Salerno)
• M.I. Weinstein (Columbia), E. Kirr (UIUC), E.
  Shlizerman (Weizmann)
• D. Hall, K. Mertes (Amherst College)
• with the gratefully acknowledged partial support
  of
• National Science Foundation (DMS and CAREER)
• Eppley Foundation for Research

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An Optical Example of Theory and Experiment
Periodic Media

• Consider Periodically Modulated Nonlinear
  Schrödinger Equation

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Modulational Instability for Temporally Periodic
Settings

• Rewrite Dynamical Equation as
• Find Plane Wave Solution and
  Perturb u0, using Linearization Ansatz
• Obtain Linear Stability Equation
• Which, using Blochs Theorem
  becomes

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An Atomic Example of Theory and Experiment
Multi-Component BECs

• Consider Two-Component Rb BEC, described by
  Coupled GP Equations
• Use the Zeroth Moment of BEC wavefunction to
  identify Loss Rates e.g

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Old vs. New Physics Augmenting the Model

• Derive in this way a Model Tailored to the
  Experimental System.
• Test it against Full Experiment, also for
  Different Atom Numbers with Excellent Results.

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Multiple Components Exciting Phase Separation
Dynamics