Quantum Institute: Visitor Schedule

The Quantum Lunch is regularly held on Thursdays in the Theoretical Division Conference Room, TA-3, Building 123, Room 121.

The organizing committee includes Ryan O. Behunin (T-4 & CNLS), Malcolm Boshier (P-21), Adolfo del Campo (T-4 & CNLS), Michael Di Rosa (C-PCS), Ivar Martin (T-4), Changhyun Ryu (P-21), Rolando D. Somma (T-4), Christopher Ticknor (T-1), and Wojciech H. Zurek (T-4).

For more information, or to nominate a speaker, contact Adolfo del Campo.

To add your name to the Quantum Lunch email list, contact Ellie Vigil.

Tuesday, February 26, 2013
2:00 PM - 3:30 PM

Speaker: Andrew Comech (Texas A&M)

Technical Host: Avadh Saxena

TOPIC: Linear stability of solitary waves in nonlinear Dirac equation

Abstract
We study the linear instability of solitary wave solutions to the nonlinear Dirac equation (known to physicists as the Soler model). That is, we linearize the equation at a solitary wave and examine the presence of eigenvalues with positive real part. We show that the linear instability of the small amplitude solitary waves is described by the Vakhitov-Kolokolov stability criterion which was obtained in the context of the nonlinear Schroedinger equation: small solitary waves are linearly unstable in dimensions 3, and generically linearly stable in 1D. A particular question is on the possibility of bifurcations of eigenvalues from the continuous spectrum; we address it using the limiting absorption principle and the Hardy-type and Carleman-type inequalities. The method is applicable to other systems, such as the Dirac-Maxwell system. Some of the results are obtained in collaboration with Nabile Boussaid, University of Franche-Comte, and Stephen Gustafson, University of British Columbia.