1. Dynamics of Qballs http://leandros.chem.demokritos.gr/qballs Phys.Rev.D62:047301,2000 L. Perivolaropoulos http://leandros.chem.democritos.gr Institute for Nuclear Physics Research Demokritos Research Center Work in collaboration with M. Axenides, E. Floratos Demokritos Research Center and S. Komineas Univ. of Bayreuth (Germany)

2. Structure of Talk 1. Introduction What is a Q Ball Q Ball Formation The Role of Dynamics 2. Q Balls on the line Existence - Stability - Virial Theorem Interactions - Scattering 3. Q Balls on the Plane Fusion or Fision? 4. Scattering in 3D 5. Conclusion Motivation: Understand the evolution of Q Balls in a cosmological setup

3. What is a Qball? Dynamically Stable Time Dependent Solution with a rotating internal phase. Its stability is due to the conservation of Noether charge. Simplest Example: Field Equation (1+1 dim): Qball ansatz: Conserved Noether Charge Solution Exists for:

4. Q Ball Formation Instabilities of Coherent Affleck-Dine Scalar due to flat directions of SUSY breaking induced potentials Example of Affleck-Dine Potential ( K < 0 ) Affleck-Dine Field: Fluctuations: Kasuya - Kawasaki hep-ph/0002285

5. The Role of Dynamics MSSM: Qballs form as condensates of squarks and sleptons with conserved charge the Baryon and Lepton number. Thus: Qballs can form by the Aflecck-Dine mechanism (Instabilities of Homogeneously Rotating AD Scalar) Large Stable Qballs can form Cold Dark Matter Unstable Qballs can lead to Baryon Asymmetry Isocurvature baryon fluctuations Q: How do interactions and scattering affect the cosmological evolution of Qballs?

6. Q Balls on the Line I: Existence - Stability Energy: For Stability: Find B, ω for 0 eigevalue Ground State x x

7. Virial Theorem The Qball energy may be written as: Rescale Spatial Coordinate x: Minimize with respect to rescaling parameter α: Virial Theorem Condition for stability always satisfied.

8. Q Balls on the Line II: Interactions - Scattering Ansatz for two interacting Qballs at distance 2 x 0 Dominant Term Analytic Numerical Spatial Oscilation Frequency is Double the Internal Rotation Symmetry Breather Oscillations

9. Scattering Define: Boosted Configuration: Initial Conditions: Evolved System Long-lived central Q Ball

10. Q Balls on the Plane Fusion or Fision I

11. Qualitative Preliminary Result (not published) Particle Behavior (pass through) Particle Behavior (merge) Soliton Behavior (fision)

12. Q Balls on the Plane Fusion or Fision Q/Q 0 : Fractional Charge in Forward Scattering

13. Scattering in 3D I Head on Collision (unpublished preliminary results)

14. Scattering in 3D II Non-zero impact parameter

15. Conclusion Studied Dynamics of Q Balls in 1D, 2D, 3D. 1D: Stability Sector, Virial Theorem, Breather Oscillations of Q Ball pairs 2D Scattering: 3D Scattering (Preliminary): Q Ring Formation Implications: Q Ball Cosmological Evolution Fision implies tha Q Ball number may increase while size decreases leading to instabilities.