1. Examples of genuinely relativistic phenomena R. Grobe ICOMP VIII, Monterey, CA October 1999 Intense Laser Physics Theory Unit Illinois State University PostdocsFaculty J.W. Braun B.A. Smetanko J.J. Csesznegi P.J. Peverly R.E. Wagner T. Shepherd S.M. Mandel A. Bergquist Undergraduate students H. Wanare P. Krekora G.H. Rutherford Q. Su R. Grobe Support : National Science Foundation, Research Corporation, Illinois State

2. Tools to explore phenomena that are genuinely relativistic Dirac : Liouville:

3. A flavor of the numerical work Discretize: r  256 3 points t  10 3 -10 6 points Split operator FFT technique Supercomputer  ≈ 4 · 256 3 · 10 6 = 10 13 complex numbers

4. Genuinely Relativistic Phenomena Zitterbewegung J.W. Braun, Q. Su & RG, PRA 59, 604 (1999) Klein-Paradox (particle pair production) J.W. Braun, Q. Su & RG, PRA 59, 604 (1999) Subnatural wave packet spreading Q. Su, B.A. Smetanko & RG, Opt. Exp. 2, 277 (1998) J.C. Csesznegi, G.H. Rutherford, Q. Su & RG, Las. Phys. 9, 41 (1999) Spin-spatial coupling in magnetic fields G.H. Rutherford & RG, PRL 81, 4772 (1998) G.H. Rutherford & RG, JPA 31, 9331 (1998) Chaos J. Kim, and H. Lee, PRE 51, 1579 (1995) How good is Liouville? R.E. Wagner, P.J. Peverly, Q. Su & RG, PRA (subm.) Counterintuitive enhancement of resonances R.E. Wagner, Q. Su & RG, PRL (subm.) Cycloatoms and dephasing P.J. Peverly, R.E. Wagner, Q. Su, & RG, Las. Phys. (in press) Scattered light spectra R.E. Wagner, Q. Su & RG, PRA 60, No.4 (1999)

5. Schr ö dinger’s Zitterbewegung small ∆x  neg. energy contrib.  “Zitter” position spin Zitterbewegung real? controversial issue... J.W. Braun, Q. Su & RG, PRA 59, 604 (1999).

6. Time - resolved Klein Paradox Interpretation still controversial... J.W. Braun, Q. Su & RG, PRA 59, 604 (1999). voltage > E kin + 2c 2

7. Stern-Gerlach separation possible for electrons ??? Pauli/Bohr: Lorentz-force “washes out” separation ?? Dirac solution : Spin separation is possible G.H. Rutherford & RG, PRL 81, 4772 (1998) and JPA 31, 9331(1998). Position SzSz SzSz SzSz inhomog. magnetic field:

8. Subnatural wave packet spreading Non-relativistic: Spreading independent of the center of mass motion Spreading is suppressed: Q. Su, B.A Smetanko and RG, Opt. Exp. 2, 277 (1998) Spatial profile becomes asymmetrical : Q. Su, B.A. Smetanko & RG, Las. Phys. 4, 93 (1998)

9. Relativity Induces Chaos non-relativistic => Liouville = Schrödinger relativistic => ??? Liouville ≈ Dirac ???? Schrödinger = NewtonDirac ≈ Liouville What a surprise... J. Kim and H. Lee, PRE 51, 1579 (1995): + relativity => chaos R.E. Wagner, P.J. Peverly, Q. Su & RG, PRA (subm.)

10. Relativity enhances resonances Myth: relativity  “heavier mass”  slower motion example: electron in laser and static magnetic field  Maximum speed v/c for each  non- relativistic LL  Fact: relativity  faster motion R. Wagner, Q. Su & RG, PRL (submitted )

11. Novel steady spatial states: Cycloatoms Non-relativisticRelativistic Orbits stay in phase Orbits dephase relativistically Time (in 2  L  75 150 500 0 y x

12. Relativistic dephasing model relativistic (exact) dephasing model Time 75 150 500 0 replace   (V 0 )

13. Q. Su, R.E. Wagner, P.J. Peverly & RG, SPIE (in press) Steady state spatial electron distributions Multiple resonances Fractional resonances  = 3   = 2  =   = 1/2  = 1/3 

14. Scattered light spectra non-relativistic relativistic x y Single orbits Corresponding spectra R.E. Wagner, Q. Su & RG, PRA 60, No.4 (1999)

15. Summary Numerical solution to the Dirac equation Relativity leads to new phenomena in the spatial and temporal dynamics subnatural spreading chaos novel resonances => novel experiments cycloatoms dephasing scattered light spectra www.phy.ilstu.edu/ILP