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LPHY 2000 Bordeaux France July 2000

Numerical solution of Dirac equation & its applications in intense laser physics Q. Su Intense Laser Physics Theory Unit Illinois State University. LPHY 2000 Bordeaux France July 2000. J. Braun P. Krekora P. Peverly R. Grobe R. Wagner. Support: NSF, Research Corporation, NCSA.

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LPHY 2000 Bordeaux France July 2000

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  1. Numerical solution of Dirac equation & its applications in intense laser physicsQ. Su Intense Laser Physics Theory UnitIllinois State University LPHY 2000 Bordeaux France July 2000 J. Braun P. KrekoraP. Peverly R. Grobe R. Wagner Support: NSF, Research Corporation, NCSA www.phy.ilstu.edu/ILP

  2. Goals Classical phase space approach valid for Non-linear systems of relativistic particles? Quantum cycloatoms Relativistic theory of tunneling Superluminal speeds

  3. Numerical techniques Liouville P. Peverly, R. Wagner, Q. Su and R. Grobe, Las Phys. 10, 303 (2000) Dirac J. Braun, Q. Su and R. Grobe, PRA 59, 604 (1999) Laser Magnetic field

  4. Maximum speed v/c for each W non- relativistic relativistic W wL R.E. Wagner, Q. Su and R. Grobe, Phys. Rev. Lett. 84, 3282 (2000)

  5. Non-relativistic Relativistic 0 75 150 y 500 x Orbits stay in phase Orbits dephase relativistically Time (in 2p/wL)

  6. Liouville Dirac Confirmed: Dirac Cycloatoms P. Krekora, R. Wagner, Q. Su and R. Grobe, PRA, submitted

  7. Summary 1 - Phase space approach valid in relativistic regime - Quantum cycloatom confirmed R.E. Wagner, Q. Su and R. Grobe, Phys. Rev. Lett. 84, 3282 (2000) P. Krekora, R. Wagner, Q. Su and R. Grobe, PRA, submitted

  8. Questions about tunneling  Dirac theory predict superluminal speeds?  Violation of causality? If v > c  Instantaneous speed inside the barrier? A.M. Steinberg, P.G. Kwiat and R.Y. Chiao, Phy. Rev. Lett. 71, 708 (1993) C. Spielmann, R. Szipöcs, A. Stingl and F. Krausz, Phys. Rev. Lett. 73, 2308 (1994) V. Gasparian, M. Ortuno, J. Ruiz and E. Cuevas, Phys. Rev. Lett. 75, 2312 (1995) L. Wang, private communications

  9. Theoretical Model Dirac 65,536 grid pts, 1,500,000 pts in time J. Braun, QS, R. Grobe, PRA 59, 604 (1999)

  10. Dirac & Schrödinger => v > c possible larger v for Dirac Dirac: + exact - stat. phase approx. Schrödinger: o exact - stat. phase approx. SPA best for broad packets

  11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Center Center Center Center Superluminal speeds = Pulse reshaping effect IQ Tunnel No violation of causality

  12. Violation of causality ? Causality violation if

  13. Tunneling dynamics under the barrier no spatial localization under the barrier

  14. Time localized state under barrier Spatially resolved tunneling velocity

  15. Summary 2  Dirac + Schrödinger theories predict superluminal effects  Causality non-violation for Dirac theory  Instantaneous tunneling velocity defined P.Krekora, QS, R.Grobe, Phys. Rev. Lett. (submitted) www.phy.ilstu.edu/ILP

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