Numerical Solutions of Dirac Equation: Applications in Intense Laser Physics
This work explores numerical solutions to the Dirac equation and their implications within intense laser physics. Presented by Q. Su and colleagues at Illinois State University, the findings include advancements in the classical phase space approach for non-linear relativistic particle systems and insights into quantum cycloatoms. The research discusses the relativistic tunneling theory and the potential for superluminal speeds, all supported by numerical techniques and collaborations with notable physicists. Critical questions about causality and tunneling dynamics are also addressed, leading to a deeper understanding of particle behavior under intense laser fields.
Numerical Solutions of Dirac Equation: Applications in Intense Laser Physics
E N D
Presentation Transcript
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
Goals Classical phase space approach valid for Non-linear systems of relativistic particles? Quantum cycloatoms Relativistic theory of tunneling Superluminal speeds
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
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)
Non-relativistic Relativistic 0 75 150 y 500 x Orbits stay in phase Orbits dephase relativistically Time (in 2p/wL)
Liouville Dirac Confirmed: Dirac Cycloatoms P. Krekora, R. Wagner, Q. Su and R. Grobe, PRA, submitted
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
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
Theoretical Model Dirac 65,536 grid pts, 1,500,000 pts in time J. Braun, QS, R. Grobe, PRA 59, 604 (1999)
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
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Center Center Center Center Superluminal speeds = Pulse reshaping effect IQ Tunnel No violation of causality
Violation of causality ? Causality violation if
Tunneling dynamics under the barrier no spatial localization under the barrier
Time localized state under barrier Spatially resolved tunneling velocity
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
