Relativistic time-dependent quantum dynamics across supercritical barriers for Klein-Gordon and Dirac particles

Abstract

We investigate wavepacket dynamics across supercritical barriers for the Klein-Gordon and Dirac equations. Our treatment is based on a multiple scattering expansion (MSE). For spin-0 particles, the MSE diverges, rendering invalid the use of the usual connection formulas for the scattering basis functions. In a time-dependent formulation, the divergent character of the MSE naturally accounts for charge creation at the barrier boundaries. In the Dirac case, the MSE converges and no charge is created. We show that this time-dependent charge behavior dynamics can adequately explain the Klein paradox in a first quantized setting. We further compare our semi-analytical wavepacket approach to exact finite-difference solutions of the relativistic wave equations.

arXiv commentSome text moved from main body to Appendices; close to published version

References in corpus (14)

• Chiral tunneling and the Klein paradox in graphene
• The Woods-Saxon Potential in the Dirac Equation
• Quantization of charged fields in the presence of critical potential steps
• Barrier Paradox in the Klein Zone
• Klein Paradox in Bosons
• Resolution of the Klein Paradox
• The role of the slope of `realistic' potential barriers in preventing relativistic tunnelling in the Klein zone
• Klein paradox for bosons, wave packets and negative tunnelling times
• Non-locality and time-dependent boundary conditions: a Klein-Gordon perspective
• A stability analysis of a real space split operator method for the Klein-Gordon equation
• Zitterbewegung and Klein-tunneling phenomena for transient quantum waves
• Quantum Charged Spinning Massless Particles in 2+1 dimensions
• Scattering of a scalar relativistic particle by the hyperbolic tangent potential
• The Klein paradox in a magnetic field: effects of electron spin

Cited by in corpus (13)

• Space-time resolved quantum field approach to Klein tunneling dynamics across a finite barrier
• Numerical simulations of quantum clock for measuring tunneling times
• Gauge waves generation and detection in Aharonov-Bohm electrodynamics
• Relativistic Bohmian trajectories and Klein-Gordon currents for spin-0 particles
• Relativistic spin-0 particle in a box: bound states, wavepackets, and the disappearance of the Klein paradox
• Beyond the light-cone propagation of relativistic wavefunctions: numerical results
• Evolution of strictly localized states in non-interacting quantum field theories with background fields
• Effects of superradiance on relativistic Foldy-Wouthuysen densities
• Quantum mechanical Gaussian wavepackets of single relativistic particles
• Tunneling dynamics of the relativistic Schrodinger/Salpeter equation
• Computational quantum field theory for fermion pair creation in 2-dimensional curved spacetimes
• Perfect transmission of a Dirac particle in one-dimension double square barrier
• Simple circuit and experimental proposal for the detection of gauge-waves