FFT-split-operator code for solving the Dirac equation in 2+1 dimensions

Solving the Dirac equation is a formidable task due to the high frequency and the degrees of freedom involved. However, this high frequency allows one to obtain an approximation to the equation. Here, we directly solve the Dirac equation using an envelope method and derive analytical solutions of Dirac wave packets to first order for the small momentum spread. We apply the insight gained from this solution to the Zitterbewegung behavior in a Dirac-like system, where we show that it is crucial to include the first-order term in our solution to correctly describe a Dirac packet.

“…A numerical approach recently has gained in popularity [13,[21][22][23][24][25]. However, neither approach provides a physical insight on the mechanism of the phenomenon.…”

Section: Introductionmentioning

confidence: 99%

Propagation of a relativistic electron wave packet in the Dirac equation

Park

2012

“…The single-particle Dirac equation is solved numerically the split-operator technique [18][19][20][21]. In this method the time-evolution operator exp[-iht] is decomposed into N t consecutive actions, each subinterval operators can be approximated by exp(-iht)≈exp[(-iVΔt/2)(-ih 0 Δt)(-iVΔt/2)] where h 0 denotes the force-free Hamiltonian.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…The operator's space and time dependence is obtained by solving the Dirac equation numerically [18][19][20][21]. This computational approach to quantum field theory has been introduced recently to study the pair-creation process with full space-time resolution.…”

Section: Introductionmentioning

confidence: 99%

Electron-positron pair creation induced by quantum-mechanical tunneling

Jiang

et al. 2011

We study the creation of electron-positron pairs from the vacuum induced by two spatially displaced static electric fields. The strength and spatial width of each localized field is less than required for pair-creation. If, however, the separation between the fields is less than the quantum mechanical tunneling length associated with the corresponding quantum scattering system, the system produces a steady flux of electron-positron pairs. We compute the time-dependence of the pair-creation probability by solving the Dirac equation numerically for various external field sequences. For the special case of two very narrow fields we provide an analytical expression for the pair-creation rate in the long-time limit.2

“…Stimulated by the resurgent interest in the Dirac equation, a plethora of propagation methods were recently developed [103][104][105][106][107][108]. However, to the best our knowledge Ref.…”

Section: Numerical Algorithmmentioning

confidence: 99%

Dirac open-quantum-system dynamics: Formulations and simulations

Cabrera¹,

Campos²,

Bondar³

et al. 2016

We present an open system interaction formalism for the Dirac equation. Overcoming a complexity bottleneck of alternative formulations, our framework enables efficient numerical simulations (utilizing a typical desktop) of relativistic dynamics within the von Neumann density matrix and Wigner phase space descriptions. Employing these instruments, we gain important insights into the effect of quantum dephasing for relativistic systems in many branches of physics. In particular, the conditions for robustness of Majorana spinors against dephasing are established. Using the Klein paradox and tunneling as examples, we show that quantum dephasing does not suppress negative energy particle generation. Hence, the Klein dynamics is also robust to dephasing.