On how the (1+1)-dimensional Dirac equation arises in classical physics

Bernard H. Lavenda

Agung Trisetyarso

We present the recent works \cite{trisetyarso2011} on the application of Darboux transformation on one-dimensional Dirac equation related to the field of Quantum Information and Computation (QIC). The representation of physical system in one-dimensional equation and its transformation due to the Bagrov, Baldiotti, Gitman, and Shamshutdinova (BBGS)-Darboux transformation showing the possibility admitting the concept of relativity and the trade-off of concurrent condition of quantum and classical physics play into the area of QIC. The applications in cavity quantum electrodynamics and on the proposal of quantum transistor are presented.

Garnet N. Ord, D. G. C. McKeon

Yu Zhang, Jianwen Xu, Zhuang Ma +4 more

The Dirac equation elucidates fundamental physical principles and predicts significant physical phenomena. Its simulation further offers explanations for subsequent physics observations. We map the 3+1-dimensional Dirac equation onto the first excited manifold of four qubits to simulate the internal four-component spinor dynamics. Additionally, we simulate two intriguing and challenging-to-implement physical phenomena: the Zitterbewegung effect and the Sauter-Schwinger effect. Compared to previous simulations, our system provides a larger parameter space, allowing for a more comprehensive exploration of physical properties. This work enhances our understanding of spinor dynamics. The Dirac equation, one of the most fundamental equations in relativistic quantum mechanics, has influenced diverse research fields. The authors demonstrate an analogue simulation of the 3+1-dimensional Dirac equation by applying parametric modulations in superconducting circuits.

Jaromir Tosiek, Luca Campobasso

Christian Koke, Changsuk Noh, Dimitris G. Angelakis

The main objective of this work is to present a theoretical proposal for an implementation of the ($2+1$)-dimensional Dirac equation in classical gravitational and electromagnetic backgrounds, in a two-dimensional waveguide array. For this, a framework for achieving site-dependent effective coupling constants in two-dimensional waveguide arrays is developed. Implementability of the Dirac equation under the proposed scheme puts minor demands on gauge and spacetime backgrounds; however, a wide array of physical spacetimes, such as all vacuum and static solutions, prove to be implementable. As an interesting and instructive example, we discuss a tabletop realization of the gravitational Aharonov-Bohm effect: After devising a thought experiment in which signatures of the gravitational Aharonov-Bohm effect could be detected, we briefly discuss how the analog of such a setting can in principle be implemented using the proposed waveguide setup.