Quantum walks, Dirac fermions, Lindblad equation, and relativistic diffusions
September 18th, 2019 PABLO ARNAULT Instituto de Física Corpuscular (IFIC)

We first present two models of one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): a model with coin-depolarizing channels, and a model with random coin operations. We then show that both these models admit the same limit to the spacetime continuum, namely, a Lindblad equation with Dirac-fermion Hamiltonian part and, as Lindblad jumps, a chirality flip and a chirality-dependent phase flip, which are two standard depolarizing channels for a two-level quantum system. We then show, both analytically and numerically, that this Lindblad equation provides a model of quantum relativistic diffusion. This model of diffusion in position space has the intriguing specificity of making sense only on originally unitary models which are relativistic, i.e., which have chirality as internal degree of freedom. For a particle with vanishing mass, our model of quantum relativistic diffusion reduces to the well-known telegraph equation, which yields propagation at short times, and diffusion at long times (and exhibits no quantumness). Finally, we show analytically that the continuum-limit procedure introduced to treat temporal coin noise on DTQWs, can be extended with spatial noise on the coin.

Seminar, September 18, 2019, 15:00. ICFO’s Seminar Room

Hosted by Prof. Maciej Lewenstein