The quantum Levy walk

Abstract

We introduce the quantum Levy walk to study transport and decoherence in a quantum random model. We have derived from second order perturbation theory the quantum master equation for a \textit{Levy-like particle}that moves along a lattice through hopping scale-free while interacting with a thermal bath of oscillators. The general evolution of the quantum Levy particle has been solved for different preparations of the system. We examine the evolution of the quantum purity, the localized correlation, and the probability to be in a lattice site, all them leading to important conclusions concerning quantum irreversibility and decoherence features. We prove that the quantum thermal mean-square displacement is finite under a constraint that is different when compared to the classical Weierstrass random walk. We prove that when the mean-square displacement is infinite the density of state has a complex null-set inside the Brillouin zone. We show the existence of a critical behavior in the continuous eigenenergy which is related to its non-differentiability and self-affine characteristics. In general our approach allows to study analytically quantum fluctuations and decoherence in a long-range hopping model.

26 pages, 6 figures

References in corpus (5)

• Survival Probabilities in Coherent Exciton Transfer with Trapping
• Photon Counting Statistics For Blinking CdSe-ZnS Quantum Dots: A Levy Walk Process
• Measurements in the Lévy quantum walk
• Universal Behavior of Quantum Walks with Long-Range Steps
• Slow Excitation Trapping in Quantum Transport with Long-Range Interactions

Cited by in corpus (8)

• Quantum walks with sequential aperiodic jumps
• Multiple transitions between normal and hyperballistic diffusion in quantum walks with time-dependent jumps
• Enhancing entanglement with the generalized elephant quantum walk from localized and delocalized states
• Scaling and crossover behaviour in a truncated long range quantum walk
• Unusual scaling in a discrete quantum walk with random long range steps
• Non-equilibrium transition from dissipative quantum walk to classical random walk
• Quantum correlations and coherence between two particles interacting with a thermal bath
• Bath-induced correlations in an infinite-dimensional Hilbert space