On the Quantum Analogue of the Levy Distribution

Bernard H. Lavenda, Mario Compiani

Yuh-Jia Lee, Hsin-Hung Shih

Skander Hachicha

We prove two characterizations of the support projection of a state evolving under the action of a quantum Markov semigroup and a quantum analogue of the Lévy–Austin–Ornstein theorem. We discuss applications to open quantum systems.

Uwe Franz, René Schott

A. V. Ponomarev, S. Denisov, Peter Hänggi A

The L\'evy distribution, previously used to describe complex behavior of classical systems, is shown to characterize that of quantum many-body systems. Using two complimentary approaches, the canonical and grand-canonical formalisms, we discovered that the momentum profile of a Tonks-Girardeau gas---a one-dimensional gas of $N$ impenetrable (hard-core) bosons--harmonically confined on a lattice at finite temperatures obeys a L\'evy distribution. Finally, we extend our analysis to different confinement setups and demonstrate that the tunable L\'evy distribution properly reproduces momentum profiles in experimentally accessible regions. Our finding allows for calibration of complex many-body quantum states by using a unique scaling exponent.

A. Romanelli

We study the quantum walk subjected to measurements with a L\'evy waiting-time distribution. We find that the system has a sub-ballistic behavior instead of a diffusive one. We obtain an analytical expression for the exponent of the power law of the variance as a function of the characteristic parameter of the L\'evy distribution.