Accelerator dynamics of a fractional kicked rotor

2006/09/14 by Alexander Iomin, A. Iomin · 2 citations
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #nlin.CD

paper · pdf · doi:10.1103/physreve.75.037201

published as Phys. Rev. E 75, 037201 (2007) · Submitted for publication in Phys. Rev. E

arxiv created 2006/09/14 · openalex publication_date 2007/03/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that the Weyl fractional derivative can quantize an open system. A fractional kicked rotor is studied in the framework of the fractional Schrödinger equation. The system is described by the non-Hermitian Hamiltonian by virtue of the Weyl fractional derivative. Violation of space symmetry leads to acceleration of the orbital momentum. Quantum localization saturates this acceleration, such that the average value of the orbital momentum can be a direct current and the system behaves like a ratchet. The classical counterpart is a nonlinear kicked rotor with absorbing boundary conditions.

Citations

• Calculus for Functions of Noncommuting Operators and General Phase-Space Methods in Quantum Mechanics. I. Mapping Theorems and Ordering of Functions of Noncommuting Operators
• On the Quantum Correction For Thermodynamic Equilibrium

Cited by

• Quantum mechanics in fractional and other anomalous spacetimes
• The DuBois–Reymond Fundamental Lemma of the Fractional Calculus of Variations and an Euler–Lagrange Equation Involving Only Derivatives of Caputo