Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0208035 · Fortschritte der Physik

Kicked rotor in Wigner phase space

M. Bienert, F. Haug, W.P. Schleich, M.G. Raizen

Published Apr 24, 2003• 7 citations
arXivHTMLPDF

Abstract

Abstract We develop the Wigner phase space representation of a kicked particle for an arbitrary but periodic kicking potential. We use this formalism to illustrate quantum resonances and anti‐resonances.
DOI
10.1002/prop.200310065

Related papers

Kicked Rotor in Wigner Phase Space

Marc Bienert, Florian Haug, Wolfgang P. Schleich +1 more

We develop the Wigner phase space representation of a kicked particle for an arbitrary but periodic kicking potential. We use this formalism to illustrate quantum resonances and anti--resonances.

•Jan 1, 2002•5 citations

Kicked-rotor quantum resonances in position space

Maxence Lepers, Véronique Zehnlé, Jean Claude Garreau

We present an approach of the kicked-rotor quantum resonances in position space, based on its analogy with the optical Talbot effect. This leads to a very simple picture of the physical mechanism underlying the dynamics and to analytical expressions for relevant physical quantities. The ballistic behavior, which is closely associated with quantum resonances, is analyzed and shown to emerge from a coherent adding of successive kicks thanks to a periodic reconstruction of the spatial wave packet.

arXiv:0711.1674•Physical Review A•Apr 24, 2008•28 citations

The Quantum Kicked Rotor: A Paradigm of Quantum Chaos. Foundational aspects and new perspectives

Giuliano Benenti, Giulio Casati, Jiangbin Gong +1 more

The kicked rotor provides a simple yet powerful model for introducing many of the central concepts of classical and quantum chaos. Despite its apparent simplicity, it exhibits rich dynamical behavior and has found applications across a wide range of fields, including atomic and optical physics, condensed matter physics, and emerging quantum technologies. This chapter begins by exploring foundational ideas using the kicked rotor as a unifying framework. We first discuss the transition from regular to chaotic motion in the classical system, and then introduce key quantum phenomena such as dynamical localization and quantum resonances. Special attention is devoted to the emergence of characteristic time scales and their role in the quantum-classical correspondence. To make these ideas more concrete, we also provide a brief overview of experimental realizations of the kicked rotor and its variants, illustrating how theoretical concepts are implemented in practice. In the second part of the chapter, we guide the reader toward more recent and advanced developments. Topics include near-resonant dynamics, topological features of kicked systems, the emergence of quantum dynamical phases inferred from classical transport properties, and extensions to non-Hermitian physics. We conclude with a discussion of open problems and future perspectives, outlining directions in which the kicked rotor continues to offer valuable insights.

quant-pharXiv:2604.12316•Apr 15, 2026•0 citations

Relativistic kicked rotor

D. U. Matrasulov, G. M. Milibaeva, Uktam Salomov +1 more

Transport properties in the relativistic analog of the periodically kicked rotor are contrasted under classically and quantum mechanical dynamics. The quantum rotor is treated by solving the Dirac equation in the presence of the time-periodic delta-function potential resulting in a relativistic quantum mapping describing the evolution of the wave function. The transition from the quantum suppression behavior seen in the nonrelativistic limit to agreement between quantum and classical analyses in the relativistic regime is discussed. The absence of quantum resonances in the relativistic case is also addressed.

Physical Review E•Jul 19, 2005•18 citations

Quantum Resonances of the Kicked Rotor and the SU(q) Group

V. V. Sokolov, O. V. Zhirov, Daniel Alonso +1 more

The quantum kicked rotor map is embedded into a continuous unitary transformation generated by a time-independent quasi Hamiltonian. In some vicinity of a quantum resonance of order q, we relate the problem to the regular motion along a circle in a (q(2)-1) component inhomogeneous "magnetic" field of a quantum particle with q intrinsic degrees of freedom described by the SU(q) group. This motion is in parallel with the classical phase oscillations near a nonlinear resonance.

arXiv:chao-dyn/9907033•Physical Review Letters•Apr 17, 2000•29 citations

Fidelity of the near-resonant quantum kicked rotor

Probst, B., R. Dubertrand, Wimberger, S.

We present a perturbative result for the temporal evolution of the fidelity of the quantum kicked rotor, i.e. the overlap of the same initial state evolved with two slightly different kicking strengths, for kicking periods close to a principal quantum resonance. Based on a pendulum approximation, we describe the fidelity for rotational orbits in the pseudo-classical phase space of a corresponding classical map. Our results are compared to numerical simulations indicating the range of applicability of our analytical approximation.

•Jan 1, 2011•3 citations
The kicked rotor provides a simple yet powerful model for introducing many of the central concepts of classical and quantum chaos. Despite its apparent simplicity, it exhibits rich dynamical behavior and has found applications across a wide range of fields, including atomic and optical physics, condensed matter physics, and emerging quantum technologies. This chapter begins by exploring foundational ideas using the kicked rotor as a unifying framework. We first discuss the transition from regular to chaotic motion in the classical system, and then introduce key quantum phenomena such as dynamical localization and quantum resonances. Special attention is devoted to the emergence of characteristic time scales and their role in the quantum-classical correspondence. To make these ideas more concrete, we also provide a brief overview of experimental realizations of the kicked rotor and its variants, illustrating how theoretical concepts are implemented in practice. In the second part of the chapter, we guide the reader toward more recent and advanced developments. Topics include near-resonant dynamics, topological features of kicked systems, the emergence of quantum dynamical phases inferred from classical transport properties, and extensions to non-Hermitian physics. We conclude with a discussion of open problems and future perspectives, outlining directions in which the kicked rotor continues to offer valuable insights.
Transport properties in the relativistic analog of the periodically kicked rotor are contrasted under classically and quantum mechanical dynamics. The quantum rotor is treated by solving the Dirac equation in the presence of the time-periodic delta-function potential resulting in a relativistic quantum mapping describing the evolution of the wave function. The transition from the quantum suppression behavior seen in the nonrelativistic limit to agreement between quantum and classical analyses in the relativistic regime is discussed. The absence of quantum resonances in the relativistic case is also addressed.
We present a perturbative result for the temporal evolution of the fidelity of the quantum kicked rotor, i.e. the overlap of the same initial state evolved with two slightly different kicking strengths, for kicking periods close to a principal quantum resonance. Based on a pendulum approximation, we describe the fidelity for rotational orbits in the pseudo-classical phase space of a corresponding classical map. Our results are compared to numerical simulations indicating the range of applicability of our analytical approximation.