Time independent description of rapidly oscillating potentials
arXiv:nlin/0302023 · doi:10.1103/PhysRevLett.91.110404
Abstract
The classical and quantum dynamics in a high frequency field are found to be described by an effective time independent Hamiltonian. It is calculated in a systematic expansion in the inverse of the frequency () to order . The work is an extension of the classical result for the Kapitza pendulum, which was calculated in the past to order . The analysis makes use of an implementation of the method of separation of time scales and of a quantum gauge transformation in the framework of Floquet theory. The effective time independent Hamiltonian enables one to explore the dynamics in presence of rapidly oscillating fields, in the framework of theories that were developed for systems with time independent Hamiltonians. The results are relevant, in particular, for exploration of the dynamics of cold atoms.
4 pages, 1 figure. Revised version
References in corpus (1)
Cited by in corpus (52)
- Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
- Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
- Many-body energy localization transition in periodically driven systems
- Colloquium: Quantum and Classical Discrete Time Crystals
- Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
- Heating and many-body resonances in a periodically driven two-band system
- Heating rates for an atom in a far-detuned optical lattice
- Floquet Weyl semimetals in light-irradiated type-II and hybrid line-node semimetals
- Parametric Instability Rates in Periodically-Driven Band Systems
- Nonlinear phase-dynamics in a driven Bosonic Josephson junction
- Variational principle for optimal quantum controls in quantum metrology
- Universal fluctuations of Floquet topological invariants at low frequencies
- Absence of Thermalization in Finite Isolated Interacting Floquet Systems
- Floquet Many-body Engineering: Topological and Many-body Physics in Phase Space Lattices
- Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitions
- Realization of a stroboscopic optical lattice for cold atoms with subwavelength spacing
- On periodically driven AdS/CFT
- Diffractionless propagation through Kapitza stratified media
- Acoustic Traps and Lattices for Electrons in Semiconductors
- Floquet Scattering Theory based on Effective Hamiltonians of Driven Systems
- Particle Motion in Rapidly Oscillating Potentials: The Role of the Potential's Initial Phase
- Manipulation of quantum particles in rapidly oscillating potentials by inducing phase hops
- Statistical periodicity in driven quantum systems: General formalism and application to noisy Floquet topological chains
- Driven power-law oscillator
- Phase transitions in intrinsic magnetic topological insulator with high-frequency pumping
- Dynamic stabilization of an optomechanical oscillator
- Characteristic, dynamic, and near saturation regions of Out-of-time-order correlation in Floquet Ising models
- Time-dependent stabilization in AdS/CFT
- Time-independent approximations for periodically driven systems with friction
- Phase-space study of surface-electrode Paul traps: Integrable, chaotic, and mixed motions
- Light-induced Odd-parity Magnetism in Conventional Collinear Antiferromagnets
- Strong Disorder Renormalization for the dynamics of Many-Body-Localized systems : iterative elimination of the fastest degree of freedom via the Floquet expansion
- Rapidly-oscillating scatteringless non-Hermitian potentials and the absence of Kapitza stabilization
- Controlling mobility via rapidly oscillating time-periodic stimulus
- Multiple topological transitions and spectral singularities in non-Hermitian Floquet systems
- Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
- Temporal homogenization of linear ODEs, with applications to parametric super-resonance and energy harvest
- Quantum Brownian motion under rapid periodic forcing
- Wave manipulation via delay-engineered periodic potentials
- Solid-state magnetic traps and lattices
- Complex-Dynamic Origin of Consciousness and the Critical Choice of Sustainability Transition
- Floquet analysis of time-averaged trapping potentials
- Effects of an oscillating field on pattern formation in a ferromagnetic thin film: Analysis of patterns traveling at a low velocity
- Quantum states of the Kapitza pendulum
- Singularities of Floquet Scattering and Tunneling
- Oscillating Fields, Emergent Gravity and Particle Traps
- Mode selectivity of dynamically induced conformation in many-body chain-like bead-spring model
- The Inverted Pendulum as a Classical Analog of the EFT Paradigm
- Low-frequency and Moiré Floquet engineering: a review
- Harmonic oscillator kicked by spin measurements: a Floquet-like system without classical analogous
- Floquet engineering and non-equilibrium topological maps in twisted trilayer graphene
- Dynamical Confinement and Magnetic Traps for Charges and Spins