Saar Rahav

Effective Hamiltonians for periodically driven systems

The dynamics of classical and quantum systems, which are driven by a high-frequency

Time independent description of rapidly oscillating potentials.

(\ensuremath{\omega})

Trapping of particles by lasers: the quantum Kapitza pendulum

field, is investigated. For classical systems, the motion is separated into a slow part and a fast part. The motion for the slow part is computed perturbatively in powers of

Stimulated coherent anti-Stokes Raman spectroscopy (CARS) resonances originate from double-slit interference of two-photon Stokes pathways

{\ensuremath{\omega}}^{\ensuremath{-}1}

Fluctuation relations and coarse-graining

to the order

Quantum-Classical Correspondence Principle for Work Distributions

{\ensuremath{\omega}}^{\ensuremath{-}4},

Quantum heat engines: A thermodynamic analysis of power and efficiency

and the corresponding time independent Hamiltonian is calculated. Such an effective Hamiltonian for the corresponding quantum problem is computed to the order

Time-dependent Hamiltonians with 100% evolution speed efficiency

{\ensuremath{\omega}}^{\ensuremath{-}4}

Manipulating stimulated coherent anti-Stokes Raman spectroscopy signals by broad-band and narrow-band pulses

in a high-frequency expansion. Its spectrum is the quasienergy spectrum of the time dependent quantum system. The classical limit of this effective Hamiltonian is the classical effective time independent Hamiltonian. It is demonstrated that this effective Hamiltonian gives the exact quasienergies and quasienergy states of some simple examples, as well as the lowest resonance of a nontrivial model for an atom trap. The theory that is developed in this paper is useful for the analysis of atomic motion in atom traps of various shapes.

Spectral statistics of rectangular billiards with localized perturbations

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 (omega) to order omega(-4). The work is an extension of the classical result for the Kapitza pendulum, which was calculated in the past to order omega(-2). 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 the 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 exploring the dynamics of cold atoms.