<i>Quantum Chaos: A New Paradigm of Nonlinear Dynamics</i>

Nakamura, Katsuhiro; Gutzwiller, Martin C.

doi:10.1063/1.2808134

Cited by 35 publications

(65 citation statements)

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“…Mesoscopic quantum dots have recently attracted much interest, as a new experimental probe for studying the manifestations of classical dynamics in quantum systems [1][2][3][4][5][6][7][8][9][10][11]. While precise details may differ between experiments, the devices generally consist of some central scattering region, patterned on a length scale smaller than the elastic mean free path, which is connected to source and drain reservoirs via tunable, quantum point contact leads.…”

Section: Introductionmentioning

confidence: 99%

The role of lead openings in regular mesoscopic billiards

Bird

Ferry

Akis

et al. 1996

Superlattices and Microstructures

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Section: Introductionmentioning

confidence: 99%

The role of lead openings in regular mesoscopic billiards

Bird

Ferry

Akis

et al. 1996

Superlattices and Microstructures

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“…However, it has been shown by several authors [14,15,16] that the parametric change of the eigenvalues and eigenstates of a Hamiltonian H = H 0 + λV upon variation of the real scalar λ can be understood as the many-particle dynamics of N fictious classical particles moving along a one dimensional curve, parametrized by the fictitious time λ (for a review of such an approach see [2,17]). The set of canonical variables in which this dynamics can be formulated as a Hamiltonian problem is given by the eigenvalues x j , their derivatives with respect to λ, p j = dx j /dλ, and the coupling strengths L ij between particle pairs, which themselves are independent dynamical variables and resemble the generalized angular momenta when the algebraic structure of the corresponding Poisson brackets is analyzed [2].…”

Section: Introductionmentioning

confidence: 99%

Nondispersive wave packets as solitonic solutions of level dynamics

Zakrzewski

Buchleitner

Delande

1997

Z. Phys. B - Condensed Matter

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We discuss the analogy between nondispersive wave packets in periodically driven hydrogen atoms and solitons as solitary wave solutions of nonlinear dynamical systems. Whereas the wave packet eigenstates should not be considered as solitons propagating in real space, they are shown to display the essential features of solitonic solutions as they propagate through the irregular lattice of quasienergy levels evolving with a fictitious time like the strength or the frequency of the driving force.

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“…One may conceive non-dispersive wave-packets as solitonic solutions of particular nonlinear equations, propagating not in time, but in parameter space [63]. The evolution of energy levels in such a space, called "parametric level dynamics", has been extensively studied (see [15,195] for reviews), both for time-independent and for periodically time-dependent systems. In the latter case, the energy levels are the quasi-energies of the Floquet Hamiltonian (see sec.…”

Section: Non-dispersive Wave-packet As a Solitonmentioning

confidence: 99%

“…For example, in CP, it has been shown that there are three eigenfrequencies, eqs. (194,195), in the harmonic approximation -see section 3.4.4. This results in a large number of excited energy levels which may have avoided crossings with the "ground state", i.e.…”

Section: Preparation Through Tailored Pulsesmentioning

confidence: 99%

Non-dispersive wave packets in periodically driven quantum systems

2002

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With the exception of the harmonic oscillator, quantum wave packets usually spread as time evolves. This is due to the non-linear character of the classical equations of motion which makes the various components of the wave packet evolve at various frequencies. We show here that, using the non-linear resonance between an internal frequency of a system and an external periodic driving, it is possible to overcome this spreading and build non-dispersive (or non-spreading) wave packets which are well localized and follow a classical periodic orbit without spreading. From the quantum mechanical point of view, the non-dispersive wave packets are time periodic eigenstates of the Floquet Hamiltonian, localized in the non-linear resonance island. We discuss the general mechanism which produces the non-dispersive wave packets, with emphasis on simple realization in the electronic motion of a Rydberg electron driven by a microwave field. We show the robustness of such wave packets for a model one-dimensional as well as for realistic three-dimensional atoms. We consider their essential properties such as the stability versus ionization, the characteristic energy spectrum and long lifetimes. The requirements for experiments aimed at observing such non-dispersive wave packets are also considered. The analysis is extended to situations in which the driving frequency is a multiple of the internal atomic frequency. Such a case allows us to discuss non-dispersive states composed of several, macroscopically separated wave packets communicating among themselves by tunneling. Similarly we briefly discuss other closely related phenomena in atomic and molecular physics as well as possible further extensions of the theory. (C) 2002 Elsevier Science B.V. All rights reserved

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Quantum Chaos: A New Paradigm of Nonlinear Dynamics

Cited by 35 publications

References 0 publications

The role of lead openings in regular mesoscopic billiards

The role of lead openings in regular mesoscopic billiards

Nondispersive wave packets as solitonic solutions of level dynamics

Non-dispersive wave packets in periodically driven quantum systems

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