Comparing the Ratchet Effects of Cold Atoms in Periodically Symmetric and Asymmetric Optical Potentials

Physics Research International ◽

10.1155/2015/706527 ◽

2015 ◽

Vol 2015 ◽

pp. 1-7

Author(s):

Nkongho Ayuketang Arreyndip ◽

Kenfack Anatole

Keyword(s):

Phase Space ◽

Floquet Theory ◽

Cold Atoms ◽

Chaotic Behaviour ◽

Time Dependent ◽

Ratchet Effect ◽

Optical Potentials ◽

Asymmetric Case ◽

Ac Fields ◽

Time Periodic

We consider a particle in a spatial symmetric/asymmetric potential driven by time periodic bichromatic AC fields of ratchet type. The associated time-dependent Schrödinger equation is conveniently tackled with the Floquet theory. We next proceed to investigate the ratchet effect induced by the driver, comparing the symmetric with the asymmetric cases. It turns out that the current in the asymmetric case is stronger than that of the symmetric one. Besides, we also investigate the case where the driver is a delta kicked acting on our spatial potential with more emphasis on its chaotic behaviour. Here we check that the current emerges as the phase space is mixed and that the system with asymmetric spatial potential becomes more chaotic than the symmetric one at low kicking strength.

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Autonomous Geometrical Mechanics

10.1093/oso/9780198822370.003.0022 ◽

2018 ◽

Author(s):

Peter Mann

Keyword(s):

Phase Space ◽

Contact Structure ◽

Invariant Tori ◽

Time Dependent ◽

Contact Structures ◽

Natural Setting ◽

Adiabatic Invariance ◽

Jet Bundle ◽

Integrability Theorem ◽

Extended Phase

This chapter examines the structure of the phase space of an integrable system as being constructed from invariant tori using the Arnold–Liouville integrability theorem, and periodic flow and ergodic flow are investigated using action-angle theory. Time-dependent mechanics is formulated by extending the symplectic structure to a contact structure in an extended phase space before it is shown that mechanics has a natural setting on a jet bundle. The chapter then describes phase space of integrable systems and how tori behave when time-dependent dynamics occurs. Adiabatic invariance is discussed, as well as slow and fast Hamiltonian systems, the Hannay angle and counter adiabatic terms. In addition, the chapter discusses foliation, resonant tori, non-resonant tori, contact structures, Pfaffian forms, jet manifolds and Stokes’s theorem.

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Time-dependent relaxed magnetohydrodynamics: Inclusion of cross helicity constraint using phase-space action

Physics of Plasmas ◽

10.1063/5.0005740 ◽

2020 ◽

Vol 27 (6) ◽

pp. 062504 ◽

Cited By ~ 1

Author(s):

R. L. Dewar ◽

J. W. Burby ◽

Z. S. Qu ◽

N. Sato ◽

M. J. Hole

Keyword(s):

Phase Space ◽

Time Dependent ◽

Space Action

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A Realization of a Quasi-Random Walk for Atoms in Time-Dependent Optical Potentials

Atoms ◽

10.3390/atoms3030433 ◽

2015 ◽

Vol 3 (3) ◽

pp. 433-449 ◽

Cited By ~ 1

Author(s):

Torsten Hinkel ◽

Helmut Ritsch ◽

Claudiu Genes

Keyword(s):

Random Walk ◽

Time Dependent ◽

Optical Potentials

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Phase space theory of Bose–Einstein condensates and time-dependent modes

Annals of Physics ◽

10.1016/j.aop.2012.06.005 ◽

2012 ◽

Vol 327 (10) ◽

pp. 2432-2490 ◽

Cited By ~ 2

Author(s):

B.J. Dalton

Keyword(s):

Phase Space ◽

Time Dependent ◽

Space Theory ◽

Phase Space Theory ◽

Bose Einstein

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CHAOTIC SCATTERING IN TIME-DEPENDENT HAMILTONIAN SYSTEMS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127491000488 ◽

1991 ◽

Vol 01 (03) ◽

pp. 667-679 ◽

Cited By ~ 12

Author(s):

YING-CHENG LAI ◽

CELSO GREBOGI

Keyword(s):

Phase Space ◽

Measure Zero ◽

Invariant Set ◽

Time Dependent ◽

Invariant Sets ◽

Physical Origin ◽

Chaotic Scattering ◽

Periodic Oscillations ◽

Surface Of Section ◽

Oscillating Potential

We consider the classical scattering of particles in a one-degree-of-freedom, time-dependent Hamiltonian system. We demonstrate that chaotic scattering can be induced by periodic oscillations in the position of the potential. We study the invariant sets on a surface of section for different amplitudes of the oscillating potential. It is found that for small amplitudes, the phase space consists of nonescaping KAM islands and an escaping set. The escaping set is made up of a nonhyperbolic set that gives rise to chaotic scattering and remains of KAM islands. For large amplitudes, the phase space contains a Lebesgue measure zero invariant set that gives rise to chaotic scattering. In this regime, we also discuss the physical origin of the Cantor set responsible for the chaotic scattering and calculate its fractal dimension.

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Energy dissipation and fluctuations in a driven liquid

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1713573115 ◽

2018 ◽

Vol 115 (14) ◽

pp. 3569-3574 ◽

Cited By ~ 11

Author(s):

Clara del Junco ◽

Laura Tociu ◽

Suriyanarayanan Vaikuntanathan

Keyword(s):

Phase Transition ◽

Steady State ◽

Time Reversal ◽

Time Dependent ◽

Time Reversal Symmetry ◽

Nonequilibrium Systems ◽

Minimal Models ◽

Stochastic Thermodynamics ◽

Periodic Steady State ◽

Time Periodic

Minimal models of active and driven particles have recently been used to elucidate many properties of nonequilibrium systems. However, the relation between energy consumption and changes in the structure and transport properties of these nonequilibrium materials remains to be explored. We explore this relation in a minimal model of a driven liquid that settles into a time periodic steady state. Using concepts from stochastic thermodynamics and liquid state theories, we show how the work performed on the system by various nonconservative, time-dependent forces—this quantifies a violation of time reversal symmetry—modifies the structural, transport, and phase transition properties of the driven liquid.

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Clocking the buildup dynamics of light-induced states through attosecond transient absorption spectrum

Journal of Physics B Atomic Molecular and Optical Physics ◽

10.1088/1361-6455/ac3847 ◽

2021 ◽

Author(s):

Xiaoxia Wu ◽

Shaofeng Zhang ◽

Difa Ye

Keyword(s):

Floquet Theory ◽

Transient Absorption ◽

Scaling Law ◽

Time Lag ◽

Time Dependent ◽

Transient Absorption Spectroscopy ◽

Transient Absorption Spectrum ◽

Wide Range ◽

Maximal Shift ◽

Buildup Time

Abstract The buildup processes of the light-induced states (LISs) in attosecond transient absorption spectroscopy are studied by solving the time-dependent Schrödinger equation and compared with the quasistatic Floquet theory, revealing a time lag of the maximal shift and strongest absorbance of the LIS with respect to the zero delay that is referred to as the buildup time. We analytically derive a scaling law for the buildup time that conﬁrms the numerical results over a wide range of detunings. Our theory veriﬁes the commonly accepted scenario of nearly instantaneous response of matter to light if the pump ﬁeld is blue-detuned, but some differences are found in the near-resonant and red-detuning cases. Implications of the buildup time in petahertz optoelectronics are discussed.

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Canonical Perturbation of a Fast Time-Periodic Hamiltonian via Liapunov-Floquet Transformation

Volume 1C: 16th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc97/vib-4107 ◽

1997 ◽

Author(s):

Eric A. Butcher ◽

S. C. Sinha

Keyword(s):

Perturbation Theory ◽

Classical Method ◽

Time Dependent ◽

Fast Time ◽

Quadratic Part ◽

Canonical Perturbation ◽

Internal Excitation ◽

Quadratic Hamiltonian ◽

Unperturbed Part ◽

Time Periodic

Abstract In this study a possible application of time-dependent canonical perturbation theory to a fast nonlinear time-periodic Hamiltonian with strong internal excitation is considered. It is shown that if the time-periodic unperturbed part is quadratic, the Hamiltonian may be canonically transformed to an equivalent form in which the new unperturbed part is time-invariant so that the time-dependent canonical perturbation theory may be successfully applied. For this purpose, the Liapunov-Floquet (L-F) transformation and its inverse associated with the unperturbed time-periodic quadratic Hamiltonian are computed using a recently developed technique. Action-angle variables and time-dependent canonical perturbation theory are then utilized to find the solution in the original coordinates. The results are compared for accuracy with solutions obtained by both numerical integration and by the classical method of directly applying the time-dependent perturbation theory in which the time-periodic quadratic part is treated as another perturbation term. A strongly excited Mathieu-Hill quadratic Hamiltonian with a cubic perturbation and a nonlinear time-periodic Hamiltonian without a constant quadratic part serve as illustrative examples. It is shown that, unlike the classical method in which the internal excitation must be weak, the proposed formulation provides accurate solutions for an arbitrarily large internal excitation.

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