Keyhole Look at Lévy Flights in Subrecoil Laser Cooling

Schaufler, S.; Schleich, Wolfgang P.; Yakovlev, V. P.

doi:10.1103/physrevlett.83.3162

Cited by 32 publications

(22 citation statements)

References 21 publications

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“…This is related to increasing interest in the yet unstudied features of the particle-transport processes in various media. For example, subdiffusion was revealed during the chargecarrier transport in amorphous semiconductors [1] and in the bubble dynamics in a polymer grid [2], whereas superdiffusion is observed in semiconductors [3,4], Richardson's turbulent diffusion [5], quantum optics [6], etc. The main feature of the anomalous diffusion is a nonlinear increase in the mean square of the process (e.g., particle coordinates) with time.…”

Section: Introductionmentioning

confidence: 99%

Accelerated superdiffusion of particles

Utkin

2005

Radiophys Quantum Electron

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We consider a new type of random walks of particles with a jump-like change in acceleration. The corresponding kinetic equations for the probability density of the particle coordinates are derived. The probability density is found to obey the fractional diffusion equation. In this case, both suband superdiffusion appear for a sufficiently rapidly decaying distribution of the random waiting times, which was not observed earlier and is a fundamentally new phenomenon in the theory of anomalous diffusion.

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Section: Introductionmentioning

confidence: 99%

Accelerated superdiffusion of particles

Utkin

2005

Radiophys Quantum Electron

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“…In the range 1 < β ≤ 2 we observe the Markovian-Lévy flights [20], this behavior is represented by the solutions (27) and (29), respectively. For the case when γ = 3/2 and γ < 2, the diffusion exhibits an increment in the amplitude and presents the sub-wave phenomena (superdiffusion), this behavior is represented by the solutions (44) and (47), respectively, the superdiffusion occurs in many physical systems such as rotating flow [43], Richardson turbulent diffusion [44], diffusion of ultracold atoms in an optical lattice [45,46] or quantum optics [47,48], the case γ = 2 represents the ballistic diffusion [20]. The general solutions of the fractional differential equations are given in terms of the Mittag-Leffler functions depending only on a small number of parameters β and γ and related to equation results in a fractal space-time geometry preserving the physical units of the system for any value taken by the exponent of the fractional derivative.…”

Section: Discussionmentioning

confidence: 99%

Modeling and simulation of the fractional space-time diffusion equation

Gómez-Aguilar

Miranda-Hernández

López

et al. 2016

Communications in Nonlinear Science and Numerical Simulation

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“…For the ageing case, one uses the general form (8) of the forward waiting time and the waiting time density (16). The ageing FPTD (cf.…”

Section: Semi-infinite Domainmentioning

confidence: 99%

Ageing first passage time density in continuous time random walks and quenched energy landscapes

Krüsemann

Godec

Metzler

2015

J. Phys. A: Math. Theor.

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We study the first passage dynamics of an ageing stochastic process in the continuous time random walk (CTRW) framework. In such CTRW processes the test particle performs a random walk, in which successive steps are separated by random waiting times distributed in terms of the waiting time probability density function ψ(t) ≃ t −1−α (0 ≤ α ≤ 2). An ageing stochastic process is defined by the explicit dependence of its dynamic quantities on the ageing time t a , the time elapsed between its preparation and the start of the observation. Subdiffusive ageing CTRWs describe systems such as charge carriers in amorphous semiconductors, tracer dispersion in geological and biological systems, or the dynamics of blinking quantum dots. We derive the exact forms of the first passage time density for an ageing subdiffusive CTRW in the semi-infinite, confined, and biased case, finding different scaling regimes for weakly, intermediately, and strongly aged systems: these regimes, with different scaling laws, are also found when the scaling exponent is in the range 1 < α < 2, for sufficiently long t a . We compare our results with the ageing motion of a test particle in a quenched energy landscape. We test our theoretical results in the quenched landscape against simulations: only when the bias is strong enough, the correlations from returning to previously visited sites become insignificant and the results approach the aging CTRW results. With small or without bias, the ageing effects disappear and a change in the exponent compared to the case of a completely annealed landscape can be found, reflecting the build-up of correlations in the quenched landscape.

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Keyhole Look at Lévy Flights in Subrecoil Laser Cooling

Abstract: We propose a method to measure the waiting-time distribution of trapped atoms in subrecoil laser cooling.

Cited by 32 publications

References 21 publications

Accelerated superdiffusion of particles

Accelerated superdiffusion of particles

Modeling and simulation of the fractional space-time diffusion equation

Ageing first passage time density in continuous time random walks and quenched energy landscapes

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