Universality in level spacing fluctuations of a chaotic optical billiard

Laprise, Jean-François; Hosseinizadeh, Ahmad; Lamy-Poirier, Joel; Zomorrodi, Reza; Kröger, J.; Kröger, H.

doi:10.1016/j.physleta.2010.02.057

Cited by 3 publications

(4 citation statements)

References 49 publications

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“…TðH sep þ hj; s; P s Þdj; (26) where T is given by Eq. (20), while the change of the area surrounded by the separatrix DS is…”

Section: Jump Of the Adiabatic Invariantmentioning

confidence: 99%

“…The magnetic billiard serves as a useful model for quantum mechanical problems 15,22,30 and modeling of magnetic properties of materials (diamagnetism, paramagnetism, conductance, magnetic edge state, etc. ), 1,20,26,31,42 interaction of matter with laser field, 21,38 and molecular/atom dynamics. 2,3,37 In the model of magnetic billiards, the magnetic field amplitude controls a regularity level of the billiard motion.…”

Section: Introductionmentioning

confidence: 99%

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Violation of adiabaticity in magnetic billiards due to separatrix crossings

Artemyev

Neishtadt

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We consider dynamics of magnetic billiards with curved boundaries and strong inhomogeneous magnetic field. We investigate a violation of adiabaticity of charged particle motion in this system. The destruction of the adiabatic invariance is due to the change of type of the particle trajectory: particles can drift along the boundary reflecting from it or rotate around the magnetic field at some distance from the boundary without collisions with it. Trajectories of these two types are demarcated in the phase space by a separatrix. Crossings of the separatrix result in jumps of the adiabatic invariant. We derive an asymptotic formula for such a jump and demonstrate that an accumulation of these jumps leads to the destruction of the adiabatic invariance.

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“…TðH sep þ hj; s; P s Þdj; (26) where T is given by Eq. (20), while the change of the area surrounded by the separatrix DS is…”

Section: Jump Of the Adiabatic Invariantmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Violation of adiabaticity in magnetic billiards due to separatrix crossings

Artemyev

Neishtadt

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In order to study the chaotic property of the Lorentz gas in the finite-horizon regime, first we construct the trajectory length matrix Λ, like in Refs. [24] and [25]. For this purpose we consider an array of three adjacent disks , as shown in Fig.…”

Section: Level Spacing Fluctuationsmentioning

confidence: 99%

“…The strategy which we use here, has been demonstrated by Laprise et al in Refs. [24] and [25]. By working on a number of classical chaotic billiards (such as Bunimovich stadium billiard, cardioid billiard and an optical stadium billiard), and using methods of quantum chaos, they have found that universal behavior also occurs in classical chaos.…”

Section: Introductionmentioning

confidence: 99%

Fluctuation Statistics and Diffusive Properties of the 2D Triangular Lorentz Gas in the Finite-Horizon Regime

Hosseinizadeh¹,

Laprise²,

Kröger³

et al. 2011

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We study chaotic behavior and diffusion in the 2D periodic Lorentz gas in the finite-horizon regime. The dynamical observable which we consider is the length of single particle's trajectories, which moves in a triangular array of rigid disks. To analyze the chaoticity of this system, we construct a matrix of the length of trajectories and perform a level spacing analysis of the spectrum of this matrix. We find that a universal behavior occurs both in level spacing distribution and spectral rigidity. In order to examine diffusion in this classical system, we investigate the variance of the length of trajectories versus number of collisions to disks. In the case where there is a finite-horizon, such a variance scales linearly with number of bounces. This shows that a normal diffusion exists and a central limit theorem is maintained in this regime.

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Universality in Statistical Measures of Trajectories in Classical Billiard Systems

Laprise

Hosseinizadeh

Kröger

2015

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For classical billiards, we suggest that a matrix of action or length of trajectories in conjunction with statistical measures, level spacing distribution and spectral rigidity, can be used to distinguish chaotic from integrable systems. As examples of 2D chaotic billiards, we considered the Bunimovich stadium billiard and the Sinai billiard. In the level spacing distribution and spectral rigidity, we found GOE behaviour consistent with predictions from random matrix theory. We studied transport properties and computed a diffusion coefficient. For the Sinai billiard, we found normal diffusion, while the stadium billiard showed anomalous diffusion behaviour. As example of a 2D integrable billiard, we considered the rectangular billiard. We found very rigid behaviour with strongly correlated spectra similar to a Dirac comb. These findings present numerical evidence for universality in level spacing fluctuations to hold in classically integrable systems and in classically fully chaotic systems.

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Universality in level spacing fluctuations of a chaotic optical billiard

Cited by 3 publications

References 49 publications

Violation of adiabaticity in magnetic billiards due to separatrix crossings

Violation of adiabaticity in magnetic billiards due to separatrix crossings

Fluctuation Statistics and Diffusive Properties of the 2D Triangular Lorentz Gas in the Finite-Horizon Regime

Universality in Statistical Measures of Trajectories in Classical Billiard Systems

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