Diffusion transitions in a 2D periodic lattice. (English) Zbl 07540485
Summary: Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional “soft” billiard, classically modeled from an optical lattice Hamiltonian system, is used to study diffusion transitions under variation of the control parameters. Sudden transitions between normal and ballistic regimes are found and characterized by inspection of topological changes in phase-space. Transitions correlated with increases in global stability area are shown to occur for energy levels where local maxima points become accessible, deviating trajectories approaching them. These instabilities promote a slowing down of the dynamics and an island myriad bifurcation phenomenon, along with the suppression of long flights within the lattice. Other diffusion regime variations occurring within small intervals of control parameters are shown to be related to the emergence of a set of orbits with long flights, thus altering the total average displacement for long integration times but without global changes in phase-space.
MSC:
| 82Cxx | Time-dependent statistical mechanics (dynamic and nonequilibrium) |
| 37Dxx | Dynamical systems with hyperbolic behavior |
| 65Lxx | Numerical methods for ordinary differential equations |
References:
| [1] | Bloch, I., Ultracold quantum gases in optical lattices, Nat Phys, 1, 23-30 (2005) |
| [2] | Bloch, I.; Dalibard, J.; Zwerger, W., Many-body physics with ultracold gases, Rev Modern Phys, 80, 885-964 (2008) |
| [3] | Hemmerich, A.; Schropp Jr, D.; Hänsch, T. W., Light forces in two crossed standing waves with controlled time-phase difference, Phys Rev A, 44, 3, 1911-1921 (1991) |
| [4] | Monteiro, T. S.; Dando, P. A.; Hutchings, N. A.C.; Isherwood, M. R., Proposal for a chaotic ratchet using cold atoms in optical lattices, Phys Rev Lett, 89, 19, 194102:1-4 (2002) |
| [5] | Kleva, R. G.; Drake, J. F., Stochastic ExB particle transport, Phys Fluids, 27, 7, 1686-1698 (1984) · Zbl 0573.76117 |
| [6] | Horton, W., Nonlinear drift waves and transport in magnetized plasma, Phys Rep, 192, 1-3, 1-177 (1990) |
| [7] | Yu, S.-P.; Muniz, J. A.; Hung, C.-L.; Kimble, H. J., Two-dimensional photonic crystals for engineering atom-light interactions, Proc Natl Acad Sci USA, 116, 26, 12743-12751 (2019) |
| [8] | Sholl, D. S.; Skodje, R. T., Diffusion of xenon on a platinum surface: The influence of correlated flights, Physica D, 71, 168-184 (1994) |
| [9] | Thommen, Q.; Garreau, J. C.; Zehnlé, V., Classical chaos with Bose-Einstein condensates in tilted optical lattices, Phys Rev Lett, 91, 21, 1-4 (2003) |
| [10] | Prants, S. V., Light-induced atomic elevator in optical lattices, JETP Lett, 104, 11, 749-753 (2016) |
| [11] | Prants, S. V.; Kon’kov, L. E., On the possibility of observing chaotic motion of cold atoms in rigid optical lattices, Quantum Electron, 47, 5, 446-450 (2017) |
| [12] | Zaslavsky, G. M.; Sagdeev, R. Z.; Chaikovsky, D. K.; Chernikov, A. A., Chaos and two-dimensional random walk in periodic and quasiperiodic fields, Sov Phys—JETP, 68, 5, 995-1000 (1989) |
| [13] | Bagchi, B.; Zwanzig, R.; Marchetti, M. C., Diffusion in a two-dimensional periodic potential, Phys Rev A, 31, 2, 892-896 (1985) |
| [14] | Machta, J.; Zwanzig, R., Diffusion in a periodic Lorentz gas, Phys Rev Lett, 50, 25, 1959-1962 (1983) · Zbl 0974.82505 |
| [15] | Kroetz, T.; Oliveira, H. A.; Portela, J. S.E.; Viana, R. L., Dynamical properties of the soft-wall elliptical billiard, Phys Rev E, 94, Article 022218 pp. (2016) |
| [16] | Kaplan, A.; Friedman, N.; Andersen, M.; Davidson, N., Stable regions and singular trajectories in chaotic soft-wall billiards, Physica D, 187, 136-145 (2004) · Zbl 1045.37055 |
| [17] | Reichl, L. E., The transition to chaos in conservative classical systems (1992), Springer-Verlag: Springer-Verlag New York · Zbl 0776.70003 |
| [18] | Argonov, V. Yu.; Prants, S. V., Fractals and chaotic scattering of atoms in the field of a standing light wave, J Exp Theor Phys, 96, 5, 832-845 (2003) |
| [19] | Argonov, V. Yu.; Prants, S. V., Nonlinear coherent dynamics of an atom in an optical lattice, J Russ Laser Res, 27, 4, 360-378 (2006) |
| [20] | Prants, S. V., Weak chaos with cold atoms in a 2D optical lattice with orthogonal polarizations of laser beams, J Russ Laser Res, 40, 3, 213-220 (2019) |
| [21] | Zaslavsky, G. M.; Tippett, M. K., Connection between recurrence-time statistics and anomalous transport, Phys Rev Lett, 67, 23, 3251-3254 (1991) |
| [22] | Zaslavsky, G. M., Chaos, fractional kinetics, and anomalous transport, Phys Rep, 371, 461-580 (2002) · Zbl 0999.82053 |
| [23] | Zaslavsky, G. M.; Stevens, D.; Weitzner, H., Self-similar transport in incomplete chaos, Phys Rev E, 48, 3, 1683-1694 (1993) |
| [24] | Chaikovsky, D. K.; Zaslavsky, G. M., Channeling and percolation in two-dimensional chaotic dynamics, Chaos, 1, 463-472 (1991) · Zbl 0902.60086 |
| [25] | Horsley, E.; Koppell, S.; Reichl, L. E., Chaotic dynamics in a two-dimensional optical lattice, Phys Rev E, 89, Article 012917 pp. (2014) |
| [26] | Porter, M. D.; Barr, A.; Barr, A.; Reichl, L. E., Chaos in the band structure of a soft Sinai lattice, Phys Rev E, 95, Article 052213 pp. (2017) |
| [27] | Porter, M. D.; Reichl, L. E., Chaos in the honeycomb optical-lattice unit cell, Phys Rev E, 93, Article 012204 pp. (2016) |
| [28] | Argonov, V. Yu.; Prants, S. V., Theory of chaotic atomic transport in an optical lattice, Phys Rev A, 75, Article 063428 pp. (2007) |
| [29] | Mandal, D.; Elskens, Y.; Leoncini, X.; Lemoine, N.; Doveil, F., Sticky islands in stochastic webs and anomalous chaotic cross-field particle transport by ExB electron drift instability, Chaos Solitons Fractals, 145, Article 110810 pp. (2021) |
| [30] | Cash, J. R.; Karp, A. H., A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides, ACM Trans Math Software, 16, 201-222 (1990) · Zbl 0900.65234 |
| [31] | Tao, M., Explicit symplectic approximation of nonseparable Hamiltonians: Algorithm and long time performance, Phys Rev E, 94, Article 043303 pp. (2016) |
| [32] | Gottwald, G. A.; Skokos, C. H.; Laskar, J., Chaos detection and predictability (2015), Springer-Verlag: Springer-Verlag Berlin Heidelberg |
| [33] | Skokos, C.; Bountis, T.; Antonopoulos, C. G.; Vrahatis, M. N., Detecting order and chaos in Hamiltonian systems by the SALI method, J Phys A: Math Gen, 37, 6269-6284 (2004) |
| [34] | Baranger, M.; Davies, K. T.R.; Mahoney, J. H., The calculation of periodic trajectories, Ann Physics, 186, 95-110 (1988) · Zbl 0651.58031 |
| [35] | Simonović, N. S., Calculations of periodic orbits: The monodromy method and application to regularized systems, Chaos, 9, 4, 854-864 (1999) · Zbl 0977.34033 |
| [36] | Elskens, Y.; Escande, D. F., Infinite resonance overlap: A natural limit for Hamiltonian chaos, Physica D, 62, 66-74 (1993) · Zbl 0783.58045 |
| [37] | de Sousa, M. C.; Caldas, I. L.; de Almeida, A. M. Ozorio; Rizzato, F. B.; Pakter, R., Alternate islands of multiple isochronous chains in wave-particle interactions, Phys Rev E, 88, Article 064901 pp. (2013) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
