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Siemens A, Schmelcher P. External-field-induced dynamics of a charged particle on a closed helix. Phys Rev E 2021; 103:052217. [PMID: 34134278 DOI: 10.1103/physreve.103.052217] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2021] [Accepted: 05/07/2021] [Indexed: 11/07/2022]
Abstract
We investigate the dynamics of a charged particle confined to move on a toroidal helix while being driven by an external time-dependent electric field. The underlying phase space is analyzed for linearly and circularly polarized fields. For small driving amplitudes and a linearly polarized field, we find a split up of the chaotic part of the phase space, which prevents the particle from inverting its direction of motion. This allows for a nonzero average velocity of chaotic trajectories without breaking the well-known symmetries commonly responsible for directed transport. Within our chosen normalized units, the resulting average transport velocity is constant and does not change significantly with the driving amplitude. A very similar effect is found in case of the circularly polarized field and low driving amplitudes. Furthermore, when driving with a circularly polarized field, we unravel a second mechanism of the split up of the chaotic phase space region for very large driving amplitudes. There exists a wide range of parameter values for which trajectories may travel between the two chaotic regions by crossing a permeable cantorus. The limitations of these phenomena, as well as their implication on manipulating directed transport in helical geometries are discussed.
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Affiliation(s)
- Ansgar Siemens
- Zentrum für Optische Quantentechnologien, Fachbereich Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Peter Schmelcher
- Zentrum für Optische Quantentechnologien, Fachbereich Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany.,Hamburg Center for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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2
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Abstract
We demonstrate that directed transport of particles in a two dimensional driven lattice can be dynamically reversed multiple times by superimposing additional spatially localized lattices on top of a background lattice. The timescales of such current reversals can be flexibly controlled by adjusting the spatial locations of the superimposed lattices. The key principle behind the current reversals is the conversion of the particle dynamics from chaotic to ballistic, which allow the particles to explore regions of the underlying phase space which are inaccessible otherwise. Our results can be experimentally realized using cold atoms in driven optical lattices and allow for the control of transport of atomic ensembles in such setups.
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Mukhopadhyay AK, Liebchen B, Schmelcher P. Simultaneous Control of Multispecies Particle Transport and Segregation in Driven Lattices. PHYSICAL REVIEW LETTERS 2018; 120:218002. [PMID: 29883160 DOI: 10.1103/physrevlett.120.218002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2017] [Revised: 02/14/2018] [Indexed: 06/08/2023]
Abstract
We provide a generic scheme to separate the particles of a mixture by their physical properties like mass, friction, or size. The scheme employs a periodically shaken two-dimensional dissipative lattice and hinges on a simultaneous transport of particles in species-specific directions. This selective transport is achieved by controlling the late-time nonlinear particle dynamics, via the attractors embedded in the phase space and their bifurcations. To illustrate the spectrum of possible applications of the scheme, we exemplarily demonstrate the separation of polydisperse colloids and mixtures of cold thermal alkali atoms in optical lattices.
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Affiliation(s)
- Aritra K Mukhopadhyay
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Benno Liebchen
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine Universität Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany
| | - Peter Schmelcher
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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Mukhopadhyay AK, Xie T, Liebchen B, Schmelcher P. Dimensional coupling-induced current reversal in two-dimensional driven lattices. Phys Rev E 2018; 97:050202. [PMID: 29906956 DOI: 10.1103/physreve.97.050202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2018] [Indexed: 06/08/2023]
Abstract
We show that the direction of directed particle transport in a two-dimensional ac-driven lattice can be dynamically reversed by changing the structure of the lattice in the direction perpendicular to the applied driving force. These structural changes introduce dimensional coupling effects, the strength of which governs the timescale of the current reversals. The underlying mechanism is based on the fact that dimensional coupling allows the particles to explore regions of phase space which are inaccessible otherwise. The experimental realization for cold atoms in ac-driven optical lattices is discussed.
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Affiliation(s)
- Aritra K Mukhopadhyay
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Tianting Xie
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- College of Mathematics, Sichuan University, Chengdu 610065, China
| | - Benno Liebchen
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine Universität Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany
| | - Peter Schmelcher
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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Wulf T, Okupnik A, Schmelcher P. Diffusion and transport in locally disordered driven lattices. CHAOS (WOODBURY, N.Y.) 2016; 26:093102. [PMID: 27781445 DOI: 10.1063/1.4961965] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density distribution which even increases towards larger positions is shown, thus yielding a highly non-Gaussian particle density evolution. As the key underlying mechanism, we identify the conversion between different components of the unperturbed systems mixed phase space which is induced by the disorder. Based on the introduction of individual conversion rates between chaotic and regular components, a theoretical model is developed which correctly predicts the scaling of the particle density. The effect of disorder on the transport properties is studied where a significant enhancement of the transport for cases of localized disorder is shown, thereby contrasting strongly the merely weak modification of the transport for global disorder.
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Affiliation(s)
- Thomas Wulf
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Alexander Okupnik
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Peter Schmelcher
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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Wulf T, Schmelcher P. Chaotic and ballistic dynamics in time-driven quasiperiodic lattices. Phys Rev E 2016; 93:042215. [PMID: 27176301 DOI: 10.1103/physreve.93.042215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2016] [Indexed: 06/05/2023]
Abstract
We investigate the nonequilibrium dynamics of classical particles in a driven quasiperiodic lattice based on the Fibonacci sequence. An intricate transient dynamics of extraordinarily long ballistic flights at distinct velocities is found. We argue how these transients are caused and can be understood by a hierarchy of block decompositions of the quasiperiodic lattice. A comparison to the cases of periodic and fully randomized lattices is performed.
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Affiliation(s)
- Thomas Wulf
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Peter Schmelcher
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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Wulf T, Petri C, Liebchen B, Schmelcher P. Symmetries and transport in site-dependent driven quantum lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042913. [PMID: 25375573 DOI: 10.1103/physreve.90.042913] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2014] [Indexed: 06/04/2023]
Abstract
We explore the quantum dynamics of particles in a spatiotemporally driven lattice. A powerful numerical scheme is developed which provides us with the Floquet modes and thus enables a stroboscopic propagation of arbitrary initial states. A detailed symmetry analysis represents the cornerstone for an intricate manipulation of the Floquet spectrum. Specifically, we show how exact crossings can be converted into avoided ones, while the widths of these resulting avoided crossings can be engineered by adjusting parameters of the local driving. Asymptotic currents are shown to be controllable over a certain parameter range.
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Affiliation(s)
- Thomas Wulf
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Christoph Petri
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Benno Liebchen
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Peter Schmelcher
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany and The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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Liebchen B, Schmelcher P. Spatiotemporal oscillation patterns in the collective relaxation dynamics of interacting particles in periodic potentials. PHYSICAL REVIEW LETTERS 2014; 112:134102. [PMID: 24745425 DOI: 10.1103/physrevlett.112.134102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2014] [Indexed: 06/03/2023]
Abstract
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative, and finite chain of interacting particles in a periodic potential towards its many particle equilibrium configuration. Specifically, we observe a transition from an in phase correlated motion via phase randomized oscillations towards oscillations with a phase difference π between adjacent particles thereby yielding the growth of long time transient spatiotemporal oscillation patterns. Parameter modifications allow for designing these patterns, including steady states and even states that combine in phase and correlated out of phase oscillations along the chain. The complex relaxation dynamics is based on finite size effects together with an evolution running from the nonlinear to the linear regime, thereby providing a highly unbalanced population of the center-of-mass and relative motion.
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Affiliation(s)
- Benno Liebchen
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Peter Schmelcher
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany and The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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