Dynamical trapping and chaotic scattering of the harmonically driven barrier

Koch, Florian R. N.; Lenz, F.; Petri, C.; Diakonos, F. Κ.; Schmelcher, Peter

doi:10.1103/physreve.78.056204

Cited by 33 publications

(51 citation statements)

References 35 publications

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“…This dynamics can be described using both theoretical and experimental approaches and can be considered using either classical or quantum characterization. Several applications have been discussed, including ballistic conductance in a periodically modulated channel [2], magnetotransport through heterostructures of GaAs/AlGaAs [3], sequential resonant tunneling in semiconductor superlattices due to intense electrical fields [4], influence of transport in the presence of microwaves [5], anomalous transmission in periodic waveguides [6], trapping in driven barriers [7], characterization of traversal time [8,9], symmetry breaking and drift of particles in a chain of potential barriers [10], Lyapunov characterization of chaotic dynamics and destruction of invariant tori [11], among many others [12,13].…”

Section: Introductionmentioning

confidence: 99%

Escape of particles in a time-dependent potential well

2011

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We investigate the escape of an ensemble of noninteracting particles inside an infinite potential box that contains a time-dependent potential well. The dynamics of each particle is described by a two-dimensional nonlinear area-preserving mapping for the variables energy and time, leading to a mixed phase space. The chaotic sea in the phase space surrounds periodic islands and is limited by a set of invariant spanning curves. When a hole is introduced in the energy axis, the histogram of frequency for the escape of particles, which we observe to be scaling invariant, grows rapidly until it reaches a maximum and then decreases toward zero at sufficiently long times. A plot of the survival probability of a particle in the dynamics as function of time is observed to be exponential for short times, reaching a crossover time and turning to a slower-decay regime, due to sticky regions observed in the phase space.

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Section: Introductionmentioning

confidence: 99%

Escape of particles in a time-dependent potential well

2011

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“…This shows that DMFT is still a full-scale many-body theory. The solution of the self-consistent equations requires the application of powerful numerical methods, in particular quantum Monte-Carlo (QMC) simulations [13,14,19], with continuous-time QMC [20] as the method of choice, the numerical renormalization group [21], the density matrix renormalization group [22], exact diagonalization [14] and Lanczos procedures [23].…”

Section: The Self-consistent Dmft Equationsmentioning

confidence: 99%

Dynamical Mean-Field Theory of Strongly Correlated Electron Systems

Vollhardt

2020

Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2019)

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Dynamical Mean-Field Theory (DMFT) has opened new perspectives for the investigation of strongly correlated electron systems and greatly improved our understanding of correlation effects in models and materials. In contrast to Hartree-Fock-type approximations the mean field of DMFT is dynamical, whereby local quantum fluctuations are fully taken into account. DMFT becomes exact in the limit of high spatial dimensions or coordination number. Using DMFT the dynamics of correlated electron systems can be investigated non-perturbatively at all interaction strengths, electron densities and temperatures. By merging density functional theory with DMFT a powerful method for the calculation of the properties of correlated electron materials has become available, which is applicable to bulk systems and heterostructures, including topological states of matter. The inclusion of non-local correlations into DMFT makes it possible to explore unconventional superconductivity and the critical behavior at thermal or quantum phase transitions. By generalizing DMFT to nonequilibrium states also the real-time dynamics of correlated systems can be investigated. In this brief review the foundations and current state of DMFT are discussed along with characteristic physical insights obtained with this approach.

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“…Note that dynamical processes occurring on length scales below the distance of adjacent Poincaré surfaces are not resolved by M A for the given choice of the surfaces. For example orbits trapped between two positions of adjacent Poincaré surfaces which are present even for oscillating repulsive barriers (see [36]), are not captured (but these are also not relevant for our work). Main features of M A can be read off directly from the setups PSS ( Fig.1 (b)).…”

Section: Block Decomposition Of the Fibonacci Latticementioning

confidence: 99%

Chaotic and ballistic dynamics in time-driven quasiperiodic lattices

Wulf

Schmelcher

2016

Phys. Rev. E

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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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Dynamical trapping and chaotic scattering of the harmonically driven barrier

Cited by 33 publications

References 35 publications

Escape of particles in a time-dependent potential well

Escape of particles in a time-dependent potential well

Dynamical Mean-Field Theory of Strongly Correlated Electron Systems

Chaotic and ballistic dynamics in time-driven quasiperiodic lattices

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