Optical Conductivity of Ultra-Cold Bosons in Optical Lattices

Grygiel, B.; Patucha, K.; Zaleski, T. A.

doi:10.12693/aphyspola.130.633

Cited by 2 publications

(2 citation statements)

References 20 publications

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“…(11) [and consequently (12)] to an equivalent autonomous system of ODEs by considering time t as an additional coordinate (see e.g. Lichtenberg & Lieberman 1992, section 1.2b), is not particularly helpful, and is better to be avoided as shown in Grygiel & Szlachetka (1995).…”

Section: Chaos Detection Techniquesmentioning

confidence: 99%

Chaos and dynamical trends in barred galaxies: bridging the gap between N-body simulations and time-dependent analytical models

Manos¹,

Machado²

2014

Monthly Notices of the Royal Astronomical Society

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Self-consistent N -body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global phase space properties, which are the underlying cause of observed structures. The potentials needed to describe self-consistent models are time-dependent. Here, we aim to investigate dynamical properties (regular/chaotic motion) of a non-autonomous galactic system, whose time-dependent potential adequately mimics certain realistic trends arising from N -body barred galaxy simulations. We construct a fully time-dependent analytical potential, modeling the gravitational potentials of disc, bar and dark matter halo, whose time-dependent parameters are derived from a simulation. We study the dynamical stability of its reduced time-independent 2-degrees of freedom model, charting the different islands of stability associated with certain orbital morphologies and detecting the chaotic and regular regions. In the full 3-degrees of freedom time-dependent case, we show representative trajectories experiencing typical dynamical behaviours, i.e., interplay between regular and chaotic motion for different epochs. Finally, we study its underlying global dynamical transitions, estimating fractions of (un)stable motion of an ensemble of initial conditions taken from the simulation. For such an ensemble, the fraction of regular motion increases with time.

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Section: Chaos Detection Techniquesmentioning

confidence: 99%

Chaos and dynamical trends in barred galaxies: bridging the gap between N-body simulations and time-dependent analytical models

Manos¹,

Machado²

2014

Monthly Notices of the Royal Astronomical Society

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“…They have investigated optical conductivity in the lattice with synthetic gauge potential which correspond to the uniform magnetic field. The Grygiel et al work has extended the earlier one [21][22][23][24] and in particular they have shown the importance of interband transitions around Dirac points for two-band system with uniform π flux.…”

Section: Introductionmentioning

confidence: 85%

Tuning linear response dynamics near the Dirac points in the bosonic Mott insulator

Sajna

2019

Annals of Physics

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Optical lattice systems offer the possibility of creating and tuning Dirac points which are present in the tight-binding lattice dispersions. For example, such a behavior can be achieved in the staggered flux lattice or honeycomb type of lattices. Here we focus on the strongly correlated bosonic dynamics in the vicinity of Dirac points. In particular, we investigate bosonic Mott insulator phase in which quasiparticle excitations have a simple particle-hole interpretation. We show that linear response dynamics around Dirac points, can be significantly engineered at least in two ways: by the type of external perturbation or by changing the lattice properties. The key role is played by the interband transitions. Moreover, we explain that the behavior of these transitions is directly connected to different energy scales of the effective hopping amplitudes for particles and holes. Presented in this work theoretical study about tunability of linear response dynamics near the Dirac points can be directly simulated in the optical lattice systems.

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Optical Conductivity of Ultra-Cold Bosons in Optical Lattices

Cited by 2 publications

References 20 publications

Chaos and dynamical trends in barred galaxies: bridging the gap between N-body simulations and time-dependent analytical models

Chaos and dynamical trends in barred galaxies: bridging the gap between N-body simulations and time-dependent analytical models

Tuning linear response dynamics near the Dirac points in the bosonic Mott insulator

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