Collective action problems and conflicting obligations

Talbot, Brian

doi:10.1007/s11098-017-0957-7

Cited by 17 publications

(18 citation statements)

References 18 publications

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“…The shape of a function that measures coherence there is the closest to the one found in the present paper for interacting bosons. In optics, this phenomenon is well known as the Talbot effect [39,40] (see also [41][42][43]). We hope that by providing an analytic formula for collapses and revivals in the BH model, our work will stimulate experiments in wider time regimes for systems such as the double well and the degenerate harmonic well [12], where this fascinating phenomena can be observed.…”

Section: Introductionmentioning

confidence: 99%

Semiclassical analysis of Bose–Hubbard dynamics

Veksler

Fishman

2015

New J. Phys.

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In this work the two-site Bose-Hubbard model is studied analytically in the limit of weak coupling u and large number of particles N. In particular, the difference in the occupation between the two sites, where initially all particles are at one site, was calculated analytically. This quantity exhibits collapses and revivals that superimpose rapid oscillations. Excellent agreement with the exact numerical solution was found. The semiclassical approximation where N 1 plays the role of Planckʼs constant was used and perturbation theory to order u 2 was applied. The occupation difference was calculated also for the case where initially both sites are occupied provided that the difference in occupation is sufficiently large. This work provides an analytical description of results that were so far found only numerically. Similar behavior and analysis are expected for a large variety of physical situations.

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Section: Introductionmentioning

confidence: 99%

Semiclassical analysis of Bose–Hubbard dynamics

Veksler

Fishman

2015

New J. Phys.

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“…We only consider one of the species, as the initial condition implies time evolution of the second component to be symmetric with respect to the center of the trap. The function g (1) is normalized such that its value is 1 on the diagonal. In Fig.…”

Section: Derivation Of Widths Of the Structuresmentioning

confidence: 99%

“…Introduction In 1836 Henry Fox Talbot, the father of photography, reported an unexpected result -a diffraction grating he was observing through a magnifying lens was reappearing repeatedly in focus as he was moving away [1]. This phenomenon, now dubbed the Talbot effect, was later explained by Lord Rayleigh in 1881 by means of Fresnel integrals describing near-field diffraction [2].…”

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confidence: 99%

Fermionic quantum carpets: From canals and ridges to solitonlike structures

Grochowski

Karpiuk

Brewczyk

et al. 2020

Phys. Rev. Research

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We report a formation of sharp, solitonlike structures in an experimentally accessible ultracold Fermi gas, as a quantum carpet solution is analyzed in a many body system. The effect is perfectly coherent in a noninteracting gas, but in the presence of repulsive interaction in a two-component system, the structures vanish at a finite time. As they disappear, the system enters a dynamical equilibrium, in which kinetic energies of atoms tend to the same average value. The coherence is revived in a strong interaction regime, with the onset of phase separation, and with a double quantum carpet appearing.

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“…The following question arises: what is the wavefield behaviour behind the object? This can be answered first in optics from the earlier work of Talbot (1836). Talbot experimentally showed that the field intensity periodically reproduces an initial periodic distribution.…”

Section: Introductionmentioning

confidence: 97%

X-ray dynamical diffraction analogues of the integer and fractional Talbot effects

Balyan

2019

J Synchrotron Radiat

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The X‐ray integer and fractional Talbot effect is studied under two‐wave dynamical diffraction conditions in a perfect crystal, for the symmetrical Laue case of diffraction. The fractional dynamical diffraction Talbot effect is studied for the first time. A theory of the dynamical diffraction integer and fractional Talbot effect is given, introducing the dynamical diffraction comb function. An expression for the dynamical diffraction polarization‐sensitive Talbot distance is established. At the rational multiple depths of the Talbot depth the wavefield amplitude for each dispersion branch is a coherent sum of the initial distributions, shifted by rational multiples of the object period and having its own phases. The simulated dynamical diffraction Talbot carpet for the Ronchi grating is presented.

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Collective action problems and conflicting obligations

Cited by 17 publications

References 18 publications

Semiclassical analysis of Bose–Hubbard dynamics

Semiclassical analysis of Bose–Hubbard dynamics

Fermionic quantum carpets: From canals and ridges to solitonlike structures

X-ray dynamical diffraction analogues of the integer and fractional Talbot effects

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