Coarsening dynamics of the<i>XY</i>model

Yurke, Bernard; Pargellis, A. N.; Kovács, Tamás; Huse, David A.

doi:10.1103/physreve.47.1525

Cited by 152 publications

(191 citation statements)

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“…Finally, we close with some physical discussion on reasons for the difference between the GP model, and quenches in the purely dissipative Model A [14,15]. The dynamics in the GP model proceeds via the annihilation of nearby vortex-antivortex pairs (in d = 2) as in Model A.…”

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confidence: 71%

Phase ordering kinetics of the Bose gas

1996

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We study the approach to equilibrium of a Bose gas to a superfluid state. We point out that dynamic scaling, characteristic of far from equilibrium phaseordering systems, should hold. We stress the importance of a non-dissipative Josephson precession term in driving the system to a new universality class. non-equilibrium phenomena in a heretofore inaccessible regime. In particular, an issue which could be experimentally investigated, and which we shall address theoretically in this paper is the following-upon quenching a Bose gas to a final temperature (T ) below T c , how does the condensate density grow with time before attaining its final equilibrium value? A few recent papers [3,4] have addressed just this question, but they have focussed on the early time (on the order of a few collision times), non-universal dynamics. However, as has also been noted recently in Ref [5], the interesting experimental questions are instead associated with the long-time dynamics involving the coarsening of the Bose condensate order parameter. This dynamics is "universal" in a sense that will be clarified below.A natural and precise language for describing the evolution of the condensate is offered by recent developments in the theory of phase-ordering dynamics in dissipative classical spin systems, as reviewed in the article by Bray [6]. In this theory, one considers the evolution of a classical spin system after a rapid quench from some high T to a low T in the ordered phase.The dynamics is assumed to be purely relaxational, and each spin simply moves along the steepest downhill direction in its instantaneous energy landscape. Locally ordered regions will appear immediately after the quench, but the orientation of the spins in each region will be different. The coarsening process is then one of alignment of neighboring regions, usually controlled by the motion and annihilation of defects (domain walls for Ising spins, vortices for XY spins etc.). A key step in the theory is the introduction of a single length scale, l(t), a monotonically increasing function of the time t, which is about the size of a typical ordered domain at time t. Provided l(t) is greater than microscopic length scales, like the range of interactions or the lattice spacing, it is believed that the late stage morphology of the system is completely characterized by l(t), and is independent of microscopic details, i.e. it is universal. This morphology is characterized by various time dependent correlation functions which exhibit universal scaling behavior.We turn then to the Bose gas. The order parameter in this case is the boson annihilation

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confidence: 71%

Phase ordering kinetics of the Bose gas

1996

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“…Here t R is again the time after which no annihilations take place. The exponent value is considerably higher than the asymptotic value (η d = 1) found in simulations of the XY model with linear damping and local interactions [1,17,35].…”

Section: A Time Evolution Of Energy and Defect Densitiesmentioning

confidence: 55%

“…These exponents show little change (within error bars) when using the Gilbert damping constant α within the range of 144428-8 0.01-0.1 and are found to be robust against adding quenched disorder of moderate strength. When α is increased further, the relaxation exponents approach the asymptotic value for the XY model with local interactions (η d = 1) [1]. This should be due to the large damping practically eliminating the precessional motion of the magnetic moments so that they align with the local effective field almost immediately; thus, the dynamics of the magnetic moments starts to resemble that of the XY model in the no-inertia (overdamped) limit.…”

Section: Discussionmentioning

confidence: 86%

“…The topic of coarsening dynamics of topological defects in diverse systems ranging from liquid crystals [1][2][3][4] to biosystems [5] and cosmology [6] has attracted considerable interest as it is related to properties of symmetry-breaking phase transitions. As the system is quenched from a hightemperature disordered phase to a low-temperature ordered phase, the symmetry of the disordered phase is broken and topological defects are generated, subsequently exhibiting slow coarsening dynamics [7].…”

Section: Introductionmentioning

confidence: 99%

“…Also, the presence of vortices is intimately related to magnetic flux closure patterns minimizing the stray field energy of micron or submicron magnetic particles [12][13][14]. While coarsening of, e.g., the domain structures in Ising and Potts types of models [15,16] as well as that of the defect structure in the XY model [1,17] have been extensively studied, less is known about the details of coarsening dynamics in soft (low-anisotropy) ferromagnetic thin films, involving the collective dynamics of vortices, antivortices, and edge defects, when all the relevant effective field terms (exchange and demagnetizing energies) are included in the description.…”

Section: Introductionmentioning

confidence: 99%

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Coarsening dynamics of topological defects in thin permalloy films

Rissanen

Laurson

2016

Phys. Rev. B

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We study the dynamics of topological defects in the magnetic texture of rectangular permalloy thin-film elements during relaxation from random magnetization initial states. Our full micromagnetic simulations reveal complex defect dynamics during relaxation towards the stable Landau closure domain pattern, manifested as temporal power-law decay, with a system-size-dependent cutoff time, of various quantities. These include the energy density of the system and the number densities of the different kinds of topological defects present in the system. The related power-law exponents assume nontrivial values and are found to be different for the different defect types. The exponents are robust against a moderate increase in the Gilbert damping constant and introduction of quenched structural disorder. We discuss details of the processes allowed by conservation of the winding number of the defects, underlying their complex coarsening dynamics.

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Unstable Growth

Mazenko

2006

Nonequilibrium Statistical Mechanics

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Coarsening dynamics of theXYmodel

Cited by 152 publications

References 12 publications

Phase ordering kinetics of the Bose gas

Phase ordering kinetics of the Bose gas

Coarsening dynamics of topological defects in thin permalloy films

Unstable Growth

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