Domain Size Distribution in Segregating Binary Superfluids

Takeuchi, Hiromitsu

doi:10.1007/s10909-016-1543-7

Cited by 13 publications

(19 citation statements)

References 11 publications

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“…Such phenomena arise in binary alloys, fluid mixtures, and polymer blends. Recently, the dynamics of phase separation have seen a revival of interest in the context of experimental [7,8] and numerical [9][10][11][12] studies of binary mixtures of Bose gases.The late time dynamics are well understood. In the absence of driving forces, a dynamic scaling regime with statistically self-similar domain morphology sets in.…”

mentioning

confidence: 99%

Phase separation and critical percolation in bidimensional spin-exchange models

Tartaglia¹,

Cugliandolo²,

Picco³

2016

EPL

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-Binary mixtures prepared in an homogeneous phase and quenched into a two-phase region phaseseparate via a coarsening process whereby domains of the two phases grow in time. With a numerical study of a spin-exchange model we show that this dynamics first take a system with equal density of the two species to a critical percolation state. We prove this claim and we determine the time-dependence of the growing length associated to this process with the scaling analysis of the statistical and morphological properties of the clusters of the two phases.Phase separation is the process whereby a binary mixture of components A and B, initially in a homogeneous phase, demix. This process leads to the coexistence of two phases: one rich in A and the other in B [1][2][3][4][5][6]. The system, initially in an unstable spatially uniform state, progressively coarsens to approach its thermodynamically stable phase-separated state. Such phenomena arise in binary alloys, fluid mixtures, and polymer blends. Recently, the dynamics of phase separation have seen a revival of interest in the context of experimental [7,8] and numerical [9][10][11][12] studies of binary mixtures of Bose gases.The late time dynamics are well understood. In the absence of driving forces, a dynamic scaling regime with statistically self-similar domain morphology sets in. This regime is well-described by an extension of the Lifshitz-Slyozov-Wagner (LSW) theory [13,14], in which the typical domain radius grows as [15] (whereas for scalar non-conserved order parameter dynamics the growing length is also given by a power law but the exponent is z d = 2). Numerical results in favour of this law were published in [15][16][17] for spin-exchange models although the growth-law can be more complex in particle or polymer phase separating systems, see e.g.[18] and references therein. The pre-asymptotic dynamics leading to this regime have not been discussed in detail in the literature. It was noticed in [19] that the low-temperature evolution of a bidimensional 50:50 binary mixture after a quench from infinite temperature shares many points in common with the one generated by Glauber single spin-flip stochastic dynamics satisfying detailed balance [20,21]. On the one hand, an early approach to critical percolation was noticed, although the time needed to reach this state was not studied in detail. On the other hand, a separation of length-scales in the statistics and morphology of finite size cluster areas and domain wall lengths was observed. Linear or planar objects that are smaller than the typical ones,, satisfy dynamic scaling with respect to d (t), while larger objects were found to be very close to the ones of critical percolation.In this Letter we characterise the early stages of the dynamical process. More precisely, we analyse the way in which the system approaches a state with a stable pattern of critical percolating domains. We monitor a number of observables (to be defined in the main part of the text) and we explain how their behaviour constitu...

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mentioning

confidence: 99%

Phase separation and critical percolation in bidimensional spin-exchange models

Tartaglia¹,

Cugliandolo²,

Picco³

2016

EPL

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“…If so, the critical exponent and the effect of the microscopic nature on the scaling behavior should be important for a deeper understanding of the physics of SSB development, e.g., seeking different scaling relations. These aspects were unclear in the previous works [21,22].…”

Section: Introductionmentioning

confidence: 85%

“…This is another expression of the dynamic-scaling law in the sense that the law is conventionally examined by observing the structure factor or the correlation function [5]. The dynamic-scaling law (1) has been experimentally [8] and numerically [7,[21][22][23] confirmed in different coarsening systems.…”

Section: A Dynamic Scaling Of Domain-area Distributionmentioning

confidence: 99%

Domain-area distribution anomaly in segregating multicomponent superfluids

Takeuchi

2018

Phys. Rev. A

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The domain-area distribution in the phase transition dynamics of Z2 symmetry breaking is studied theoretically and numerically for segregating binary Bose-Einstein condensates in quasi-twodimensional systems. Due to the dynamic scaling law of the phase ordering kinetics, the domain-area distribution is described by a universal function of the domain area, rescaled by the mean distance between domain walls. The scaling theory for general coarsening dynamics in two dimensions hypothesizes that the distribution during the coarsening dynamics has a hierarchy with the two scaling regimes, the microscopic and macroscopic regimes with distinct power-law exponents. The power law in the macroscopic regime, where the domain size is larger than the mean distance, is universally represented with the Fisher's exponent of the percolation theory in two dimensions. On the other hand, the power-law exponent in the microscopic regime is sensitive to the microscopic dynamics of the system. This conjecture is confirmed by large-scale numerical simulations of the coupled Gross-Pitaevskii equation for binary condensates. In the numerical experiments of the superfluid system, the exponent in the microscopic regime anomalously reaches to its theoretical upper limit of the general scaling theory. The anomaly comes from the quantum-fluid effect in the presence of circular vortex sheets, described by the hydrodynamic approximation neglecting the fluid compressibility. It is also found that the distribution of superfluid circulation along vortex sheets obeys a dynamic scaling law with different power-law exponents in the two regimes. An analogy to quantum turbulence on the hierarchy of vorticity distribution and the applicability to chiral superfluid 3 He in a slab are also discussed.

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“…This relation can be derived by considering the conservation laws for N 1 and N 2 , the detail of which is described in the Appendix D. Substituting Eqs. (37), (38), and (40) into Eq. (39), we obtain d dt L dp (t) ∝ L dp (t) −2 (L dp Λξ), L dp (t) −1 (L dp Λξ).…”

Section: B Growth Law Of Dropletsmentioning

confidence: 99%

Scale-invariant relaxation dynamics in two-component Bose-Einstein condensates with large particle-number imbalance

et al. 2020

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We theoretically study the scale-invariant relaxation dynamics in segregating two-component Bose-Einstein condensates with large particle-number imbalance, and uncover that random walk of droplet for the minor component plays a fundamental role in the relaxation process. Our numerical simulations based on the binary Gross-Pitaevskii model reveal the emergence of the dynamical scaling during the relaxation, which is a hallmark of scale-invariant dynamics, in a correlation function for the minor condensate. Tracking exponents characterizing the dynamical scaling in time, we find out a crossover phenomenon that features the change in power exponents of the correlation length. To understand the fundamental mechanism inherent in the scale-invariant relaxation dynamics, we construct a random walk model for droplets. Employing the model, we analytically derive the 1/3 and 1/2 power laws and predict the crossover of the scaling. These exponents are in reasonable agreement with the values obtained in the numerical calculations. We also discuss a possible experimental setup for observing the scale-invariant dynamics. arXiv:1907.13007v1 [cond-mat.quant-gas]

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Domain Size Distribution in Segregating Binary Superfluids

Cited by 13 publications

References 11 publications

Phase separation and critical percolation in bidimensional spin-exchange models

Phase separation and critical percolation in bidimensional spin-exchange models

Domain-area distribution anomaly in segregating multicomponent superfluids

Scale-invariant relaxation dynamics in two-component Bose-Einstein condensates with large particle-number imbalance

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