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Hiromitsu Takeuchi
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Domain size distribution in phase separating binary Bose--Einstein condensates is studied theoretically by numerically solving the Gross--Pitaevskii equations at zero temperature. We show that the size distribution in the domain patterns arising from the dynamic instability obeys a power law in a scaling regime according to the dynamic scaling analysis based on the percolation theory. The scaling behavior is kept during the relaxation development until the characteristic domain size becomes comparable to the linear size of the system, consistent with the dynamic scaling hypothesis of the phase-ordering kinetics. Our numerical experiments indicate the existence of a different scaling regime in the size distribution function, which can be caused by the so-called coreless vortices.
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The domain-area distribution in the phase transition dynamics of ${rm Z}_2$ symmetry breaking is studied theoretically and numerically for segregating binary Bose--Einstein condensates in quasi-two-dimensional 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 Fishers 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.
Percolation theory is applied to the phase-transition dynamics of domain pattern formation in segregating binary Bose--Einstein condensates in quasi-two-dimensional systems. Our finite-size-scaling analysis shows that the percolation threshold of the initial domain pattern emerging from the dynamic instability is close to 0.5 for strongly repulsive condensates. The percolation probability is universally described with a scaling function when the probability is rescaled by the characteristic domain size in the dynamic scaling regime of the phase-ordering kinetics, independent of the intercomponent interaction. It is revealed that an infinite domain wall sandwiched between percolating domains in the two condensates has an noninteger fractal dimension and keeps the scaling behavior during the dynamic scaling regime. This result seems to be in contrast to the argument that the dynamic scale invariance is violated in the presence of an infinite topological defect in numerical cosmology.
We study theoretically nonlinear dynamics induced by shear-flow instability in segregated two-component Bose-Einstein condensates in terms of the Weber number, defined by extending the past theory on the Kelvin-Helmholtz instability in classical fluids. Numerical simulations of the Gross-Pitaevskii equations demonstrate that dynamics of pattern formation is well characterized by the Weber number $We$, clarifying the microscopic aspects unique to the quantum fluid system. For $We lesssim 1$, the Kelvin-Helmholtz instability induces flutter-finger patterns of the interface and quantized vortices are generated at the tip of the fingers. The associated nonlinear dynamics exhibits a universal behavior with respect to $We$. When $We gtrsim 1$ in which the interface thickness is larger than the wavelength of the interface mode, the nonlinear dynamics is effectively initiated by the counter-superflow instability. In a strongly segregated regime and a large relative velocity, the instability causes transient zipper pattern formation instead of generating vortices due to the lack of enough circulation to form a quantized vortex per a finger. While, in a weakly segregating regime and a small relative velocity, the instability leads to sealskin pattern in the overlapping region, in which the frictional relaxation of the superflow cannot be explained only by the homogeneous counter-superflow instability. We discuss the details of the linear and nonlinear characteristics of this dynamical crossover from small to large Weber numbers, where microscopic properties of the interface become important for the large Weber number.
We study the necessary condition under which a resonantly driven exciton polariton superfluid flowing against an obstacle can generate turbulence. The value of the critical velocity is well estimated by the transition from elliptic to hyperbolic of an operator following ideas developed by Frisch, Pomeau, Rica for a superfluid flow around an obstacle, though the nature of equations governing the polariton superfluid is quite different. We find analytical estimates depending on the pump amplitude and on the pump energy detuning, quite consistent with our numerical computations.
We study possible superfluid states of the Rashba spin-orbit coupled (SOC) spinor bosons with the spin anisotropic interaction $ lambda $ hopping in a square lattice. The frustrations from the non-abelian flux due to the SOC leads to novel spin-bond correlated superfluids. By using a recently developed systematic order from quantum disorder analysis, we not only determine the true quantum ground state, but also evaluate the mass gap in the spin sector at $ lambda < 1 $, especially compute the the excitation spectrum of the Goldstone mode in the spin sector at $ lambda=1 $ which would be quadratic without the analysis. The analysis also leads to different critical exponents on the two sides of the 2nd order transition driven by a roton touchdown at $ lambda=1 $. The intimate analogy at $ lambda=1 $ with the charge neutral Goldstone mode in the pseudo-spin sector in the Bilayer quantum Hall systems at the total filling factor $ u_T=1 $ are stressed. The experimental implications and detections of these novel phenomena in cold atoms loaded on a optical lattice are presented.
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