Domain Size Distribution in Segregating Binary Superfluids

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.Comment: 7 pages, 2 figure

Domain-area distribution anomaly in segregating multicomponent superfluids

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 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.Comment: 9 pages, 5 figure

Quantum and thermal phase transitions in the Bechgaard salts and their analogs

In order to investigate quantum and thermal phase transitions in the Bechgaard salts and their sulfur analogs, we perform finite-temperature Hartree-Fock calculations in one dimension with particular emphasis on the interplay between charge ordering and lattice instability. The coexisting charge- and spin-density-wave state as well as its precursor fluctuations in (TMTSF)2PF6 and the lattice tetramerization in (TMTTF)2ReO4 are well interpreted.Comment: 2 pages, 3 figures embedded, submitted to Synth. Me

Type III Dyson Sphere of Highly Advanced Civilizations around a Super Massive Black Hole

We describe a new system for a society of highly advanced civilizations around a super massive black hole (SMBH), as an advanced Type III "Dyson Sphere", pointing out an efficient usage of energy for the advanced civilizations. SMBH also works as a sink for waste materials. Here we assume that Type III civilisations of Kardashev classification [1] form a galactic club [2] in a galaxy, and the energy from the SMBH will be delivered to the club members, forming an energy control system similar to power grids in our present society. The energy is probably transmitted by a sharp beam with coherent electro-magnetic waves, which provide a new concept for the search for extraterrestrial intelligence (SETI) via detection of such energy transmission signals. This expands the search window for other intelligences within the Universe.Comment: 4 pages, 1 color pag

Nambu-Goldstone modes in segregated Bose-Einstein condensates

Nambu-Goldstone modes in immiscible two-component Bose-Einstein condensates are studied theoretically. In a uniform system, a flat domain wall is stabilized and then the translational invariance normal to the wall is spontaneously broken in addition to the breaking of two U(1) symmetries in the presence of two complex order parameters. We clarify properties of the low-energy excitations and identify that there exist two Nambu-Goldstone modes: in-phase phonon with a linear dispersion and ripplon with a fractional dispersion. The signature of the characteristic dispersion can be verified in segregated condensates in a harmonic potential.Comment: 5 pages, 3 figure

Rabi-coupled Countersuperflow in Binary Bose-Einstein Condensates

We show theoretically that periodic density patterns are stabilized in two counter-propagating Bose-Einstein condensates of atoms in different hyperfine states under Rabi coupling. In the presence of coupling, the relative velocity between two components is localized around density depressions in quasi-one-dimensional systems. When the relative velocity is sufficiently small, the periodic pattern reduces to a periodic array of topological solitons as kinks of relative phase. According to our variational and numerical analyses, the soliton solution is well characterized by the soliton width and density depression. We demonstrate the dependence of the depression and width on the Rabi frequency and the coupling constant of inter-component density-density interactions. The periodic pattern of the relative phase transforms continuously from a soliton array to a sinusoidal pattern as the period becomes smaller than the soliton width. These patterns become unstable when the localized relative velocity exceeds a critical value. The stability-phase diagram of this system is evaluated with a stability analysis of countersuperflow, by taking into account the finite-size-effect owing to the density depression.Comment: 9 pages, 8 figure

Counterflow Quantum Turbulence and the Instability in Two-component Bose-Einstein Condensates

We theoretically study the nonlinear dynamics of the instability of counter-superflow in two miscible Bose-Einstein condensates. The condensates become unstable when the relative velocity exceeds a critical value, which is called counter-superflow instability. We reveal that the counter-superflow instability can lead to quantum turbulence by numerically solving the coupled Gross-Pitaevskii equations. The modes amplified by the instability grow into solitons and decay into quantized vortices.Eventually, the vortices become tangled and quantum turbulence of two superfluids. We show that this process may occur in experiments by investigating the dynamics in a 2D trapped system.Comment: 7 pages, 5 figures, submitted to Journal of Low Temperature Physic

Is a doubly quantized vortex dynamically unstable in uniform superfluids?

We revisit the fundamental problem of the splitting instability of a doubly quantized vortex in uniform single-component superfluids at zero temperature. We analyze the system-size dependence of the excitation frequency of a doubly quantized vortex through large-scale simulations of the Bogoliubov--de Gennes equation, and find that the system remains dynamically unstable even in the infinite-system-size limit. Perturbation and semi-classical theories reveal that the splitting instability radiates a damped oscillatory phonon as an opposite counterpart of a quasi-normal mode.Comment: 8 pages, 6 figure

PAKE-based mutual HTTP authentication for preventing phishing attacks

This paper describes a new password-based mutual authentication protocol for Web systems which prevents various kinds of phishing attacks. This protocol provides a protection of user's passwords against any phishers even if dictionary attack is employed, and prevents phishers from imitating a false sense of successful authentication to users. The protocol is designed considering interoperability with many recent Web applications which requires many features which current HTTP authentication does not provide. The protocol is proposed as an Internet Draft submitted to IETF, and implemented in both server side (as an Apache extension) and client side (as a Mozilla-based browser and an IE-based one). The paper also proposes a new user-interface for this protocol which is always distinguishable from fake dialogs provided by phishers

Phase ordering percolation and an infinite domain wall in segregating binary Bose-Einstein condensates

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.Comment: 8 pages, 4 figure