Majorana bound state in rotating superfluid 3He-A between parallel plates

A concrete and experimentally feasible example for testing the putative Majorana zero energy state bound in a vortex is theoretically proposed for a parallel plate geometry of superfluid $^3$He-A phase. We examine the experimental setup in connection with ongoing rotating cryostat experiments. The theoretical analysis is based on the well-established Ginzburg--Landau functional, supplemented by microscopic calculations of the Bogoliubov--de Gennes equation, both of which allow the precise location of the parameter regions of the Majorana state to be found in realistic situations.Comment: 5 pages, 4 figure

Spontaneous mass current and textures of p-wave superfluids of trapped Fermionic atom gases at rest and under rotation

It is found theoretically based on the Ginzburg-Landau framework that p-wave superfluids of neutral atom gases in three dimension harmonic traps exhibit spontaneous mass current at rest, whose direction depends on trap geometry. Under rotation various types of the order parameter textures are stabilized, including Mermin-Ho and Anderson-Toulouse-Chechetkin vortices. In a cigar shape trap spontaneous current flows longitudial to the rotation axis and thus perpendicular to the ordinary rotational current. These features, spontaneous mass current at rest and texture formation, can be used as diagnoses for p-wave superfluidity.Comment: 5 pages, 5 figure

Stability of half quantum vortex in rotating superfluid 3He-A between parallel plates

We have found the precise stability region of the half quantum vortex (HQV) for superfluid $^3$He A phase confined in parallel plates with a narrow gap under rotation. Standard Ginzburg-Landau free energy, which is well established, is solved to locate the stability region spanned by temperature $T$ and rotation speed ($/Omega$). This $/Omega$-$T$ stability region is wide enough to check it experimentally in available experimental setup. The detailed order parameter structure of HQV characterized by A$_1$ core is given to facilitate the physical reasons of its stability over other vortices or textures.Comment: 5 pages, 4 figure

Majorana surface states of superfluid 3He A- and B-phases in a slab

Motivated by experiments on the superfluid 3He confined in a thin slab, we design a concrete experimental setup for observing the Majorana surface states. We solve the quasi-classical Eilenberger equation, which is quantitatively reliable, to evaluate several quantities, such as local density of states (LDOS), mass current for the A-phase, and spin current for the B-phase. In connection with realistic slab samples, we consider the upper and lower surfaces and the side edges including the corners with several thicknesses. Consequently the influence on the Majorana zero modes from the spatial variation of l-vector for the A-phase in thick slabs and the energy splitting of the zero-energy quasi-particles for the B-phase confined in thin slabs are demonstrated. The corner of slabs in the B-phase is accompanied by the unique zero-energy LDOS of corner modes. On the basis of the quantitative calculation, we propose several feasible and verifiable experiments to check the existence of the Majorana surface states, such as the measurement of specific heat, edge current, and anisotropic spin susceptibility.Comment: 13 pages, 10 figures, published versio

Edge Current due to Majorana Fermions in Superfluid 3^3He A- and B-Phases

We propose a method utilizing edge current to observe Majorana fermions in the surface Andreev bound state for the superfluid $^3$He A- and B-phases. The proposal is based on self-consistent analytic solutions of quasi-classical Green's function with an edge. The local density of states and edge mass current in the A-phase or edge spin current in the B-phase can be obtained from these solutions. The edge current carried by the Majorana fermions is partially cancelled by quasiparticles (QPs) in the continuum state outside the superfluid gap. QPs contributing to the edge current in the continuum state are distributed in energy even away from the superfluid gap. The effect of Majorana fermions emerges in the depletion of the edge current by temperature within a low-temperature range. The observations that the reduction in the mass current is changed by $T^2$-power in the A-phase and the reduction in the spin current is changed by $T^3$-power in the B-phase establish the existence of Majorana fermions. We also point out another possibility for observing Majorana fermions by controlling surface roughness.Comment: 13 pages, 4 figures, published versio

Imaging Simulations of the Sunyaev-Zel'dovich Effect for ALMA

We present imaging simulations of the Sunyaev-Zel'dovich effect of galaxy clusters for the Atacama Large Millimeter/submillimeter Array (ALMA) including the Atacama Compact Array (ACA). In its most compact configuration at 90GHz, ALMA will resolve the intracluster medium with an effective angular resolution of 5 arcsec. It will provide a unique probe of shock fronts and relativistic electrons produced during cluster mergers at high redshifts, that are hard to spatially resolve by current and near-future X-ray detectors. Quality of image reconstruction is poor with the 12m array alone but improved significantly by adding ACA; expected sensitivity of the 12m array based on the thermal noise is not valid for the Sunyaev-Zel'dovich effect mapping unless accompanied by an ACA observation of at least equal duration. The observations above 100 GHz will become excessively time-consuming owing to the narrower beam size and the higher system temperature. On the other hand, significant improvement of the observing efficiency is expected once Band 1 is implemented in the future.Comment: 16 pages, 12 figures. Accepted for publication in PASJ. Note added in proof is include

Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential

We review some recent results on nonlinear Schrodinger equations with potential, with emphasis on the case where the potential is a second order polynomial, for which the interaction between the linear dynamics caused by the potential, and the nonlinear effects, can be described quite precisely. This includes semi-classical regimes, as well as finite time blow-up and scattering issues. We present the tools used for these problems, as well as their limitations, and outline the arguments of the proofs.Comment: 20 pages; survey of previous result

First mesopause temperature measurements using sodium lidar observations in the Antarctic region

The mesopause temperature structure was observed using a sodium temperature lidar system at Syowa Station (69°00\u27 S, 39°35\u27 E), beginning in February 2000. The laser transmitter was newly developed and included two injection-seeded Nd: YAG lasers. Regular observations were performed using the two-frequency technique as demonstrated by C.Y. She et al. (Geophys. Res. Lett., 17, 929, 1990), with a spatial resolution of about 1 km and a temporal resolution of 6 min. The temperature structures of the 85km to 105km region of the upper atmosphere were measured by Na D_2 Doppler profile-fitting as well as the two-frequency technique. Temperatures derived from the two techniques agreed well and were consistent with the MSIS 90 model temperature structure. Night-time temperature variations over a 15-hour period were measured in May 2000. A large temperature fluctuation with an interval of about 4 hours, and an amplitude of 60 K (probably caused by gravity waves) was observed. From the average night temperature profile, the mesopause was determined to be located at 102km, and have a temperature of 180K. These values are similar to winter values observed in the northern hemisphere

Edge mass current and roles of Majorana Fermions in superfluid 3He A-phase

The total angular momentum associated with the edge mass current flowing at the boundary in the superfluid $^3$He A-phase confined in a disk is proved to be $L=N\hbar/2$, consisting of $L^{\rm MJ}=N\hbar$ from the Majorana quasi-particles (QPs) and $L^{\rm cont}=-N\hbar/2$ from the continuum state. We show it based on an analytic solution of the chiral order parameter for quasi-classical Eilenberger equation. Important analytic expressions are obtained for mass current, angular momentum, and density of states (DOS). Notably the DOS of the Majorana QPs is exactly $N_0/2$ ($N_0$: normal state DOS) responsible for the factor 2 difference between $L^{\rm MJ}$ and $L^{\rm cont}$. The current decreases as $E^{-3}$ against the energy $E$, and $L(T) \propto -T^2$. This analytic solution is fully backed up by numerically solving the Eilenberger equation. We touch on the so-called intrinsic angular momentum problem.Comment: 5 pages, 3 figures, published versio

The Sunyaev-Zel'dovich Effect at Five Arc-seconds: RXJ1347.5-1145 Imaged by ALMA

We present the first image of the thermal Sunyaev-Zel'dovich effect (SZE) obtained by the Atacama Large Millimeter/submillimeter Array (ALMA). Combining 7-m and 12-m arrays in Band 3, we create an SZE map toward a galaxy cluster RXJ1347.5-1145 with 5 arc-second resolution (corresponding to the physical size of 20 kpc/h), the highest angular and physical spatial resolutions achieved to date for imaging the SZE, while retaining extended signals out to 40 arc-seconds. The 1-sigma statistical sensitivity of the image is 0.017 mJy/beam or 0.12 mK_CMB at the 5 arc-second full width at half maximum. The SZE image shows a good agreement with an electron pressure map reconstructed independently from the X-ray data and offers a new probe of the small-scale structure of the intracluster medium. Our results demonstrate that ALMA is a powerful instrument for imaging the SZE in compact galaxy clusters with unprecedented angular resolution and sensitivity. As the first report on the detection of the SZE by ALMA, we present detailed analysis procedures including corrections for the missing flux, to provide guiding methods for analyzing and interpreting future SZE images by ALMA.Comment: 20 pages, 13 figures. Accepted for publication in PAS