Determinantal process starting from an orthogonal symmetry is a Pfaffian process

When the number of particles $N$ is finite, the noncolliding Brownian motion (BM) and the noncolliding squared Bessel process with index $\nu > -1$ (BESQ$^{(\nu)}$) are determinantal processes for arbitrary fixed initial configurations. In the present paper we prove that, if initial configurations are distributed with orthogonal symmetry, they are Pfaffian processes in the sense that any multitime correlation functions are expressed by Pfaffians. The $2 \times 2$ skew-symmetric matrix-valued correlation kernels of the Pfaffians processes are explicitly obtained by the equivalence between the noncolliding BM and an appropriate dilatation of a time reversal of the temporally inhomogeneous version of noncolliding BM with finite duration in which all particles start from the origin, $N \delta_0$, and by the equivalence between the noncolliding BESQ$^{(\nu)}$ and that of the noncolliding squared generalized meander starting from $N \delta_0$.Comment: v2: AMS-LaTeX, 17 pages, no figure, corrections made for publication in J.Stat.Phy

Lifetime measurement of the ^3P_2 metastable state of strontium atoms

We have measured the lifetime of the 5s5p ^3P_2 metastable state of strontium atoms by magneto-optically trapping the decayed atoms to the ground state, which allowed sensitive detection of the rare decay events. We found that the blackbody radiation-induced decay was the dominant decay channel for the state at T = 300 K. The lifetime was determined to be 500^{+280}_{-130} s in the limit of zero temperature.Comment: 4 pages, 3 figures, submitted to Physical Review Letter

Testing Lorentz Symmetry with the Double Chooz Experiment

4 pages, 1 figure, presented at the Sixth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 17-21, 20134 pages, 1 figure, presented at the Sixth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 17-21, 2013The Double Chooz reactor-based oscillation experiment searches for an electron antineutrino disappearance signal to investigate the neutrino mass matrix mixing angle theta 13. Double Chooz's reported evidence for this disappearance is generally interpreted as mass-driven mixing through this parameter. However, the electron antineutrino candidates collected by the experiment can also be used to search for a signature of the violation of Lorentz invariance. We study the sidereal time dependence of the antineutrino signal rate and probe Lorentz violation within the Standard-Model Extension (SME) framework. We find that the data prefer the sidereal time independent solution, and a number of limits are applied to the relevant SME coefficients, including the first constraints on those associated with Lorentz violation in the e-tau mixing sector

Nuclear effects in neutrino-nucleus interactions

An accurate description of the nuclear response functions for neutrino scattering in the Gev region is essential for the interpretation of present and future neutrino oscillation experiments. Due to the close similarity of electromagnetic and weak scattering processes, we will review the status of the scaling approach and of relativistic modeling for the inclusive electron scattering response functions in the quasielastic and $\Delta$-resonance regions. In particular, recent studies have been focused on scaling violations and the degree to which these imply modifications of existing predictions for neutrino reactions. We will discuss sources and magnitude of such violations, emphasizing similarities and differences between electron and neutrino reactions.Comment: 7 pages, 5 figures, Proceeding of the XVIII International School on Nuclear Physics, Neutron Physics and Applications, September 21 - 27, 2009 Varna, Bulgari

Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems

As an extension of the theory of Dyson's Brownian motion models for the standard Gaussian random-matrix ensembles, we report a systematic study of hermitian matrix-valued processes and their eigenvalue processes associated with the chiral and nonstandard random-matrix ensembles. In addition to the noncolliding Brownian motions, we introduce a one-parameter family of temporally homogeneous noncolliding systems of the Bessel processes and a two-parameter family of temporally inhomogeneous noncolliding systems of Yor's generalized meanders and show that all of the ten classes of eigenvalue statistics in the Altland-Zirnbauer classification are realized as particle distributions in the special cases of these diffusion particle systems. As a corollary of each equivalence in distribution of a temporally inhomogeneous eigenvalue process and a noncolliding diffusion process, a stochastic-calculus proof of a version of the Harish-Chandra (Itzykson-Zuber) formula of integral over unitary group is established.Comment: LaTeX, 27 pages, 4 figures, v3: Minor corrections made for publication in J. Math. Phy

Quantum walks and orbital states of a Weyl particle

The time-evolution equation of a one-dimensional quantum walker is exactly mapped to the three-dimensional Weyl equation for a zero-mass particle with spin 1/2, in which each wave number k of walker's wave function is mapped to a point \vec{q}(k) in the three-dimensional momentum space and \vec{q}(k) makes a planar orbit as k changes its value in [-\pi, \pi). The integration over k providing the real-space wave function for a quantum walker corresponds to considering an orbital state of a Weyl particle, which is defined as a superposition (curvilinear integration) of the energy-momentum eigenstates of a free Weyl equation along the orbit. Konno's novel distribution function of quantum-walker's pseudo-velocities in the long-time limit is fully controlled by the shape of the orbit and how the orbit is embedded in the three-dimensional momentum space. The family of orbital states can be regarded as a geometrical representation of the unitary group U(2) and the present study will propose a new group-theoretical point of view for quantum-walk problems.Comment: REVTeX4, 9 pages, 1 figure, v2: Minor corrections made for publication in Phys.Rev.

Test of Lorentz Violation with Astrophysical Neutrino Flavor

Presented at the Seventh Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 20-24, 201

Effect of New Physics in Astrophysical Neutrino Flavor

The authors acknowledge support from the Wisconsin IceCube Particle Astrophysics Center FIG. 4 (color). (WIPAC). C. A. and J. S. were supported in part by the National Science Foundation (Grants No. OPP-0236449 and No. PHY-0969061) and by the University of Wisconsin Research Committee with funds granted by the Wisconsin Alumni Research Foundation. T. K. is supported by STFC, UK

Absence of an Almeida-Thouless line in Three-Dimensional Spin Glasses

We present results of Monte Carlo simulations of the three-dimensional Edwards-Anderson Ising spin glass in the presence of a (random) field. A finite-size scaling analysis of the correlation length shows no indication of a transition, in contrast to the zero-field case. This suggests that there is no Almeida-Thouless line for short-range Ising spin glasses.Comment: 4 pages, 4 figures, 1 tabl