Wavelet representations and Fock space on positive matrices

We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in that special case. Each of these representations is shown to have tractable finite-dimensional co-invariant doubly-cyclic subspaces. Further, motivated by these representations, we introduce a general Fock-space Hilbert space construction which yields creation operators containing the Cuntz--Toeplitz isometries as a special case.Comment: 32 pages, LaTeX ("amsart" document class), one EPS graphic file used for shading, accepted March 2002 for J. Funct. Ana

A Detailed Monte-Carlo Simulation for the Belle TOF System

We have developed a detailed Monte Carlo simulation program for the Belle TOF system. Based on GEANT simulation, it takes account of all physics processes in the TOF scintillation counters and readout electronics. The simulation reproduces very well the performance of the Belle TOF system, including the dE/dx response, the time walk effect, the time resolution, and the hit efficiency due to beam background. In this report, we will describe the Belle TOF simulation program in detail.Comment: To be submitted to NI

Antiferromagnetic Domains and Superconductivity in UPt3

We explore the response of an unconventional superconductor to spatially inhomogeneous antiferromagnetism (SIAFM). Symmetry allows the superconducting order parameter in the E-representation models for UPt3 to couple directly to the AFM order parameter. The Ginzburg-Landau equations for coupled superconductivity and SIAFM are solved numerically for two possible SIAFM configurations: (I) abutting antiferromagnetic domains of uniform size, and (II) quenched random disorder of `nanodomains' in a uniform AFM background. We discuss the contributions to the free energy, specific heat, and order parameter for these models. Neither model provides a satisfactory account of experiment, but results from the two models differ significantly. Our results demonstrate that the response of an E_{2u} superconductor to SIAFM is strongly dependent on the spatial dependence of AFM order; no conclusion can be drawn regarding the compatibility of E_{2u} superconductivity with UPt3 that is independent of assumptions on the spatial dependence of AFMComment: 12 pages, 13 figures, to appear in Phys. Rev.

Boundary Effects on Dynamic Behavior of Josephson-Junction Arrays

The boundary effects on the current-voltage characteristics in two-dimensional arrays of resistively shunted Josephson junctions are examined. In particular, we consider both the conventional boundary conditions (CBC) and the fluctuating twist boundary conditions (FTBC), and make comparison of the obtained results. It is observed that the CBC, which have been widely adopted in existing simulations, may give a problem in scaling, arising from rather large boundary effects; the FTBC in general turn out to be effective in reducing the finite-size effects, yielding results with good scaling behavior. To resolve the discrepancy between the two boundary conditions, we propose that the proper scaling in the CBC should be performed with the boundary data discarded: This is shown to give results which indeed scale well and are the same as those from the FTBC.Comment: RevTex, Final version to appear in Phys. Rev.

Neutrino Mass from R-parity Violation in Split Supersymmetry

We investigate how the observed neutrino data can be accommodated by R-parity violation in Split Supersymmetry. The atmospheric neutrino mass and mixing are explained by the bilinear parameters $\xi_i$ inducing the neutrino-neutralino mixing as in the usual low-energy supersymmetry. Among various one-loop corrections, only the quark-squark exchanging diagrams involving the order-one trilinear couplings $\lambda'_{i23,i32}$ can generate the solar neutrino mass and mixing if the scalar mass $m_S$ is not larger than $10^9$ GeV. This scheme requires an unpleasant hierarchical structure of the couplings, e.g., $\lambda_{i23,i32}\sim 1$, $\lambda'_{i33} \lesssim 10^{-4}$ and $\xi_i \lesssim 10^{-6}$. On the other hand, the model has a distinct collider signature of the lightest neutralino which can decay only to the final states, $l_i W^{(*)}$ and $\nu Z^{(*)}$, arising from the bilinear mixing. Thus, the measurement of the ratio; $\Gamma(e W^{(*)}) : \Gamma(\mu W^{(*)}) : \Gamma(\tau W^{(*)})$ would provide a clean probe of the small reactor and large atmospheric neutrino mixing angles as far as the neutralino mass is larger than 62 GeV.Comment: 10 pages, 3 figures, version submitted to JHE

Dynamic instabilities induced by asymmetric influence: Prisoners' dilemma game on small-world networks

A two-dimensional small-world type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node with a finite density of directed random links to the other nodes in the network, is numerically investigated. It is shown that the degree of cooperation does not remain at a steady state level but displays a punctuated equilibrium type behavior manifested by the existence of sudden breakdowns of cooperation. The breakdown of cooperation is linked to an imitation of a successful selfish strategy of the influential node. It is also found that while the breakdown of cooperation occurs suddenly, the recovery of it requires longer time. This recovery time may, depending on the degree of steady state cooperation, either increase or decrease with an increasing number of long range connections.Comment: 5 pages, 6 figure

Steady water waves with multiple critical layers: interior dynamics

We study small-amplitude steady water waves with multiple critical layers. Those are rotational two-dimensional gravity-waves propagating over a perfect fluid of finite depth. It is found that arbitrarily many critical layers with cat's-eye vortices are possible, with different structure at different levels within the fluid. The corresponding vorticity depends linearly on the stream function.Comment: 14 pages, 3 figures. As accepted for publication in J. Math. Fluid Mec

Cognitive Ability and Cardiovascular Control in Intellectually and Developmentally Disabled People

Earlier, we examined positive effects of hyperoxic air on the cognitive ability of intellectually and developmentally disabled people (IDDP). In this study, correlation between cognitive performance in the visual matching task and heart rate (HR) was investigated under normal air conditions. Eighteen men (mean age 28.7 ± 5.0 year) and 22 women (mean age 35.5 ± 6.9 year) with an assessed disability level of 2.3 ± 0.6 participated. The experiment consisted of three phases, a total of 7 min, including the rest (3 min), control (2 min), and visual matching task 2 min phases. The HR in visual matching task phase increased, compared to those in the rest and control phases. The cognitive ability in the visual matching task correlated with the HR values; the response time showed a negative correlation with HR, while the accuracy rate showed a positive correlation. Thus, adaptive changes in cardiovascular regulation probably related to cognitive efforts and emotional excitation should be considered a noticeable factor influencing brain supply with oxygen in IDDP (similarly to healthy people). The result of this study agrees with the earlier obtained indications that hyperoxic air can positively affect the cognitive performance in IDDP.Раніше ми вивчали позитивні впливи повітря, збагаченого киснем, на когнітивні здатності людей з недостатнім інтелектуальним розвитком (НІР). У нашій роботі ми досліджували кореляцію між показниками когнітивної активності в тесті візуальної відповідності та частотою серцевих скорочень (ЧСС) у таких суб’єктів в умовах дихання нормальним повітрям. У тестах брали участь 18 чоловіків (середній вік 28.7 ± 5.0 року) та 22 жінки (35.5 ± 6.9 року) з оцінкою рівня інтелектуального розвитку 2.3 ± 0.6. Експеримент (загальна тривалість 7 хв) складався з трьох фаз: стан розслаблення (3 хв), контроль (2 хв) та тест візуальної відповідності (2 хв). Величини ЧСС у межах цього тесту порівняно з величинами в умовах розслаблення й контролю зростали. Показники когнітивних здібностей корелювали з величинами ЧСС; кореляція часу відповіді була негативною, а точності відповіді – позитивною. Отже, адаптивні зміни регуляції серцево-судинної системи, мабуть, пов’язані з когнітивними зусиллями та емоційним збудженням, є істотним фактором, який впливає на постачання мозку киснем у людей із НІР (як і у здорових людей). Результати нашої роботи узгоджуються з отриманими раніше свідоцтвами про те, що дихання повітрям, збагаченим киснем, позитивно впливає на когнітивні можливості людей із НІР

Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem

The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann's 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the long-time behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the "quantum H-theorem", is actually a much weaker statement than Boltzmann's classical H-theorem, the other theorem, which he calls the "quantum ergodic theorem", is a beautiful and very non-trivial result. It expresses a fact we call "normal typicality" and can be summarized as follows: For a "typical" finite family of commuting macroscopic observables, every initial wave function $\psi_0$ from a micro-canonical energy shell so evolves that for most times $t$ in the long run, the joint probability distribution of these observables obtained from $\psi_t$ is close to their micro-canonical distribution.Comment: 34 pages LaTeX, no figures; v2: minor improvements and additions. The English translation of von Neumann's article is available as arXiv:1003.213