Gravitational effects in quantum mechanics

To date, both quantum theory and Einstein’s theory of general relativity have passed every experimental test in their respective regimes. Nevertheless, almost since their inception, there has been debate surrounding whether they should be unified, and by now, there exists strong theoretical arguments pointing to the necessity of quantising the gravitational field. In recent years, a number of experiments have been proposed which, if successful, should give insight into features at the Planck scale. Here, we review some of the motivations, from the perspective of semi-classical arguments, to expect new physical effects at the overlap of quantum theory and general relativity. We conclude with a short introduction to some of the proposals being made to facilitate empirical verification.     

Improved Statistically Optimal Nearfield Acoustical Holography in subsonically moving fluid medium

Statistically Optimal Nearfield Acoustical Holography (SONAH) can be used to reconstruct three-dimensional sound fields by projecting two-dimensional data measured on a “small” aperture that partially covers a composite sound source in a “static” fluid medium. Here, an improved SONAH procedure is proposed that includes the mean flow effects of a moving fluid medium while the sound source and receivers are stationary. The backward projection performance of the proposed procedure is further improved by using a wavenumber filter to suppress subsonic noise components. Through numerical simulations at Mach 0.6, it is shown that the improved procedure can accurately reconstruct sound source locations and radiation patterns: e.g., the spatially averaged reconstruction errors of the conventional and improved SONAH procedures are 15.40 dB and 0.19 dB, respectively, for a monopole simulation and 21.60 dB and 0.19 dB for an infinite-size panel. The wavenumber filter further reduces spatial noise, e.g., decreasing the reconstruction error from 1.73 dB to 0.19 dB for the panel simulation. An existing data measured in a wind tunnel operating at Mach 0.12 is reused for the validation. The locations and radiation patterns of the two loudspeakers are successfully identified from the sound fields reconstructed by using the proposed SONAH procedure.     

Analysis of one-dimensional Helmholtz equation with PML boundary

In this paper, the linear conforming finite element method for the one-dimensional Bérenger's PML boundary is investigated and well-posedness of the given equation is discussed. Furthermore, optimal error estimates and stability in the L²$L^2$ or H¹$H^1$-norm are derived under the assumption that h$h$, h²ω²$h^2{\omega }^2$ and h²ω³$h^2{\omega }^3$ are sufficiently small, where h$h$ is the mesh size and ω$\omega$ denotes a fixed frequency. Numerical examples are presented to validate the theoretical error bounds.     

Frequency modules and nonexistence of quasi-periodic solutions of nonlinear evolution equations

This paper gives lower estimates for the frequency modules of almost periodic solutions to equations of the form , where A generates a strongly continuous semigroup in a Banach space , F(t,x) is 2π-periodic in t and continuous in (t,x), and f is almost periodic. We show that the frequency module ℳ(u) of any almost periodic mild solution u of (*) and the frequency module ℳ(f) of f satisfy the estimate e ^{2π iℳ(f)}⊂e ^{2π iℳ(u)}. If F is independent of t, then the estimate can be improved: ℳ(f)⊂ℳ(u). Applications to the nonexistence of quasi-periodic solutions are also given.     

Photoelectrochemical cells using metal-decorated carbon nanotube electrodes

We fabricated the photoelectrochemical (PEC) cells using n-type TiO₂ and metal (Pt, Pd)-decorated carbon nanotubes (CNTs) as an anode and a cathode, respectively. Photovoltaic effects were clearly observed. Compared with conventional PEC cell with Pt cathode, a larger photo-voltage was found in the PEC cells with the metal-decorated CNT cathode due to p-type semiconducting properties of CNTs. Additionally, we connected two PEC cells in series to decompose water into oxygen and hydrogen. Indeed, the connected PEC cells yielded the photo-voltage of about 1.35 V, which is larger than 1.23 V required for water splitting. This result demonstrates the possibility of hydrogen generation using the connected PEC cells without an external bias.     

Constraining WIMP magnetic moment from CDMS II experiment

We consider a degenerate or a nearly degenerate dark matter sector where a sizable magnetic moment of a (almost) Dirac type neutral dark matter candidate N is anticipated. Then, due to soft photon exchange, the cross-section in direct detection of N   can be enhanced at low Q²$Q^2$ region. We discuss the implication of this type of models in view of the recent CDMS II report.     

An example of nonuniqueness of the cauchy problem for the heat equation

We give an example of non trivial solution of the homogeneous Cauchy problem of the heat equation, which is, for each t, bounded in the space variables.     

Interatomic electronic decay driven by nuclear motion

The interatomic electronic decay after inner-valence ionization of a neon atom by a single photon in a neon-helium dimer is investigated. The excited neon atom relaxes via interatomic Coulombic decay and the excess energy is transferred to the helium atom and ionizes it. We show that the decay process is only possible if the dimer's bond stretches up to 6.2 ?, i.e., to more than twice the equilibrium interatomic distance of the neutral dimer. Thus, it is demonstrated that the electronic decay, taking place at such long distances, is driven by the nuclear motion.     

Anomalously suppressed localization in the two-channel Anderson model

We study numerically the localization properties of a two-channel quasi-one-dimensional Anderson model with uncorrelated diagonal disorder within the nearest-neighbor tight-binding approximation. We calculate and analyze the disorder-averaged transmittance and the Lyapunov exponent. We find that the localization of the entire system is enhanced by increasing the interchain hopping strength t?. From the numerical investigation of the energy dependence of the Lyapunov exponent for many different interchain hopping strengths, we find that apart from the band center anomaly, which usually occurs in strictly one-dimensional disordered systems, additional anomalies appear at special spectral points. They are found to be associated with the interchain hopping strength and occur at E = ± t?/2 and ± t?. We find that the anomalies at E = ± t? are associated with the π-coupling occurring within one energy band and those at E = ± t?/2 are associated with the π-coupling occurring between two different energy bands. Despite having a similar origin, these two anomalies have distinct characteristics in their dependence on the strength of disorder. We also show that for a suitable range of parameter values, effectively delocalized states are observed in finite-size systems.