K+→μ+νμννˉK^{+}\rightarrow \mu^{+}\nu_{\mu} \nu \bar \nu and K+→e+νeννˉK^{+}\rightarrow e^{+}\nu_{e} \nu \bar \nu decays within the Chiral Perturbation Theory

Decays $K^{+} \rightarrow \mu^{+}\nu_{\mu} \nu \bar \nu$ and $K^{+}\rightarrow e^{+}\nu_{e} \nu \bar \nu$ are examined to the leading order in momenta in the framework of Chiral Perturbation Theory. Predictions of the Standard Model for the muon and electron differential energy spectra and branching ratios of $K_{\mu 3 \nu}$ and $K_{e 3 \nu}$ are presented.Comment: 10 pages, 4 figures; v2: Introduction and Conclusion extended, journal versio

Inverse problems of symbolic dynamics

This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval exchange transformation. Rauzy graphs language can express many important combinatorial and some dynamical properties. In this case combinatorial properties are considered as being generated by substitutional system, and dynamical properties are considered as criteria of superword being generated by interval exchange transformation. As a consequence, one can get a morphic word appearing in interval exchange transformation such that frequencies of letters are algebraic numbers of an arbitrary degree. Concerning multydimensional systems, our main result is the following. Let P(n) be a polynomial, having an irrational coefficient of the highest degree. A word $w$ (w=(w_n), n\in \nit) consists of a sequence of first binary numbers of $\{P(n)\}$ i.e. $w_n=[2\{P(n)\}]$. Denote the number of different subwords of $w$ of length $k$ by $T(k)$ . \medskip {\bf Theorem.} {\it There exists a polynomial $Q(k)$, depending only on the power of the polynomial $P$, such that $T(k)=Q(k)$ for sufficiently great $k$.

Non-relativistic limit of multidimensional gravity: exact solutions and applications

It is found the exact solution of the Poisson equation for the multidimensional space with topology $M_{3+d}=\mathbb{R}^3\times T^d$. This solution describes smooth transition from the newtonian behavior $1/r_3$ for distances bigger than periods of tori (the extra dimension sizes) to multidimensional behavior $1/r^{1+d}_{3+d}$ in opposite limit. In the case of one extra dimension $d=1$, the gravitational potential is expressed via compact and elegant formula. These exact solutions are applied to some practical problems to get the gravitational potentials for considered configurations. Found potentials are used to calculate the acceleration for point masses and gravitational self-energy.It is proposed models where the test masses are smeared over some (or all) extra dimensions. In 10-dimensional spacetime with 3 smeared extra dimensions, it is shown that the size of 3 rest extra dimensions can be enlarged up to submillimeter for the case of 1TeV fundamental Planck scale $M_{Pl(10)}$. In the models where all extra dimensions are smeared, the gravitational potential exactly coincides with the newtonian one regardless of size of the extra dimensions. Nevertheless, the hierarchy problem can be solved in these models.Comment: LaTex file, 18 pages, 4 figure

Near-field terahertz imaging using sub-wavelength apertures without cutoff

We demonstrate near-field imaging capabilities of a conical waveguide without cutoff using broadband terahertz (THz) radiation. In contrast to conventional conically tapered waveguides, which are characterized by strong suppression of transmission below the cutoff frequency, the proposed structure consists of two pieces, such that there is an adjustable gap along the length of the waveguide. We also ensure that the sidewalls are thin in the vicinity of the gap. The combination of these geometrical features allow for significantly enhanced transmission at frequencies below the cutoff frequency, without compromising the mode confinement and, consequently, the spatial resolution when used for imaging applications. We demonstrate near-field imaging with this probe simultaneously at several frequencies, corresponding to three regimes: above, near and below the cutoff frequency. We observe only mild degradation in the image quality as the frequency is reduced below the cutoff frequency. These results suggest that further refinements in the probe structure will allow for improved imaging capabilities at frequencies well below the cutoff frequency

Electrostatic traps for dipolar excitons

We consider the design of two-dimensional electrostatic traps for dipolar indirect excitons. We show that the excitons dipole-dipole interaction, combined with the in-plane electric fields that arise due to the trap geometry, constrain the maximal density and lifetime of trapped excitons. We derive an analytic estimate of these values and determine their dependence on the trap geometry, thus suggesting the optimal design for high density trapping as a route for observing excitonic Bose-Einstein condensation.Comment: 5 pages, 3 figures. This 2nd version contains a revised Fig.3 + minor revisions to the discussion and abstrac

Modes in silver-iodide-lined hollow metallic waveguides mapped by terahertz near-field time-domain microscopy

Thin dielectric layers inside hollow metallic waveguides are used to improve the waveguide transmission characteristics as the dominant waveguide mode changes into the hybrid HE11 mode. We investigate the effect of 1 μm thick silver iodide (AgI) coatings on the fundamental modes in cylindrical waveguides at terahertz (THz) frequencies, in the regime of the dielectric layer being thinner than the optimal thickness hopt(2 THz) ̃ 20 μm. In the region of 1-3.2 THz, the lowest-order modes are similar in profile to the TE11 and TM11 modes, as determined by the timeresolved near-field measurements and verified numerically. Higher-order modes are detected experimentally as mode mixtures due to the multimode propagation. Numerical electromagnetic modeling is applied to resolve the mode structure ambiguity, allowing us to correlate experimentally detected patterns with a superposition of the TM11 and the higher-order mode, TE12. Mode profiles determined here indicate that in the regime of ultrathin dielectric (h c 0.1γeff ), the dielectric layer does not transform the dominant mode into the low-loss HE11 mode. Experimental mode patterns similar to the HE11 and the TE01 modes nevertheless can be formed due to mode beating. The results indicate that the Ag/AgI waveguides can be used for guiding THz waves in the TE01 mode or the TE12 mode with high discrimination against other modes. © 2012 Optical Society of America