Towards reliable calculations of the correlation function

The correlation function of two identical pions interacting via Coulomb potential is computed for a general case of anisotropic particle's source of finite life time. The effect of halo is taken into account as an additional particle's source of large spatial extension. Due to the Coulomb interaction, the effect of halo is not limited to very small relative momenta but it influences the correlation function in a relatively large domain. The relativistic effects are discussed in detail and it is argued that the calculations have to be performed in the center-of-mass frame of particle's pair where the (nonrelativistic) wave function of particle's relative motion is meaningful. The Bowler-Sinyukov procedure to remove the Coulomb interaction is tested and it is shown to significantly underestimate the source's life time.Comment: 18 pages, presented at XIth International Workshop on Correlation and Fluctuation in Multiparticle Production, Hangzhou, China, November 21-24, 200

Renormalization and Essential Singularity

In usual dimensional counting, momentum has dimension one. But a function f(x), when differentiated n times, does not always behave like one with its power smaller by n. This inevitable uncertainty may be essential in general theory of renormalization, including quantum gravity. As an example, we classify possible singularities of a potential for the Schr\"{o}dinger equation, assuming that the potential V has at least one $C^2$ class eigen function. The result crucially depends on the analytic property of the eigen function near its 0 point.Comment: 12 pages, no figures, PTPTeX with amsfonts. 2 pages added for detail

Bosonization solution of the Falicov-Kimball model

We use a novel approach to analyze the one dimensional spinless Falicov-Kimball model. We derive a simple effective model for the occupation of the localized orbitals which clearly reveals the origin of the known ordering. Our study is extended to a quantum model with hybridization between the localized and itinerant states; we find a crossover between the well-known weak- and strong-coupling behaviour. The existence of electronic polarons at intermediate coupling is confirmed. A phase diagram is presented and discussed in detail.Comment: RevTex, 10 pages, 1 figur

Gravitational Waves in a Shallow Compressible Liquid

This paper develops the theory of the propagation of waves through a horizontally stratified compressible liquid under the influence of gravity, with two simplifying assumptions: (1) The wave amplitudes are small, so that a linear or first-order theory suffices; (2) the liquid is assumed to be shallow so that the lengths of all waves are large in comparison with the liquid depth

Air Bubble Breakwater

This paper considers one aspect of the effectiveness of a single or repeated air bubble screen as a breakwater for gravitational waves in shallow water. The aspect considered arises from the change in density and compressibility of the bubbly water as compared with normal water outside the screen. The effects of currents produced by the mass of rising bubbles will be discussed elsewhere. use is made here of the notation and some results from another paper entitled 'Gravitational Waves in a Shallow Compressible Liquid;' equations from that paper are denoted by primes. The properties of bubbly water are considered first, then the transmission of waves through a single bubble screen, and finally the transmission through a series of equally spaced screens

Adiabatic theorems for linear and nonlinear Hamiltonians

Conditions for the validity of the quantum adiabatic approximation are analyzed. For the case of linear Hamiltonians, a simple and general sufficient condition is derived, which is valid for arbitrary spectra and any kind of time variation. It is shown that in some cases the found condition is necessary and sufficient. The adiabatic theorem is generalized for the case of nonlinear Hamiltonians

Gauge transformation through an accelerated frame of reference

The Schr\"{o}dinger equation of a charged particle in a uniform electric field can be specified in either a time-independent or a time-dependent gauge. The wave-function solutions in these two gauges are related by a phase-factor reflecting the gauge symmetry of the problem. In this article we show that the effect of such a gauge transformation connecting the two wave-functions can be mimicked by the effect of two successive extended Galilean transformations connecting the two wave-function. An extended Galilean transformation connects two reference frames out of which one is accelerating with respect to the other.Comment: 7 Pages, Latex fil

Tunable-diode laser absorption spectrometry

Tunable-diode laser absorption spectrometry (TDLAS) affords a number of advantages for atmospheric measurements. It is a universal method, applicable, in principle, to all gases of atmospheric interest. Because of its extremely high spectral resolution it provides unequivocal identification of the target species, with no interferences from other gases. It provides real-time, in situ measurements with time resolutions better than 1 minute. The sensitivity of the current TDLAS system is marginally capable of measuring HO2. This species exists in the troposphere at concentrations which are up to 2 orders of magnitude higher than those of HO and, in addition, is much less susceptible to removal by the surfaces of the instrument and its sampling system. HO2 is an important HO sub x species in its own right but can also give direct information on the HO concentration by virtue of the rapid partitioning between these two species. The addition of the high-frequency modulation technique to the TDLAS system would ensure its ability to measure HO2 under most atmospheric conditions. The ability of the TDLAS to measure hydrogen peroxide (H2O2) in the ambient atmosphere was also demonstrated. H2O2 measurements give a clear indication of HO sub x mixing ratios and are also important as a photolytic source of HO and as an important oxidant for other atmospheric consitituents such as SO2

Evolution of a localized electron spin in a nuclear spin environment

Motivated by recent interest in the role of the hyperfine interaction in quantum dots we study the dynamics of a localized electron spin coupled to many nuclei. An important feature of the model is that the coupling to an individual nuclear spin depends on its position in the quantum dot. We introduce a semi-classical description of the system valid in the limit of a large number of nuclei and analyze the resulting classical dynamics. Contrary to a natural assumption, the correlation functions of electron spin with an arbitrary initial condition show no decay in time. Rather, they exhibit complicated undamped oscillations. This may be attributed to the fact that the system has many integrals of motion and is close to an integrable one. The ensemble averaged correlation functions do exhibit a slow decay (1/ln(t)) for t -> \infty.Comment: 11 pages, 11 figures, revtex4 styl