Functional representation of the partition function and phase transitions in the Hubbard model

The functional representation of the partition function for the Hubbard model with strong Coulomb repulsion is obtained in the form of an integral with respect to auxiliary Grassmann variables. The approximate study of the phase transitions shows:

1. for a small doping constant δ, the system is an antiferromagnetic dielectric;
2. for δ≥t/V, the system is a ferromagnetic metal if U/t>10 and superconducting metal if U/t? 10. Bibliography:13 titles.

     

Photonuclear reactions on molybdenum isotopes

The results of experimentally and theoretically studying the photodisintegration of molybdenum isotopes are presented. The yields of various photonucleon reactions on stable molybdenum isotopes were determined by the gamma-activation method. Use was made of bremsstrahlung photons from an electron accelerator that were characterized by the endpoint energies of 19.5, 29.1, and 67.7 MeV. Reactions involving the emission of up to three nucleons from the target nucleus were observed. The experimental results in question were compared with theoretical predictions based on the combined photonucleon-reaction model and obtained for 15 molybdenum isotopes. The relations between basic photonucleon reactions on the molybdenum isotopes considered in our present study were explained.     

Boundary observation and exact control of multilayered piezoelectric body

This paper considers the transmission problem for the system of piezoelectricity having piecewise constant coefficients. Under suitable geometric conditions imposed on the domain and the interfaces where the coefficients have a jump discontinuity, results on boundary observation and exact controllability are established. Copyright © 2003 John Wiley & Sons, Ltd.     

Kinetics of carbon nanopillar formation on a pyrolytic graphite surface during reactions induced by a focused electron beam

The results from a series of height measurements of carbon nanopillars formed during residual hydrocarbon deposition on a pyrographite surface by a focused electron beam in an SEM are presented. The high initial velocity of the pillars’ vertical growth can be explained by the dominant role of surface diffusion in the influx of molecules to the irradiated area. It is shown that progressive contamination of the substrate at distances up to several micrometers from the point of impact of the primary beam delays growth, and, in the case of long-time exposure, results in the evaporation of the pillars.     

Photonic band gap in the visible range in a three-dimensional solid state lattice

We report on the photonic band gap effect in the visible range in a three-dimensional dielectric lattice formed by closely packed silica spherical clusters and by interconnected cavities filled with various liquids. The spectral position and the spectral width of the optical "stop-band" depend on the lattice period and on the relative sphere/cavity refraction indexn. The stop band peak wavelength shows a linear dependence on n. Transmission characteristics of the lattice have been successfully simulated by numerical calculations within the framework of a quasicrystalline approximation.     

Multiparticle photonuclear reactions in <Superscript>203</Superscript>Tl nuclei

The thallium isotopes ²⁰³Tl and ²⁰⁵Tl were irradiated using a beam of bremsstrahlung gamma quanta with the maximum energy E _γ ^m = 50 MeV from an RTM-70 electron racetrack microtron installed at the Scobeltsyn Nuclear Physics Research Institute (Lomonosov Moscow State University, Russia). The gamma spectra of the residual activity were measured for an irradiated sample. Photonuclear reactions in the ²⁰³Tl nuclei with emission from one to four neutrons were observed experimentally. The relative yields of the reactions ²⁰³Tl(γ,n)²⁰²Tl, ²⁰³Tl(γ,2n)²⁰¹Tl, ²⁰³Tl(γ,3n)²⁰⁰Tl, and ²⁰³Tl(γ,4n)¹⁹⁹Tl were determined for the first time.     

Quantum Integrable and Nonintegrable Nonlinear Schrödinger Models for Realizable Bose–Einstein Condensation in d+1 Dimensions (d = 1, 2, 3)

We evaluate finite-temperature equilibrium correlators for thermal time ordered Bose fields to good approximations by new methods of functional integration in d=1,2,3 dimensions and with the trap potentials V(r)0. As in the translationally invariant cases, asymptotic behaviors fall as to longer-range condensate values for and only for d=3 in agreement with experimental observations; but there are generally significant corrections also depending on due to the presence of the traps. For d=1, we regain the exact translationally invariant results as the trap frequencies 0. In analyzing the attractive cases, we investigate the time-dependent c-number Gross–Pitaevskii (GP) equation with the trap potential for a generalized nonlinearity –2c||²ⁿ and c<0. For n=1, the stationary form of the GP equation appears in the steepest-descent approximation of the functional integrals. We show that collapse in the sense of Zakharov can occur for c=0 and nd2 and a functional E _NLS[]0 even when V(r)0. The singularities typically arise as -functions centered on the trap origin r=0.     

Time-Dependent Correlators of Local Spins of the One-Dimensional XY Heisenberg Chain

Time-dependent temperature correlators of the anisotropic Heisenberg XY chain are calculated by the integration techniques with respect to Grassmann variables. For a chain of length M, the correlators are represented as the determinants of 2M × 2M matrices. In the thermodynamic limit, the correlation functions are expressed in terms of the Fredholm determinants of linear integral operators with matrix kernels. Bibliography: 32 titles.     

Kerr constant of water

Measurements are conducted of the Kerr constant of ultrapure water with resistivity 10⁷ · cm. Values of the Kerr constant of (3.26 ± 0.10) · 10^-7 and (2.29 ± 0.07) · 10^-7 esu were obtained at a temperature of 30 °C for wavelengths of 441.6 nm and 632.8 nm.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 157–160, January–February, 1976.The authors wish to express their appreciation to D. D. Ryutov for useful discussion.