On the integrals of motion for an exactly solvable model of interacting fermions

Based on the Lax formalism, integrals of motion are constructed for the Sutherland hyperbolic systems of particles with internal degrees of freedom (su(n) spins) situated in an external field with the Morse potential characterized by the parameter τ². It is shown that the corresponding infinite-dimensional algebra determining the hidden symmetry of the systems is not of the Yangian type.     

Intensity parameters of Tm3+ and Er3+ in borate,phosphate and germanate glasses

Intensity parameters τ_λ of the Judd-Ofelt expression were obtained from oscillator strengths of the electronic transitions of Tm³⁺ and Er³⁺ in the visible and infrared part of the spectra. The parameters are interpreted by means of static and dynamic crystal field expansion. The τ_λ 's of Tm³⁺, Er³⁺ and Eu³⁺ are expressed as a function of the h (covalency parameter) parameter of the glass. It is concluded that vibrational interaction plays a dominant role in the origin of the forced electric dipole transitions of Tm³⁺ and Er³⁺ in glasses.     

On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order

The broken symmetry state with off-diagonal long-range order (ODLRO), which is characterized by the vacuum expectation value of the operator of creation of the conserved quantum number Q, has the time-dependent order parameter. However, the breaking of the time translation symmetry is observable only if the charge Q is not strictly conserved and may decay. This dichotomy is resolved in systems with quasi-ODLRO. These systems have two well separated relaxation times: the relaxation time τ _Q of the charge Q and the energy relaxation time τ _E . If τ _Q ? τ _E , the perturbed system relaxes first to the state with the ODLRO, which persists for a long time and finally relaxes to the full equilibrium static state. In the limit τQ → ∞, but not in the strict limit case when the charge Q is conserved, the intermediate ODLRO state can be considered as the ground state of the system at fixed Q with the observable spontaneously broken time translation symmetry. Examples of systems with quasi-ODLRO are provided by superfluid phase of liquid ⁴He, Bose-Einstein condensation of magnons (phase coherent spin precession) and precessing vortices.     

无序Cu33Y67低温电阻和磁阻中的相互作用和弱定域化

文中报道非晶Cu₃₃Y₆₇低温电阻和磁阻的测量结果。这种合金是在He气氛中以熔化-自旋技术制备的。相互作用效果可以为4.5K以下的低温电阻提供一个-T^1/2形式的贡献。在稍高的温度,其变化规律也可以通过相互作用和弱定域化的联合来解释。上至1.8T的磁阻测量揭示出一个具有自旋-轨道散射较强影响的弱定域化效果。Cu₃₃Y₆₇的磁阻测量值比弱定域化预言的大。如果把弱定域化的理论预言强度增大3倍,则可以在 关键词：     

Flow of 2D atomic hydrogen over the surface of liquid <Superscript>4</Superscript>He

Experimental evidence has been obtained for the hydrodynamic flow of a 2D gas of hydrogen atoms adsorbed on the surface of liquid helium. The observed flow manifestations are consistent with the concepts of the quantum hydrodynamics of the helium surface. This circumstance allows both investigation of the interaction of 2D hydrogen with ripplons and surface ³He quasiparticles and possible future observation of the superfluidity of the 2D Bose gas of hydrogen atoms. The experimental results on thermal compression make it possible to estimate the characteristic times of the transfer of longitudinal momentum between the subsystems of hydrogen and ³He atoms bound to the surface (τ_H3), as well as from ripplons to the substrate (τ_R). The value τ_H3 ～ 4 × 10^?8 s agrees with a value calculated using the mean-field parameter U₃₀ for the interaction of hydrogen atoms with the ground surface state of ³He. At the same time, τ_R is more than an order of magnitude shorter than the value obtained in experiments by Mantz et al. Phys. Rev. Lett. 44, 66 (1980) [Erratum: Phys. Rev. Lett. 44, 1094 (1980)]. This discrepancy can be attributed to the dependence of the ripplon momentum relaxation rate on the substrate roughness scale.     

Die Anlagerung radioaktiver Atome an Aerosole (Schwebstoffe)

The attachment of the decay products of thorium emanation to aerosol particles has been studied. The dependence of the attached activity on the particle size was determined for spherical particles with radiiR ranging from 0·04 to 0·6 microns. The particles used were homogeneous dioctylphthalate droplets and polystyrene micro-spheres. It is found that the attached activity is proportional toR ²/(1+hR). This dependence can be derived theoretically by considering the deposition to be solely governed by the diffusion process (not by electrostatic forces) and assuming a quasi-stationary density distribution for the diffusing atoms. The constanth is uniquely determined by the average gaskinetic velocity and the diffusion constant of the diffusing atoms. For the decay products of thorium and radium emanation (atomic weight ≈210)h ≈ 7 · 10⁴ cm^?1. The derived equation holds for a wide range of particle sizes: For the particles with radii larger than about 10^?4 cm this means that the attachment is proportional to the radius; for particle radii below about 10^?6 cm it is proportional to the surface (R²) of the particles. It is also possible to derive an expression for the time-dependence of the attachment process from the theoretical considerations. The rate at which the average concentration of the radioactive atoms decreases is proportional to exp ?t/τ where τ=1+hR/πR² N¯ v (¯ v=average gaskinetic velocity of the diffusing atoms;N=aerosol concentration).     

Evaluation of the time of prompt-fission-neutron emission from 252Cf by measuring a two-particle correlation function

The time of prompt-fission-neutron emission from ²⁵²Cf is evaluated at τ₀≥(1?2)×10^?19 s by measuring a two-neutron correlation function. The final-state interaction of identical neutrons emitted by moving fission fragments is taken into account.     

Relaxation to a Perpetually Pulsating Equilibrium

Paper in honour of Freeman Dyson on the occasion of his 80th birthday. NormalN-body systems relax to equilibrium distributions in which classical kinetic energy components are 1/2kT, but, when inter-particle forces are an inverse cubic repulsion together with a linear (simple harmonic) attraction, the system pulsates for ever. In spite of this pulsation in scale,r(t), other degrees of freedom relax to an ever-changing Maxwellian distribution. With a new time, τ, defined so thatr ²d/dt = d/dτ it is shown that the remaining degrees of freedom evolve with an unchanging reduced Hamiltonian. The distribution predicted by equilibrium statistical mechanics applied to the reduced Hamiltonian is an ever-pulsating Maxwellian in which the temperature pulsates liker ^-2. Numerical simulation with 1000 particles demonstrate a rapid relaxation to this pulsating equilibrium.     

Conductivity of Wigner liquid

The conductivity of two-dimensional electron systems with low carrier concentration is considered on the basis of the previously suggested model (Fermi liquid with a soft mode) under the assumption that the equilibrium in each of the (fermion and boson) subsystems is established faster than the impurity relaxation and the relaxation between the subsystems (hydrodynamic approximation). The conductivity of the system depends on three characteristic times: τ₁(τ₂) is determined by the fermion (boson) impurity scattering and τ₁₂ is determined by the friction between the subsystems; the respective temperature dependences are obtained. The conductivity is related to the relaxation time τ in the usual way, and τ obeys the relationship τ^?1=τ ₁ ^?1 +(τ₂+τ₁₂)^?1. It follows from the results obtained that the resistivity of pure samples should increase with temperature and tend towards saturation.     

Superfluorescence and amplified spontaneous emission in an inhomogeneously broadened medium

The emission from a high gain pencil-shaped volume of inhomogeneously broadened (T¹₂) and initially completely inverted two-level atoms is described fully quantum-mechanically taking into account propagation along the pencil axis. The emission is shown to be superfluorescence for T¹₂ ? √τRτD and amplified spontaneous emission for τR ? T¹₂ ? √τRτD, where τR and τD are the collective decay time and the delay time of pure (T¹₂ = ∞) superfluorescence, respectively.     

Electron-phonon interaction and current in strong electric fields

Using the Houston-wave approach we investigate the electron-phonon interaction in electric fieldsF which are sufficiently strong to change an electron's Bloch state drastically during the relaxation time τ, but still too weak to support standing electron waves between the band edges. We calculate τ for the low density, high temperature limit and find τ～F ^?1/2. The electric current in the field region of the “hot electrons” between its ohmic rise and its decrease proportional toF ^?1 is determined. Its increase withF ^+1/2 in the limit of relatively low fields agrees with Shockley's result.     

Quark-gluon plasma formation in heavy-ion collision

To account for the non-equilibrium character of quark-gluon plasma formation in relativistic heavy-ion collisions, it is proposed to use the product of energy density ? and interaction time τ_int (rather than ?) as the critical quantity for plasma formation. In a geometrical model, τ is approximated by the transit time, and ? by the maximum energy density calculated in the center-of-mass frame. For central collisions, an analytical expression for ?·τ is given. As an example, the systems ¹⁶O + ¹⁶O and ²⁰⁸Pb + ²⁰⁸Pb are investigated as functions of c.m. energy, and their respective suitability for plasma formation is discussed.     

Relaxationsphänomene in Mössbauerspektren von Magnetisierten paramagnetischen Substanzen. I [(Fe x,Al1-x )NH4(SO4)2· 12H2O]

The Fe³⁺-spin in alums of type (Fe _x , A1_1-x )NH₄(SO₄)₂ · 12 H₂O interacts (i) with the crystal lattice viaLS-coupling, and (ii) with the spins of the adjacent Fe³⁺-ions via magnetic dipole-dipole interaction. These interactions lead to a time fluctuation of the spin direction, characterized by correlation times τ _c and τ′ _c of increasing order. The times may be deduced from the⁵⁷Fe-Mössbauer spectra of the alums, τ _c from the width, and τ′ _c ≈τ _c from the position of the hyperfine structure lines. The theoretical interpretation of the Mössbauer spectra is relatively simple, when (i) the spin-lattice interaction gets frozen in, and (ii) a strong applied magnetic fieldH _a decouples the spins of the Fe³⁺-ion and the⁵⁷Fe-nucleus. The spectra were taken, therefore, at 4.2 °K and 8 kOe≦H _a ≦ 54 kOe. According to the 1/r ³-dependence of the magnetic dipole-dipole interaction τ _c should be related tox, the Fe-concentration, τ _c ·x≈τ₀=const. Forx≧0.5 our experimental results are in agreement with this rule when τ₀=(1.5±0.5) · 10^?9 s. For an alum withx=0.26, however, the observed spectra cannot be explained in terms of temporal spin fluctuations, at least not in the framework of the models which are available now. Here, presumedly, the electron spins of adjacent Fe³⁺-ions are coupled to more or less isolated and, consequently, relatively stationary spin clusters of various sizes, leading to many time independent internal magnetic fields. A treatment of this proposal is in preparation.     

用正电子湮没技术研究形变铁的恢复

本文介绍应用正电子湮没寿命和多普勒加宽方法研究60％形变铁等时退火各阶段中缺陷的恢复行为,实验结果说明正电子湮没平均寿命τ及多普勒加宽的S参数都是退火温度的函数,完整晶体中湮没寿命τ_f=111±lPS,缺陷中湮没寿命τ_d=162±lps,本文还根据捕获模型计算了正电子的捕获速率及τ₁,结果证明与理论预期的完全一致,经计算得出捕获正电于的相对缺陷浓度的范围为10^-7-10^-4数量级。 关键词：     

Electron spin relaxation of gadolinium (III) complexes in dimethylformamide solution

The characteristics of spontaneous Raman scattering from solutions of diatomic molecules are reviewed, especially with regard to what they may tell one about the dynamics of molecular motion. In the limit of extreme motional narrowing the polarized component of the Q branch is a lrentzian with a width which depends upon the rate (τ^-1) of dephasing of the molecular vibrations. An approximate, closed, quantum-mechanical expression for the contribution of ‘translational-translational’ quasielastic scattering to τ^-1, called τ_ph ^-1(T-T), is derived. The translational states of the liquid are determined by invoking the Lennard-Jones-Devonshire (LJD) cell model. The full LJD cell potential is replaced by an harmonic approximation thereto. The dependence of the τ_ph(T-T) upon thermodynamic variables and microscopic properties is discussed. The derived expression for τ_ph ^-1 (T-T) is then used to compute upper bounds on τ for liquid N₂ and O₂, for which experimental data are available. It is concluded that the T-T quasielastic scattering mechanism is essentially negligible and that other mechanisms must be dominant in determining τ. In particular, it is suggested that solvent-induced vibrational-reorientational coupling may be quite important.     

Phonon heating of two-dimensional exciton gases in GaAs/AlGaAs quantum wells

We report the first measurements of the interaction of non-equilibrium phonons with two-dimensional exciton gases (2DExGs). The rise in the effective temperature of the 2DExG produced by the phonons depends on the width of the quantum well and the exciton sheet density and hence on the ratio τ^?1 (ex-ph)/τ^?1 (ex-ex). The dependence of the effective temperature rise on this ratio is attributed to the non-equilibrium frequency distribution of the phonons incident on the 2DExG.     

Attractive and repulsive dispersion forces between biomolecules in aqueous solution

It has been shown before [1] that two large molecular systems having low-lying giant dipole vibrations may interact through strong long-range forces. This paper deals with the influence of a polar medium with Debye dispersion on this interaction between the molecules. It is shown that besides the normal van der Waals attraction also repulsion can occur, but this only in a limited range of the molecular eigenfrequencies just above the characteristics relaxation frequency τ^?1 of the medium.     

Determination of the mean life of some excited nuclear states by Moessbauer experiments

Mean lives of several excited nuclear states have been determined using the Moessbauer effect. The mean life is deduced by interpolating the experimental line width to zero effective thickness of the resonance absorber. An improved expression is used for the interpolation. The results are: τ(140 keV level of⁹⁹Tc)=277(14)ps τ(136 keV level of¹⁸¹Ta)=55 (3)ps τ(129 keV level of¹⁹¹Ir)=129 (2)ps τ(139 keV level of¹⁹³Ir)=115 (3)ps τ(77 keV level of¹⁹⁷Au)=2.73 (2)ns.     

Measurements of the upper and lower level lifetime in He-Se lasers

The lifetimes τ₂ and τ₁ of the upper and lower levels of the 5227 Å (5p ⁴D_{$\text{7}\text{2}$}→5s ⁴P_5/2) laser transition in He-Se were measured. The obtained values are: τ₂=(18.5±1.85) × 10^-9 sec; τ₁=(2±0.4) × 10^-9 sec. The value of τ₂ was determined by measuring the time constant of the transient in the fluorescent emission consecutive to a sudden interruption of the laser oscillation inside the cavity.The value of τ₁ was determined by measuring the change induced by one laser transition on the unsaturated gain of another laser transition sharing the same lower level. Finally the “radiation trapping” factor is evaluated, thus ruling out the possibility that radiation trapping might be responsible for saturation in the laser output versus discharge current.     

Influence of molecular motions on NQR echoes

The influence of thermal molecular motions on spin echo decay in pure nuclear quadrupole resonance (NQR) is considered. Our calculations show that the Hahn echo decay is caused by dipole-dipole interaction of the nuclear spins and is strongly affected by molecular mobility that can lead to the shortening of the echo decay with increased temperature. Slow molecular motion yields an exponential τ₃ time dependence, while fast motion yields an exponential decay. The outlined theory allows us to explain an unusual shortening of the³⁵Cl NQR echo decay on heating in thiourea-C₂Cl₆ inclusion compound.