Diffusion in a periodic potential with a local perturbation

We consider the diffusion of a particle at X_t in a drift field derived from a smooth potential of the formV+B, whereV is periodic andB is a bump of compact support. With no bump,B=0, the mean squared displacementE(t) E |X _t – X₀|² =D(V)t +C +O(e ^–t ),>0, in any dimension. WhenB0, we establish in one dimension the asymptotic expansion , 0, ast. Our analysis relies on the Nash estimates developed in previous work for the transition density of the process and their consequences for the analytic structure,of the Laplace transform ofE(t).     

Monte Carlo simulation of phase separation and clustering in the ABV model

As a model for a binary alloy undergoing an unmixing phase transition, we consider a square lattice where each site can be either taken by an A atom, a B atom, or a vacancy (V), and there exists a repulsive interaction between AB nearest neighbor pairs. Starting from a random initial configuration, unmixing proceeds via random jumps of A atoms or B atoms to nearest neighbor vacant sites. In the absence of any interaction, these jumps occur at jump rates _A and _B, respectively. For a small concentration of vacancies (c _v=0.04) the dynamics of the structure factorS(k,t) and its first two momentsk ₁(t),k ₂ ² (t) is studied during the early stages of phase separation, for several choices of concentrationc _B of B atoms. Forc _B=0.18 also the time evolution of the cluster size distribution is studied. Apart from very early times, the mean cluster sizel(t) as well as the moments of the structure function depend on timet and the ratio of the jump rates (= _B/ _A) only via a scaled timet/(). Qualitatively, the behavior is very similar to the direct exchange model containing no vacancies. Consequences for phase separation of real alloys are briefly discussed.     

Transient optically detected ESR in the excited state of ruby

The dynamics of the(² E) state of Cr³⁺ in Al₂O₃ have been investigated. After excitation by a short laser pulse (<10ns) the relative intensity of the optically detected ESR signal (ODMR) as a function of the delay timet _d after the excitation is measured. A remarkable increase was found upon lengtheningt _d, while the line width remained constant. This increasing population difference of the Zeeman levels of(² E) can be explained by different resonant-reabsorption induced effective lifetimes. The experimental data could be reproduced by use of a phenomenological model.     

Schwinger mechanism for gluon-pair production in the presence of arbitrary time-dependent chromo-electric field

We study the Schwinger mechanism for gluon-pair production in the presence of an arbitrary time-dependent chromo-electric background field E ^a (t) with arbitrary color index a=1,2,…,8 in SU(3) by directly evaluating the path integral. We obtain an exact expression for the probability of non-perturbative gluon-pair production per unit time per unit volume and per unit transverse momentum, , from arbitrary E ^a (t). We show that the tadpole (or single-gluon) effective action does not contribute to the non-perturbative gluon-pair production rate, . We find that the exact result for non-perturbative gluon-pair production is independent of all the time derivatives , where n=1,2,…,∞, and that it has the same functional dependence on the two Casimir invariants, [E ^a (t)E ^a (t)] and [d _abc E ^a (t)E ^b (t)E ^c (t)]², as the constant chromo-electric field E ^a result with the replacement: E ^a →E ^a (t). This result relies crucially on the validity of the shift conjecture, which has not yet been established. This result may be relevant to the study of the production of a non-perturbative quark–gluon plasma at RHIC and LHC.     

Experimental investigation of vibrational excitations in230Th

Nuclear levels in²³⁰Th have been investigated in the decay of²³⁰Pa, the²³⁰Th(d, pn) reaction and the²³²Th(p, t) reaction. TheK =0 ₁ ⁺ , 2 ₁ ⁺ , and 2 ₂ ⁺ bands with band heads at 635, 781, and 1010 keV were observed up to the 8⁺, 9⁺, and 7⁺ levels, respectively. A second excited 0⁺ level was identified at 1297 keV which might be interpreted as the usual shape-oscillation. The branching ratios of theE2 transitions from the 0 ₁ ⁺ , 2 ₁ ⁺ , and 2 ₂ ⁺ bands are explained in the framework of the rotational model by taking into account the coupling of these bands with the ground-state band, and the coupling between the 0 ₁ ⁺ and 2 ₁ ⁺ band. A strong enhancement ofE2 transitions from the 2 ₁ ⁺ to the 0 ₁ ⁺ band reported earlier is not confirmed. For the octupole vibrations withK =0^–, 1^–, and 2^– theE1 branching ratios are analyzed in terms of the Coriolis coupling of these bands. An almost complete experimental set ofE1 transition moments from these negative-parity bands to the 0 _g ⁺ , 0 ₁ ⁺ , and 2 ₁ ⁺ bands was obtained. It is suggested that octupole correlations might be important in explaining theseE1 moments.We appreciate the help of Mr. Assmus with the proton irradiations and the financial support of the Kernforschungszentrum Karlsruhe GmbH. This work was supported by the Deutsche Forschungsgemeinschaft (grants Bo 1109/1-1, Gr 894/2-1, Gu 179/3-1 and He 1316/2-3) and by the Volkswagen Stiftung.     

Excitations in Heisenberg spin glasses

Within the RPA approach forT=0, the excitations of the Heisenberg spin glass system Eu _x Sr_1–x S are studied by numerical methods, using a continued fraction algorithm. Both the density of statesg(E) and also the spectral functionS(q,E) are calculated for systems with (16)³ sites, withx=0.4, 0.5, and 0.6 (spin glass phase), and also forx0.7 (ferromagnetic phase). Forq-vectors within the (1,1,1) plane,S(q,E) shows magnon peaks even in the spin glass phase, over the whole range ofq. However, these peaks are quite broad, and there is considerable intensity at small energies even for largeq, leading to a finite intercept ofg(E) forE0. Over a large temperature range, the specific heat is approximately linear inT forx0.7.     

Anderson localization in different one-dimensional systems with off-diagonal disorder and spin-dependence

The localization properties of certain spin-dependent, one-dimensional electronic systems with only off-diagonal disorder are studied. In higher dimensions (d=2,3) the models considered would correspond to different universality classes, whereas ford=1 no qualitative difference is found: ForE=0, all eigenstates are exponentially localized, whereas forE0 the localization length diverges logarithmically, such that exactly atE=0 the geometric average of the transmission coefficient would decay with increasing chain lengthL as exp (-const. ·L ^1/2), instead of the usual, exponential decay.ForE=0, in the interior of the band, the localization lengthr ₀ diverges W ₂ ^–2 in the limit of weak disorder (W ₂0), whereas just at the band edge one has roughlyr ₀W ₂ ^–2/3. A universal recursion relation, depending only on the energy and on certain randomly distributed determinants, determines the localization length and the density of states for all systems considered.     

Statistical mechanics of rotating systems

A microcanonical distribution function depending on the total energyE and thez-componentM of the total angular momentum of a rotating system is examined. ForM=0 the generalized microcanonical ensemble is found to give the same entropy as the usual microcanonical ensemble. The moment of inertia of a rotating gas is calculated, and the kinetic energy of rotation is given as a power series in the small parameterM ²/2I ₀E_int, whereI ₀ is the moment of inertia of the gas at rest andE _int the internal energy.     

Orbital Divergence and Relaxation in the Gravitational N-Body Problem

One of the fundamental aspects of statistical behaviour in many-body systems is exponential divergence of neighbouring orbits, which is often discussed in terms of Liapounov exponents. Here we study this topic for the classical gravitational N-body problem. The application we have in mind is to old stellar systems such as globular star clusters, where N10⁶, and so we concentrate on spherical, centrally concentrated systems with total energy E<0. Hitherto no connection has been made between the time scale for divergence (denoted here by t _e ) and the time scale on which the energies of the particles evolve because of two-body encounters (i.e., the two-body relaxation time scale, t _r ), even though both may be calculated by similar considerations. In this paper we give a simplified model showing that divergence in phase space is initially roughly exponential, on a timescale proportional to the crossing time (defined as a mean time for a star to cross from one side of the system to another). In this phase t _e <<t _r , if N is not too small (i.e., N30). After several e-folding times, the model shows that the divergence slows down. Thereafter the divergence (measured by the energies of the bodies) varies with time as t ^1/2, on a timescale nearly proportional to the familiar two-body relaxation timescale, i.e., t _e t _r in this phase. These conclusions are illustrated by numerical results.     

Magnetic field dependent splitting of doubly degenerate phonon states in anhydrous cerium-trichloride

The Raman spectra of single crystals of hexagonal CeCl₃ have been investigated atT=2K in external magnetic fieldsB up to 6 T. The crystal field states of the 4f ¹(² F _5/2)-configuration of Ce³⁺ show a linear Zeeman-splitting. Two degenerate phonon states (197 cm^–1(E _1g), 109 cm^–1(E _2g)) also split in the magnetic field. ForB parallel to the optic axisZ the field dependence of the splitting is similar to the behaviour reported earlier for Ce F₃ and NdF₃ (linear splitting at low fields, which is followed by a saturation at high fields). ForBZ a splitting of the same phonons proportional toB ² is observed in CeCl₃, which was not found in the other compounds. The linewidths of the electronic transitions and of the split phonon components are reduced with increasing magnetic fieldstrength.The field- and temperature dependences of the phonon energies can be explained quantitatively using results of the theory of the 4f-electron-phonon interaction as developed for the cooperative Jahn-Teller-effect or for the magneto-elastic interaction. The experimental results forBZ require an interaction Hamiltonian which is bilinear in the electronic and phonon operators, respectively. The conclusions are supported by group theoretical considerations.The experiments described here have been performed at the Technische Hochschule Darmstadt, Institut für Festkörperphysik II, Fachgebiet Technische Physik as a project of the Sonderforschungsbereich Festkörperspektroskopie SFB65, supported by the Deutsche Forschungsgemeinschaft     

Far-Infrared Laser Stark Spectroscopy of CH3OD

The high resolution Stark spectra of the singly deuterated methanol isotope, CH₃OD, have been studied using the HCN laser with Stark fields up to approximately 60 000 V/cm. Numerous families of absorption lines have been observed in both parallel and perpendicular polarizations, resulting in the following assignments: with the 311 m line – J _K = 18₁ 18₀ E ₂, _t = 1; and with the 337 m line – J _k = 6₄ 5₃ E ₂, _t = 0 and J _K = 14₆ 13₅ A, _t = 1. Zero-field frequencies for the assigned transitions are in agreement with Fourier transform measurements and those calculated from the available molecular constants.     

Convergence of Chorin-Marsden product formula in the half-plane

Consider a viscous incompressible fluid in the half-plane and letu _t be a solution of the Navier-Stokes equation. In this paper we prove that the product formula (E _t/n G _t/n u) ⁿ u ₀, whereE _t is the Euler flow,G _t is the heat flow and is a suitable operator describing the vorticity production due to the boundary, converges uniformly tou _t in the limitn .Research supported by Ministero della Pubblica Istruzione, CNR contract No. 84.00016.02 and GNFM     

The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines

In this paper a microscopic quantum mechanical model of computers as represented by Turing machines is constructed. It is shown that for each numberN and Turing machineQ there exists a HamiltonianH _N ^Q and a class of appropriate initial states such that if c is such an initial state, then _Q ^N (t)=exp(–1H _N ^Q t) _Q ^N (0) correctly describes at timest ₃,t ₆,,t _3N model states that correspond to the completion of the first, second, , Nth computation step ofQ. The model parameters can be adjusted so that for an arbitrary time interval aroundt ₃,t ₆,,t _3N, the machine part of _Q ^N (t) is stationary.     

Field screening in insulating crystals: The quasistatic case

A study is made of a metal-dielectric-semiconductor-dielectric-metal structure subjected to a linearly increasing external voltage. On the assumption of quasistatic screening conditions, the carrier-density and field distribution in the near-anode and nearcathode regions of the semiconductor are determined. This distribution proves to be nonuniform not only in the region of the surface space charge induced by the external field, but also within the interior of the semiconductor to a depth E₀·t_M/₀, where is the lifetime and the mobility of the carriers, E₀/₀ is the rise rate of the external field, and t_M is the Maxwellian relaxation time. The character of the distribution for opposite faces of the semiconductor is different, since in the near-cathode region for n-type semiconductors allowance must be made for the effect of the uncompensated space charge of the current carriers on the conductivity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 7–10, February, 1973.We are indebted to G. M. Guro and V. B. Sandomirskii for a discussion of the work.     

The origin of double inflation

Double inflation is a typical solution of fourth-order gravity, $$L_{grav} = M^2 R - R^2 /6$$ minimally coupled to a scalar field with mass m, and 0pl. For equipartition of initial conditions at the Planck era, being equivalent to the Gibbons-Hawking-Stewart measure, we get the probability of double inflation to be about $$p = 1 - mM/M_{pl}^2 $$ Fort → ∞ and a scalar field or ideal fluid as source, the solutions for the scale factor oscillate around a～t^2/3, thus theR ² term gives effectively dustthe dark matter of the universe. The big bang is generically ofa ～ t^1/2 type, independent of the matter. ForM=0 and radiation as source the exact solutiona(t)=[sinh(2H ₀ t)]^1/2 supports the attractor property of the de Sitter solution.     

Experimental constraints on the phase in the Cabibbo-Kobayashi-Maskawa matrix

Using experimental results on |V _ub /V _cb |, (K⁰), (B⁰) and two experimental limits onm _t , and assuming that these five observations are fully described by standard physics, we determine values and errors for the two CKM matrix parameters and with a maximum-likelihood fit. The results depend strongly onf _B ; (, ) lies in the first quadrant forf _B >180 MeV and in the second forf _B <180 mev.=" as=" functions=">f _B , we present also values and errors onm _t , ₁₃, |V _td |, arg(V _td ), and M(B _s )/(B _s ).     

Ionization of Coulomb Systems in {\mathbb{R}^3} by Time Periodic Forcings of Arbitrary Size

We analyze the long time behavior of solutions of the Schrödinger equation ${i\psi_t=(-\Delta-b/r+V(t,x))\psi}We analyze the long time behavior of solutions of the Schr?dinger equation iy_t=(-D-b/r+V(t,x))y{i\psi_t=(-\Delta-b/r+V(t,x))\psi}, x ? \mathbbR³{x\in\mathbb{R}^3}, r =  |x|, describing a Coulomb system subjected to a spatially compactly supported time periodic potential V(t, x) =  V(t +  2π/ω, x) with zero time average.     

Kramers time in weakly nonpotential systems

We consider a bistable Fokker-Planck system with a known stationary distribution and a small nonpotential part in the drift force. We perform a perturbation calculation of its Kramers time, _K, and compare it with the corresponding time, _K ⁽⁰⁾ , for the potential system which has the same stationary distribution. We show that _K/ _K ⁽⁰⁾ depends only on the properties of the drift force close to the saddle-point.The authors would like to dedicate this work to their colleagues Y. Orlov, R. Nazarian, and V. Brailovski.     

Energy relaxation in aϕ 4 with long range interactions

We investigate the influence of long range interactions on the relaxation behaviour of a lattice model with an on-site potential of ⁴-type and infinite range harmonic interactions. For finite number of particlesN, it is shown that the autocorrelation functions <E _n(t)E _n > of the fluctuations of the one-particle energiesE _n(t) decays exponentially. The corresponding relaxation time is proportional toN and is given by (T, N) =N₀(T). The temperature dependent time scale ₀ can explicitly be related to the dynamics of a one-particle correlator of the noninteracting system. The results are derived using Mori-Zwanzig projection formalism. The corresponding memory kernel is calculated within a mode coupling approximation and by a perturbative approach. Both results agree in leading order in 1/N. It is speculated that any interaction of range generates a timescale .