Feynman integral and complex classical trajectories

Let _t be an analytic solution of the Schrödinger equation with the initial condition . Let _t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then _t (x) _t (x)¹ ( _t (x)), where _t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.     

Continuum tight binding models and quantum transport in the presence of dynamical disorder

Continuum limits of various tight binding linear chain lattices used in the author's recent study of quantum transport in the presence of dynamical disorder, are analyzed from the point of view of their energy level spectra when disorder is absent. These spectra show a linear dispersion similar to that in the Luttinger model, and describe the energy levels of the corresponding discrete systems in the range of midband wavevectors. Next, the more conventional longwavelength continuum limit, which describes the energy levels of the actual discrete systems near the bottom of the bands is discussed. On the basis of these properties it is argued that the applicability of the continuum models to the study of dynamical properties is restricted to low frequencies in the range of low lying excitations, near the midband Fermi level in half-filled band situations in the case of the midband models, and near the bottom of a nearly empty band for the longwavelength models. Finally, it is shown that in the presence of dynamic disorder the longwavelength continuum limit of a single-band tight-binding model leads to nondiffusive motion, with a mean squared displacement <x ²(t)>t ³, fort.     

Random walks on cubic lattices with bond disorder

We consider diffusive systems with static disorder, such as Lorentz gases, lattice percolation, ants in a labyrinth, termite problems, random resistor networks, etc. In the case of diluted randomness we can apply the methods of kinetic theory to obtain systematic expansions of dc and ac transport properties in powers of the impurity concentrationc. The method is applied to a hopping model on ad-dimensional cubic lattice having two types of bonds with conductivity and ₀=1, with concentrationsc and 1–c, respectively. For the square lattice we explicitly calculate the diffusion coefficientD(c,) as a function ofc, to O(c²) terms included for different ratios of the bond conductivity. The probability of return at long times is given byP ₀(t) [4D(c,)t]^–d/2, which is determined by the diffusion coefficient of the disordered system.     

Long range scattering for nonlinear Schrödinger equations in one space dimension

We consider the scattering problem for the nonlinear Schrödinger equation in 1+1 dimensions: where = /x,R{0},R,p>3. We show that modified wave operators for (*) exist on a dense set of a neighborhood of zero in the Lebesgue spaceL ²(R) or in the Sobolev spaceH ¹(R)., The modified wave operators are introduced in order to control the long range nonlinearity |u|² u.Laboratoire associé au Centre National de la Recherche Scientifique     

On the hole spectral function of the Emery model

We discuss the spectral function of a single O hole generated in a two-dimensional CuO₂-lattice at half-filling. The latter constitutes the most important structural element of high-T _c superconducting materials. The system is described by the so-called extended Hubbard or Emery model. Strong electronic correlations which are incorporated in the model prevent the usual evaluation of Green functions based on Wick's theorem and using diagram techniques. For that reason we apply a new cumulant approach to dynamical correlation functions introduced recently. As a result we find that the local one-O hole excitation spectrum has two structured absorption regions around the bare O energy _p and around _p + due to charge fluctuations of Cu holes. Here is the bare charge transfer gap. The width of the absorption regime around _p is of the order of several timest _pd ² /, wheret _pd is the hopping integral between Cu and O holes.     

Orbiting test masses for an equivalence principle space experiment

Deviations from the equivalence principle can be found by observations of the orbital periods of masses in a two body system, in a drag free satellite in geosynchronous orbit. At this altitude the Earth gravitational field tides allow close stable circular motion, within a 30 cm lobe, of a small test mass around the centre of the primary mass, of 75 kg. The repulsive fifth force ought to slow the orbital Newtonian period. A precise clock and laser interferometry provide the determination of in the range between 1 and 10²cm and of if larger than 10^–4.2 or 10^–5, for an uncertainty of the value of the constant of gravitation equal to 10^–5 or 10^–6, respectively ( and are the coupling coefficient to gravity and range of action of the fifth force). In the latter case, for around 10 cm, the fifth force may be detected for larger than 10^–5.5. This experiment may verify the principle of equivalence at short range improving the actual limits from one to two and a half orders of magnitude. The range of action,, up to several meters can be observed with this local experimental concept, but only for large values of, which have been excluded recently by ground experiments.     

Quantum shot noise: Expansions in powers of the pulse density

Quantum shot noise consists of individual pulses which contribute time-dependent (operator) potentials toward a total potentialV(t). The averaged quantity T exp _t0 ^t dtV(t) in general can no longer be calculated explicitly, in contrast to the classical case, and expansions are of interest. Noncommutative cumulant expansions are not directly applicable if the correlation functions ofV(t) have singularities, as happens in applications. It is shown here that these expansions, when applied to quantum shot noise, can be partially summed to give expansions in powers of the pulse density. Three types of such expansions are established explicitly, and for two of them the derivation is direct. For one of them the first-order approximation is closely connected to the so-called unified theory of spectral-line broadening.     

Evidence for incipient O dimerization and absence of Cu+3 in temperature-dependent XPS of highT c superconducting oxides

From temperature-dependent X-ray photoemission (XPS) spectra between 300 and 10 K of Sr doped La₂CuO₄ and 123 compounds (YBa₂Cu₃O_7–) we deduce the absence of the Cu3d ⁸(Cu³⁺) configuration in the ground state of these Mott insulators. The metallic character of these samples and involving those Cu atoms which are relevant for the superconducting properties arises from (d ⁹ p ⁶)+(d ¹⁰ p ⁵) valence fluctuations, while the superconducting transition is indicated to be closely related to an incipient oxygen dimerization which is best detected upon cooling far belowT _c .     

Nonradiative excitation energy transport in one-component disordered systems

High-accuracy Monte Carlo simulations of the time-dependent excitation probabilityG ^s (t) and steady-state emission anisotropyr _M /r _0M for one-component three-dimensional systems were performed. It was found that the values ofr _M /r _0M obtained for the averaged orientation factor only slightly overrate those obtained for the real values of the orientation factor _ik ² . This result is essentially different from that previously reported. Simulation results were compared with the probability coursesG ^s (t) andR(t) obtained within the frameworks of diagrammatic and two-particle Huber models, respectively. The results turned out to be in good agreement withR(t) but deviated visibly fromG ^s (t) at long times and/or high concentrations. Emission anisotropy measurements on glycerolic solutions of Na-fluorescein and rhodamine 6G were carried out at different excitation wavelengths. Very good agreement between the experimental data and the theory was found, with _ex0-0 for concentrations not exceeding 3.5·10^–2 and 7.5·10^–3 M in the case of Na-fluorescein and rhodamine 6G, respectively. Up to these concentrations, the solutions investigated can be treated as one-component systems. The discrepancies observed at higher concentrations are caused by the presence of dimers. It was found that for _ex <_0-0 (Stokes excitation) the experimental emission anisotropies are lower than predicted by the theory. However, upon anti-Stokes excitation (_ex>_0-0), they lie higher than the respective theoretical values. Such a dispersive character of the energy migration can be explained qualitatively by the presence of fluorescent centers with 0-0 transitions differing from the mean at _0-0.     

Experimental survey of the sticking problem in muon catalyzed dt fusion

The sticking process dt + n, which constitutes the most severe limit to the number of fusions which a muon can catalyze, is reviewed. Many attempts were made to determine by calculations and measurements the probability for initial sticking _s ⁰ (immediately after dt fusion) and for final sticking _s (after the came to rest). Previous results based on neutron disappearance rates and on the observation of -X-rays were controversial and also in some disagreement with theory. New data are reported from PSI on direct observation of final sticking, using a setup with the St. Petersburg ionization chamber. These data mark a significant improvement in reliability and may clarify questions concerning previous discrepancies. The new results is _s(0.56±0.04)%, lower than the theory prediction _s=(0.65±0.03)%, at medium density.     

A finite size analysis of the structure factor in the antiferromagnetic Heisenberg (AFH) model

From a finite size analysis we extract the structure factorS(p, N=) of the one dimensional AFH-model in the groundstate: The gross structure is well described byL (p) = –ln(1– ^p ). The fine structure which only contributes a few percent reveals a pronounced non-linear behavior inL(p) with a maximum atp=0.20 and a minimum atp=0.82.     

Effect of electron-hole scattering on the resistivity and Hall coefficient in YBaCuO

Coupled electron-hole (e-h) Boltzmann equations are applied to evaluate the resistivity and Hall coefficientR _H for a two-band model system with e-h, impurity, and phonon scatterings. We show that the anomalous temperature dependences =T andR _H ^–1 =T observed on YBaCuO compounds can be obtained by assuming a special two-band model in which the e-h scattering is responsible for the resistivity and the chemical potential varies linearly with temperature.     

An interaction of nucleons at an energy between 1014 and 1015 eV/nucleon

A jet (0+14) with primary energy {3.3 _{– 2.2} ^{+ 5.3} }. 10¹⁴ eV/nucl. was observed in the I-stack. An interaction with very small multiplicity (n _s =3or 4)found in the axis of the jet is probably caused by another nucleon from the -primary. 10 particles of the narrow cone have opening angles of some 10^–4 radians, 4 particles in the diffuse cone are emitted at angles of a few 10^–2 radians. A pronounced anisotropy exists in the C. M. system. The coefficient of inelasticity 0.1was calculated directly extrapolating the measured energies of secondaries. The interpretation of the whole event is in good agreement with Heisenberg's theory of multiple production of particles.     

A comment on an exact solution with a stiff equation of state

Recently, an analytical stellar model with a stiff equation of state and density distribution= _c (1-r ²/r _o ² ) was presented. We show that such a solution cannot exist.     

Ergodic properties of infinite-dimensional stochastic systems

The ergodic properties of two stochastic models _I and _II are investigated. Each model is described by a fieldx(t),t > 0, on the lattice =Z ^d,d < . For _I,x(t) evolves according to the equations wherex _s (t) R for eachs eF. Here the {w_s(t): s } are independent, one-dimensional Wiener processes, ₂ is a bounded interaction between adjacent lattice sites, and the potentials ₁ and ₂ satisfy appropriate regularity conditions. It is shown that for each model,x(t) is a Markov process on an infinite-dimensional phase spaceX. The probability measures onX that satisfy the Dobrushin-Lanford-Ruelle (DLR) conditions are stationary for this process and have a mixing property. Moreover, for _I any stationary, time-reversal-invariant probability measure that has certain regularity properties must satisfy the DLR conditions.This paper is based on a portion of the author's Ph.D. thesis.⁽²⁾     

Some problems of quantum mechanics possessing a non-negative phase-space distribution function

In order to clarify physical consequences due to the presence of a set of auxiliary functions _k (q,t) in quantum mechanics with a non-negative phase-space distribution function, the simplest quantum-mechanical problems are solved. It is shown that _k (q,t) influence upon the results of a problem. Therefore it is supposed that _k (q, t) reflect some physical reality (subquantum situation), interacting with a mechanical system. In particular the subquantum situation determines the minimum coordinate and momentum uncertainties ((q)² and (p)²) as well as the coordinate distribution of a fixed system and the momentum distribution of a free system. These results provide the opportunity to formulate the notion of a stationary homogeneous isotropic subquantum situation. Supposing thatq andp are small an attempt is made to develop an approximate method of solutions (quasi-orthodox approximation). Energy spectrum of an electron in a hydrogen atom is found in the second order of this approximation.On leave of absence from Peoples' Friendship University, Chair of Theoretical Physics, 3, Ordjonikidze Street, B-302, Moscow, U.S.S.R.     

Hyper-Kähler metrics and a generalization of the Bogomolny equations

We generalize the Bogomolny equations to field equations on ^{3 n} and describe a twistor correspondence. We consider a general hyper-Kähler metric in dimension 4n with an action of the torusT ⁿ compatible with the hyper-Kähler structure. We prove that such a metric can be described in terms of theT ⁿ -solution of the field equations coming from the twistor space of the metric.     

Dirac's cosmology with varying cosmological constant

The phenomenological approach to investigating the decay of the vacuum energy density is generalized in the spirit of Dirac's large number hypothesis. Different arguments are outlined to justify an universal dependence of the type =H ² ( is a pure number andH is the Hubble parameter). Such time-varying A does change the predictions of the earlier Dirac's cosmology. The deceleration parameter (q ₀=(2–)/(1+)) and the age parameter (H ₀t₀=(1+)/3) are now compatible with the observations. The model also allows a power-law inflationary phase and a rate of matter creation smaller than the one present in the steady state universe.     

Natural boundaries for area-preserving twist maps

We consider KAM invariant curves for generalizations of the standard map of the form (x, y)=(x+y, y+f(x)), wheref(x) is an odd trigonometric polynomial. We study numerically their analytic properties by a Padé approximant method applied to the function which conjugates the dynamics to a rotation +. In the complex plane, natural boundaries of different shapes are found. In the complex plane the analyticity region appears to be a strip bounded by a natural boundary, whose width tends linearly to 0 as tends to the critical value.     

Bianchi VI cosmological models representing perfect fluid and radiation with electric-type free gravitational fields

A homogeneous Bianchi type VI_h cosmological model filled with perfect fluid, null electromagnetic field and streaming neutrinos is obtained for which the free gravitational field is of the electric type. The barotropic equation of statep = (–1) is imposed in the particular case of Bianchi VI₀ string models. Various physical and kinematical properties of the models are discussed.