Time evolution of wave-packets in quasi-1D disordered media

We have investigated numerically the quantum evolution of a -like wave-packet in a quenched disordered medium described by a tight-binding Hamiltonian with long-range hopping (band random matrix approach). We have obtained clean data for the scaling properties in time and in the bandwidth b of the packet width and its fluctuations with respect to disorder realizations. We confirm that the fluctuations of the packet width in the steady-state show an anomalous scaling [0pt] with [0pt] . This can be related to the presence of non-Gaussian tails in the distribution of [0pt]. Finally, we have analysed the steady state probability profile and we have found 1/b corrections with respect to the theoretical formula derived by Zhirov in the limit, except at the origin, where the corrections are . Received 6 August 1999 and Received in final form 22 October 1999     

Inelastic cross-sections and natural lifetimes for the 62D3/2, 5/2 and 82S1/2 states of Rb

The results of an experimental study of population dynamics following excitation of [0pt] and [0pt] states of rubidium are reported. Excitation transfer and quenching cross-sections in collisions with ground state rubidium atoms, and natural lifetimes have been measured. The experiment was performed in a vapour cell, using pulsed two-photon excitation and photon counting detection. The analysis of time dependent signals was based on a rate equation model in which transitions induced by thermal radiation have been accounted for. The measurements yielded following results: (1) [0pt] state J-mixing cross-section: [0pt] ; (2) cross-sections for [0pt] excitation transfer process: [0pt] ; (3) quenching cross-sections: [0pt] , [0pt] , [0pt] ; [0pt](4) radiative lifetimes: [0pt] ns, [0pt] ns, [0pt] ns. Received 1st December 1998 and Received in final form 17 May 1999     

Renormalization-Group Method for Reduction of Evolution Equations; Invariant Manifolds and Envelopes

The renormalization group (RG) method as a powerful tool for reduction of evolution equations is formulated in terms of the notion of invariant manifolds. We start with derivation of an exact RG equation which is analogous to the Wilsonian RG equations in statistical physics and quantum field theory. It is clarified that the perturbative RG method constructs invariant manifolds successively as the initial value of evolution equations, thereby the meaning to set t₀=t is naturally understood where t₀ is the arbitrary initial time. We show that the integral constants in the unperturbative solution constitutes natural coordinates of the invariant manifold when the linear operator A in the evolution equation is semi-simple, i.e., diagonalizable; when A is not semi-simple and has a Jordan cell, a slight modification is necessary because the dimension of the invariant manifold is increased by the perturbation. The RG equation determines the slow motion of the would-be integral constants in the unperturbative solution on the invariant manifold. We present the mechanical procedure to construct the perturbative solutions hence the initial values with which the RG equation gives meaningful results. The underlying structure of the reduction by the RG method as formulated in the present work turns out to completely fit to the universal one elucidated by Kuramoto some years ago. We indicate that the reduction procedure of evolution equations has a good correspondence with the renormalization procedure in quantum field theory; the counter part of the universal structure of reduction elucidated by Kuramoto may be Polchinski's theorem for renormalizable field theories. We apply the method to interface dynamics such as kink–anti-kink and soliton–soliton interactions in the latter of which a linear operator having a Jordan-cell structure appears.     

Reaction kinetics in polymer melts

We study the reaction kinetics of end-functionalized polymer chains dispersed in an unreactive polymer melt. Starting from an infinite hierarchy of coupled equations for many-chain correlation functions, a closed equation is derived for the 2nd order rate constant k after postulating simple physical bounds. Our results generalize previous 2-chain treatments (valid in dilute reactants limit) by Doi [#!doi:inter2!#], de Gennes [#!gennes:polreactionsiandii!#], and Friedman and O'Shaughnessy [#!ben:interdil_all_aip!#], to arbitrary initial reactive group density n₀ and local chemical reactivity Q. Simple mean field (MF) kinetics apply at short times, .For high Q, a transition occurs to diffusion-controlled (DC) kinetics with (where x_t is rms monomer displacement in time t) leading to a density decay . If n₀ exceeds the chain overlap threshold, this behavior is followed by a regime where during which k has the same power law dependence in time, , but possibly different numerical coefficient. For unentangled melts this gives while for entangled cases one or more of the successive regimes ,t ^-3/8 and t ^-3/4 may be realized depending on the magnitudes of Q and n₀. Kinetics at times longer than the longest polymer relaxation time are always MF. If a DC regime has developed before then the long time rate constant is where R is the coil radius. We propose measuring the above kinetics in a model experiment where radical end groups are generated by photolysis. Received: 2 June 1998 / Revised: 9 July 1998 / Accepted: 10 July 1998     

On the implicit integral character of Roothaan's expansion

The molecular generator coordinate Hartree-Fock method is reviewed. The connection between a quadrature solution of the generator coordinate Hartree-Fock equations and Roothaan's equations is stressed. The relation between linear expansion coefficients and generator coordinate weight functions is discussed and a numerical and analytical example is provided for the 1s orbital of the hydrogen atom represented as the integral transform of a Gaussian function. For the same example, the Gauss-Labatto quadrature is employed to emphasize the implicit integral character of Roothaan's equations. As a major conclusion, the interpretation that every LCAO calculation is actually performing integrations of the Griffin-Wheeler equations is advanced. Basis sets are therefore abscissas of the implicit quadrature used in the integration, whereas the linear coefficients automatically incorporate the corresponding weights. Subsequently, it is shown how to extract the generator coordinate weight function from the LCAO coefficients which has the advantage of being a characteristic of the physical system under study and not of the particular calculation being carried out. As such, basis set design becomes how to efficiently sample the weight function. Received: 13 June 1998 / Received in final form: 12 August 1998 / Accepted: 14 September 1998     

The Fermi-sea-like limit of the composite fermion wave function

The experimentally observed filling factors of the fractional quantum Hall effect can be described in terms of the composite fermion wave function of the Jastrow-Slater form [0pt] fully projected into the lowest Landau level. The Slater determinant of the above composite fermion wave function represents the filled Landau levels of composite fermions evaluated at the corresponding reduced magnetic field. For a system of fermions studied in the thermodynamic limit, we prove that in the even-denominator-filled state limit (when the number of filled Landau levels of composite fermions becomes infinite), the above composite fermion wave function exactly transforms into the Rezayi-Read Fermi-sea-like wave function [0pt] constructed by attaching 2m flux quanta to the Slater determinant of two-dimensional free fermions at the density corresponding to that filling. We study the composite fermion wave function and its evolution into the Fermi-sea-like wave function for a range of filling factors very close to the even-denominator-filled state. Received 19 March 1999     

Exactly solvable models through the generalized empty interval method,for multi-species interactions

Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for E _n(t)'s, the expectation value of the product of certain linear combination of the number operators on n consecutive sites at time t. The constraints are solved for the single-species left-right-symmetric systems. Also, examples of multi-species system for which the evolution equations of E _n(t)'s are closed, are given. Received 25 September 2002 / Received in final form 3 December 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: mamwad@iasbs.ac.ir     

Velocity measurement of a settling sphere

We study experimentally the motion of a solid sphere settling under gravity in a fluid at rest. The particle velocity is measured with a new acoustic method. Variations of the sphere size and density allow measurements at Reynolds numbers, based on limit velocity, between 40 and 7 000. At all Reynolds numbers, our observations are consistent with the presence of a memory-dependent force acting on the particle. At short times it has a t ^-1/2 behaviour as predicted by the unsteady Stokes equations and as observed in numerical simulations. At long times, the decay of the memory (Basset) force is better fitted by an exponential behaviour. Comparison of the dynamics of spheres of different densities for the same Reynolds number show that the density is an important control parameter. Light spheres show transitory oscillations at Re∼ 400, but reach a constant limit speed. Received 12 April 2000 and Received in final form 13 July 2000     

The microstructure of hydrogen- and deuterium-doped nanocrystalline palladium studied by small-angle neutron scattering

By means of small-angle neutron scattering the microstructure of two nanocrystalline Pd samples (prepared by inert gas condensation) has been studied at room temperature in a Q-range from [0pt] to [0pt] . An additional subsequent doping of the two samples with H as well as with D (concentrations < 4 at%) caused contrast variations that provided more detailed structural information. The measured scattering intensity was modeled by a Porod contribution from large heterogenities (e.g. pores) and a contribution from spherical grains with a log-normal distribution of their radii. To account for the presence of grain boundaries, the grains were considered to be surrounded by a shell with a reduced Pd density and a thickness half as large as the thickness of the grain boundaries. For the above model, the data of the H-doped, D-doped and undoped sample were simultaneously fitted with one single set of adjustable parameters. The fits yielded for the two samples volume-weighted mean grain radii of 10 nm and 13 nm. The values for the grain boundary thickness lie between 0.2 and 0.8 nm. Almost all of the H- and D-atoms are, at low hydrogen concentrations, located in the grain boundaries. Received 1 May 2000     

Time dependence in quantum mechanics

It is shown that the time-dependent equations (Schr?dinger and Dirac) for a quantum system can be derived from the time-independent equation for the larger object of the system interacting with its environment, in the limit that the dynamical variables of the environment can be treated semiclassically. The time which describes the quantum evolution is then provided parametrically by the classical evolution of the environment variables. The method used is a generalization of that known for a long time in the field of ion-atom collisions, where it appears as a transition from the full quantum mechanical perturbed stationary states to the impact parameter method in which the projectile ion beam is treated classically. Received 25 October 1999     

Non-linear evolution of step meander during growth of a vicinal surface with no desorption

Step meandering due to a deterministic morphological instability on vicinal surfaces during growth is studied. We investigate nonlinear dynamics of a step model with asymmetric step kinetics, terrace and line diffusion, by means of a multiscale analysis. We give the detailed derivation of the highly nonlinear evolution equation on which a brief account has been given [6]. Decomposing the model into driving and relaxational contributions, we give a profound explanation to the origin of the unusual divergent scaling of step meander (where F is the incoming atom flux). A careful numerical analysis indicates that a cellular structure arises where plateaus form, as opposed to spike-like structures reported erroneously in reference [6]. As a robust feature, the amplitude of these cells scales as t ^1/2, regardless of the strength of the Ehrlich-Schwoebel effect, or the presence of line diffusion. A simple ansatz allows to describe analytically the asymptotic regime quantitatively. We show also how sub-dominant terms from multiscale analysis account for the loss of up-down symmetry of the cellular structure. Received 4 May 2000 and Received in final form 8 September 2000     

Magnetic tunneling told to ignorants by two ignorants

Magnetic tunneling of a large spin subject to the Hamiltonian is investigated by elementary methods for weak fields H. In zero field (H=0) the tunnel frequency in the ground state is found to be equal to [0pt] multiplied by a quantity whose variation with s is slower than exponential. This result coincides with that of path integral methods [#!schi!#]. For the values of the longitudinal field which allow tunneling, the tunnel frequency is shown to vanish when H _y =0 for certain “diabolic" values of [0pt] , in qualitative agreement with experiments by Wernsdorfer and Sessoli. The particular case H _z =0 was already obtained by Garg by means of path integrals. The diabolic values of are in agreement with numerical results but, as already noticed by Wernsdorfer and Sessoli, they disagree with the experimental ones. This may be an effect of higher order anisotropy terms, which is briefly addressed in the conclusion. Received 17 May 2000     

Shear-driven heat flow in absence of a temperature gradient

Jaynesian statistical inference is used to predict that steady, non-uniform Couette flow in a simple liquid will generate a heat flux proportional to the gradient of the square of the strain-rate when the temperature gradient is negligible. The heat flux is divided into phonon and self-diffusion components, with the latter coupling to the elastic strain and inelastic strain-rate. Operators for all these are substituted into the information-theoretic phase-space distribution. By taking moments of an exact equation for this distribution derived by Robertson, one obtains an evolution equation for the self-diffusion component of the heat flux which, in a steady state, predicts shear-driven heat flow. Received 10 September 1998     

Bistable behaviour in squeezed vacua: I. Stationary analysis

A time-independent theoretical and numerical analysis of an optical bistable model of two-level atoms in a ring cavity, driven by a coherent field and in contact with a squeezed vacuum field is presented in the two cases of absorptive and dispersive optical bistability (OB). In the former case, a suitable choice of the phase of the squeezed vacuum field reduces the threshold for OB to occur compared with the normal vacuum case. In the latter case, regions of OB are identified as one or two disconnected simple closed curves depending on the cooperation parameter [0pt] : is the maximum possible value of the critical value of C at fixed values of the squeezed vacuum field parameters. Phase switching effects between different (output) states of the system is investigated in detail. In the absorptive case, one- or two-way optical switching is possible depending on [0pt] . We also present results which demonstrate more complicated switching behaviour in the dispersive case. Received 12 March 1999 and Received in final form 20 August 1999     

Enskog-Landau kinetic equation for multicomponent mixture. Analytical calculation of transport coefficients

The Enskog-Landau kinetic equation is considered to describe non-equilibrium processes of a mixture of charged hard spheres. This equation has been obtained in our previous papers by means of the non-equilibrium statistical operator method. The normal solution of this kinetic equation found in the first approximation using the standard Chapman-Enskog method is given. On the basis of the found solution the flows and transport coefficients have been calculated. All transport coefficients for multicomponent mixture of spherical Coulomb particles are presented analytically for the first time. Numerical calculations of thermal conductivity and thermal diffusion coefficient are performed for some specific mixtures of noble gases of high density. We compare the calculations with those ones for point-like neutral and charged particles. Received 10 June 1999 and Received in final form 15 October 1999     

On global solutions of the Maxwell-Dirac equations

We prove, for the Maxwell-Dirac equations in 1+3 dimensions, that modified wave operators exist on a domain of small entire test functions of exponential type and that the Cauchy problem, inR ⁺×R ³, has a unique solution for each initial condition (att=0) which is in the image of the wave operator. The modification of the wave operator, which eliminates infrared divergences, is given by approximate solutions of the Hamilton-Jacobi equation, for a relativistic electron in an electromagnetic potential. The modified wave operator linearizes the Maxwell-Dirac equations to their linear part.Dedicated to Walter Thirring on his 60^th birthdayThis work is dedicated to Walter Thirring upon the occasion of his sixtieth birthday with appreciation and friendship     

Improved modeling of flows down inclined planes

New models of film flows down inclined planes have been derived by combining a gradient expansion at first or second order to weighted residual techniques with polynomials as test functions. The two-dimensional formulation has been extended to account for three-dimensional flows as well. The full second-order two-dimensional model can be expressed as a set of four coupled evolution equations for four slowly varying fields, the thickness h, the flow rate q and two other quantities measuring the departure from the flat-film semi-parabolic velocity profile. A simplified model has been obtained in terms of h and q only. Including viscous dispersion effects properly, it closely sticks to the asymptotic expansion in the appropriate limit. Our new models improve over previous ones in that they remain valid deep into the strongly nonlinear regime, as shown by the comparison of our results relative to travelling-wave and solitary-wave solutions with those of both direct numerical simulations and experiments. Received 14 September 1999 and Received in final form 6 January 2000     

On N-wave type systems and their gauge equivalent

The class of nonlinear evolution equations (NLEE) - gauge equivalent to the N-wave equations related to the simple Lie algebra are derived and analyzed. They are written in terms of (x, t) ∈ satisfying r = rank nonlinear constraints. The corresponding Lax pairs and the time evolution of the scattering data are found. The Zakharov-Shabat dressing method is appropriately modified to construct their soliton solutions. Received 20 October 2001 / Received in final form 30 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: gerjikov@inrne.bas.bg