The metal-semiconductor transition in amorphous Si1−x Cr x films:T 0.19-contribution to the metallic conductivity

A detailed phenomenological re-analysis of previously published conductivity data, (T, x), is presented. It is based on the investigation of differences, (T, x ₁)–(T, x ₂). In this way, the cusp-like low-temperature term is amplified against the other temperature dependent contributions. This term can be described by wherep=0.19±0.03. It is present, if (4.2 K,x) exceeds 260 ^–1 cm^–1, at least up to (4.2 K,x)1350 ^–1 cm^–1 and forT60 K. But it is absent, if (4.2 K,x)180 ^–1 cm^–1. The disappearance of this contribution should be related to the metal-semiconductor transition, taking place atx _c 0.14. On the other hand, the presence of a term proportional toT ^1/2, as predicted by Altshuler and Aronov, seems unlikely.It is argued that the term should be related to the interplay of electron-electron interaction and disorder. The comparison with data from the literature shows that this contribution might also be present in heavily doped crystalline semiconductors.     

On absence of diffusion near the bottom of the spectrum for a random Schrödinger operator onL 2(ℝ)+

We consider a random Schrödinger operator onL ²(^v) of the form , {C _i} being a covering of ^v with unit cubes around the sites of ^v and {q _i} i.i.d. random variables with values in [0, 1]. We assume that theq _i's are continuously distributed with bounded densityf(q) and that 0<P(q ₀<1/2)=<1. Then we show that an ergodic mean of the quantity dx|x|²|(exp(itH ))(x)|²t ^–1 vanishes provided =g _E(H ), where is well-localized around the origin andg _E is a positiveC -function with support in (0,E),EE*(, |f|). Our estimate ofE*(, |f|) is such that the set {x ^v |V (x) E*(, |f|)} may contain with probability one an infinite cluster of cubes {C _i} which are nearest neighbours. The proof is based on the technique introduced by Fröhlich and Spencer for the analysis of the Anderson model.Work supported in part by C.N.R. (Italy) and NAVF (Norway)On leave of absence from Instituto di Fisica Università di Roma, Italia     

Layering transition in SOS model with external magnetic field

For the SOS model defined by the Hamiltonian , where _x , _x ,{1,2,...},h>0,x ^d ,d2 it is shown that in the low-temperature region an infinite sequence of first-order phase transitions takes place whenh»0 and the temperature is fixed.     

The Heisenberg ferromagnet as a quantum field theory

We consider a lattice of spin 1/2 ions, described by the discrete form of the current commutation relationsJ _i J _(i) =1/2, [J _i ,J _i ]=i _ij J _i where =1, 2, 3 andi label the lattice sites. The algebra is realized as the Clifford algebra over a Hilbert space. The equations of motion are specified by a formal Hamiltonian of the Heisenberg form: , wheref _ij 0 and only a finite numberQ of ions are linked to any given lattice site. We prove that the Hamiltonian is non-negative in a representation of , and has a ground state exhibiting ferromagnetism. The time displacement group acts continuously on , inducing automorphisms. is asymptotically abelian with respect to the space translations of the lattice.The model is an example of an algebraic quantum field theory and possesses a broken symmetry, the rotation group 0(3). The consequent Goldstone theorem is proved, namely, there is no energy gap in the spectrum ofH.     

MultipletSO(n+1) scalar fields driving eternal expansion in closed (D+1)-dimensional FLRW cosmologies

The possibility of having a de Sitter asymptotic stage free of choice of the value of the positive cosmological constant (no critical ) is analyzed in a closed FLRW universe which starts from a quiescent phase of evolution and ends into a textured phase by taking into account multipletSO(n+1) scalar fields.On leave of absence from Universidade Federal do Rio de Janeiro, RJ, Brazil     

First experiment to test whether space-time is flat. II. Effects of orbit

The gyroscope in an orbiting satellite will be acted on by additional gravitational fields due to the rotation of the earth and due to the orbital velocity of the satellite. According to special relativistic gravitational theory, we deduce _L ^(S) —the gyroscope's precession rate due to the orbital velocity—and _S ^(S) —the gyroscope's precession rate due to the earth's rotation in the polar orbit case. The results are _L ^(S) = (2/3) _L ^(G) , _S ^(S) = (3/2) cos (1 - sin² cos²)^1/2 _S ^(G) , where and are the gyroscope's polar angles, and _L ^(G) and _S ^(G) are the geodetic and frame-dragging precession rates predicted by general relativity, respectively.     

On the cauchy problem for the discrete Boltzmann equation with initial values inL 1 + (ℝ)

We prove a global existence theorem for a discrete velocity model of the Boltzmann equation when the initial values _i (x) have finite entropy and, for some constant>0, (1+|x|) _i (x)L ₁ ⁺ ().     

The transverse correlation length for randomly rough surfaces

It is shown by numerical simulations for a random, one-dimensional surface defined by the equationx ₃=(x ₁), where the surface profile function (x ₁) is a stationary, stochastic, Gaussian process, that the transverse correlation lengtha of the surface roughness is a good measure of the mean distance d between consecutive peaks and valleys on the surface. In the case that the surface height correlation function (x ₁)(x ₁)/²(x ₁)=W (|x ₁–x ₁|) has the Lorentzian formW(|x ₁|)=a ²/(x ₁ ² +a ²) we find that d=0.9080a; when it has the Gaussian formW(|x ₁|)=exp(–x ₁ ² /a ²), we find that d=1.2837a; and when it has the nonmonotonic formW(|x ₁|)=sin(x ₁/a)/(x ₁/a), we find that d=1.2883a. These results suggest that d is larger, the faster the surface structure factorg(|Q|) [the Fourier transform ofW(|x ₁|)] decays to zero with increasing |Q|. We also obtain the functionP(itx ₁), which is defined in such a way that, ifx ₁=0 is a zero of (x ₁),P(x ₁)dx ₁ is the probability that the nearest zero of (x ₁) for positivex ₁ lies betweenx ₁ andx ₁+dx ₁.     

Expectation Values of Observables in Time-Dependent Quantum Mechanics

Let U(t) be the evolution operator of the Schrödinger equation generated by a Hamiltonian of the form H ₀(t) + W(t), where H ₀(t) commutes for all twith a complete set of time-independent projectors . Consider the observable A=_j P _jjwhere _j j , >0, for jlarge. Assuming that the matrix elements of W(t) behave as for p>0 large enough, we prove estimates on the expectation value for large times of the type where >0 depends on pand . Typical applications concern the energy expectation H₀(t) in case H ₀(t) H ₀or the expectation of the position operator x²(t) on the lattice where W(t) is the discrete Laplacian or a variant of it and H ₀(t) is a time-dependent multiplicative potential.     

Enhancement of activated decay of metastable states by resonant pumping

We consider the effect of a high-frequency pumping cost on the escape rate of a classical underdamped Brownian particle out of a deep potential well. The energy dependence of the oscillation frequency(E) is assumed to be weak on the scale of thermal energy,_E(0)T(0)T/V₀ (0)[_E(0) is the derivative of(E) atE= 0,V ₀ is the barrier height,V ₀ T]. The quadratic-in- contribution to the decay rate is calculated in two different regimes: (1) for the case of resonance of the pumping frequency with the nth harmonic of the internal motion at an energye, when = n(e); (2) for a rollout region of the basic resonance near the bottom of the potential well, when ¦-(0)¦ and is the damping coefficient. In the latter case the absorption spectrum and the enhancement of the decay rate are calculated as functions of two reduced parameters, the anharmonicity of the potential,v _E (0)T/, and the resonance mismatch, [ —(0)]/. It is shown that the effect of the pumping increases with diminishing ¦v¦ and at small v is proportional tov ^–1. In this regime, the dependence on is stepwise: the pumping contribution is large for v > 0 and small for v < 0. In the frame of our theory, the decay rate is invariant against the simultaneous alternation of the signs of andv. The spectrum of the energy absorption has the standard Lorentzian shape in the absence of anharmonicity,v=0, and with increasing of ¦v¦ shifts and widens retaining its bell-shape form.     

Correlation inequalities for two-component hypercubicϕ 4 models

A collection of new and already known correlation inequalities is found for a family of two-component hypercubic ⁴ models, using techniques of duplicated variables, rotated correlation inequalities, and random walk representation. Among the interesting new inequalities are: rotated very special Dunlop-Newman inequality _1,x ² ; _1,z ² + _2g ² 0, rotated Griffiths I inequality _{1,x 1,y} ; _1z ² 0, and anti-Lebowitz inequalityu ₄ ¹¹¹¹ >-0.     

Instability in degenerate two-photon running wave laser

The stability of the homogeneously broadened and degenerate two-photon running wave laser is analysed by using the full set of matter-field equations. The stability depends on the relative size of the relaxation constants. For 2k>1+r(k=/,r=/; is the cavity loss of the field and , are the longitudinal and transversal decay constants, respectively) no stable lasing state exists. Forr<k<(1+r)/2 an instability occurs. With the decrease in pumping the stable lasing state loses its stability due to Hopf-bifurcation.     

Metastable states in the van der Waals-Maxwell theory

A slight modification of the recent Penrose and Lebowitz treatment of thermodynamic metastable states is presented. For the case of periodic boundary conditions, this modification allows the condition of metastability to be extended to all the metastable states in the van der Waals-Maxwell theory of the liquid-vapor phase transition, that is, for all states satisfyingf ₀()+1/2 ²>f(, 0+) andf₀()+x>0 wheref(, 0+) is the (stable) Helmholtz free energy density of the generalized van der Waals-Maxwell theory andf ₀() is the Helmholtz free energy density of a reference system with no long-range interaction, is a mean field-type term arising from a long-range Kac interaction, is the overall mean particle density, andx is any positive number. For the case of rigid-wall boundary conditions, a more restrictive condition is placed onx.     

Long-range correlations at depinning transitions

Semi-infinite systems are considered with long-range surface fields B _z ^–(1+r) for large distancesz from the surface. The influence of such fields on the global phase diagram and on the critical singularities of depinning transitions is studied within Landau theory. For |B|0, the correlation length diverges as b ^–1/2 withb=|Bln|B^–(1+r). For finiteB, t ^v withv =(2+r)/(2+2r) wheret measures the distance from bulk coexistence. In the latter case, a Ginzburg criterion leads to the upper critical dimensiond ^*=(2+3r)/(2+r).     

Massive spin-two particle in a gravitational field

The spin-two particle is described by a symmetric tensorh subject to the subsidiary conditionsh = h =0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh a symmetric third-rank tensor = as well as a vector fieldA have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh , andA independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh as well as the generalization of the wave equationD D h + 2R h -R h -R h +g R h +Rh =m ² h Finally, variation with respect tog yields the energy-momentum tensor.     

Holes in the probability density of strongly colored noise driven systems

A qualitative change in the topology of the joint probability densityP(,x), which occurs for strongly colored noise in multistable systems, has recently been observed first by analog simulation (F. Moss and F. Marchesoni,Phys. Lett. A 131:322 (1988)) and confirmed by matrix continued fraction methods (Th. Leiber and H. Riskin, unpublished), and by analytic theory (P. Hänggi, P. Jung, and F. Marchesoni,J. Stat. Phys., this issue). Systems studied were of the classx=–U(x)/x+(t,), whereU(x) is a multistable potential and (t, ) is a colored, Gaussian noise of intensityD, for which =0, and (t) (s)=(D/)exp(–t–s/). When the noise correlation time is smaller than some critical value ₀, which depends onD, the two-dimensional densityP(,x) has the usual topology [P. Jung and H. Risken,Z. Phys. B 61:367 (1985); F. Moss and P. V. E. McClintock,Z. Phys. B 61:381 (1985)]: a pair of local maxima ofP(,x), which correspond to a pair of adjacent local minima ofU(x), are connected by a single saddle point which lies on thex axis. When >₀, however,the single saddle disappears and is replaced by a pair of off-axis saddles. A depression, or hole, which is bounded by the saddles and the local maxima thus appears. The most probable trajectory connecting the two potential wells therefore does not pass through the origin for >₀, but instead must detour around the local barrier. This observation implies that successful mean-first-passage-time theories of strongly colored noise driven systems must necessarily be two dimensional (Hänggiet al.). We have observed these holes for several potentialsU(x): (1)a soft, bistable potential by analog simulation (Moss and Marchesoni); (2) a periodic potential [Th. Leiber, F. Marchesoni, and H. Risken,Phys. Rev. Lett. 59:1381 (1987)] by matrix continued fractions; (3) the usual hard, bistable potential,U(x)=–ax ²/2+bx ⁴/4, by analog simulations only; and (4) a random potential for which the forcingf(x)=–U(x)/x is an approximate Gaussian with nonzero correlation length, i.e., colored spatiotemporal noise, by analog simulation. There is a critical curve ₀(D) in the versusD plane which divides the two topological behaviors. For a fixed value ofD, this curve is shifted toward larger values of ₀ for progressively weaker barriers between the wells. Therefore, strong barriers favor the observation of this topological transformation at smaller values of . Recently, an analytic expression for the critical curve, valid asymptotically in the small-D limit, has been obtained (Hänggiet al.).This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

Ballistic annihilation and deterministic surface growth

A model of deterministic surface growth studied by Krug and Spohn, a model of the annihilating reactionA+Binert studied by Elskens and Frisch, a one-dimensional three-color cyclic cellular automaton studied by Fisch, and a particular automaton that has the number 184 in the classification of Wolfram can be studied via a cellular automaton with stochastic initial data called ballistic annihilation. This automaton is defined by the following rules: At timet=0, one particle is put at each integer point of . To each particle, a velocity is assigned in such a way that it may be either +1 or –1 with probabilities 1/2, independent of the velocities of the other particles. As time goes on, each particle moves along at the velocity assigned to it and annihilates when it collides with another particle. In the present paper we compute the distribution of this automaton for each timet . We then use this result to obtain the hydrodynamic limit for the surface profile from the model of deterministic surface growth mentioned above. We also show the relation of this limit process to the process which we call moving local minimum of Brownian motion. The latter is the processB _x ^min ,x , defined byB _x ^min min{B _y ;x–1yx+1} for everyx , whereB _x ,x , is the standard Brownian motion withB ₀=0.     

Existence of solutions for Schrödinger evolution equations

We study the existence, uniqueness and regularity of the solution of the initial value problem for the time dependent Schrödinger equationiu/t=(–1/2)u+V(t,x)u,u(0)=u ₀. We provide sufficient conditions onV(t,x) such that the equation generates a unique unitary propagatorU(t,s) and such thatU(t,s)u ₀C ¹(,L ²) C ⁰(H ²( ⁿ )) foru ₀H ²( ⁿ ). The conditions are general enough to accommodate moving singularities of type x^–2+(n4) or x^–n/2+(n3).     

Theory of percolation in fluids of long molecules

We use the reference interaction site model (RISM) integral equation theory to study the percolation behavior of fluids composed of long molecules. We examine the roles of hard core size and of length-to-width ratio on the percolation threshold. The critical density _c is a nonmonotonic function of these parameters exhibiting competition of different effects. Comparisons with Monte Carlo calculations of others are reasonably good. For critical exponents, the theory yields =2=2 for molecules of any noninfinite lengthL. WhenL is very large, the theory yields _cL ^–2. These predictions compare favorably with observations of the conductivity for random assemblies of conductive fibers. The threshold region where asymptotic scaling holds requires the correlation length (/ _c ) ^–v to be much larger thanL. Evidently, the range of densities in this region diminishes asL increases, requiring that density deviations from _c be no larger thanL ^–2. Otherwise, crossover behavior will be observed.     

The spectrum of a quasiperiodic Schrödinger operator

The spectrum (H) of the tight binding Fibonacci Hamiltonian (H _mn= _m,n+1+ _m+1,n + _m,n v(n),v(n)= ((n–1)), 1/ is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any , and (H) is a Cantor set for 4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for 16.On leave from the Central Research Institute for Physics, Budapest, Hungary