Broad histogram relation is exact

The Broad Histogram is a method designed to calculate the energy degeneracy g(E) from microcanonical averages of certain macroscopic quantities N _up and N _dn. These particular quantities are defined within the method, and their averages must be measured at constant energy values, i.e. within the microcanonical ensemble. Monte-Carlo simulational methods are used in order to perform these measurements. Here, the mathematical relation allowing one to determine g(E) from these averages is shown to be exact for any statistical model, i.e. any energy spectrum, under completely general conditions. We also comment about some troubles concerning the measurement of the quoted microcanonical averages, when one uses a particular approach, namely the energy random walk dynamics. These troubles appear when movements corresponding to different energy jumps are performed using the same probability, and also when the correlations between successive averaging states are not adequately treated: they have nothing to do with the method itself. Received: 29 May 1998 / Received in final form: 12 June 1998 / Accepted: 13 June 1998     

Atomic Compton profiles within different exchange-only theories

The impulse Compton Profiles (CPs) J(q) and the expectation values for some inert gas atoms (He-Kr) are computed and compared within the Harbola-Sahni (HS), Hartree-Fock (HF) theories and a Self-Interaction-Corrected (SIC) density functional model. The Compton profiles for excited states of helium atom are also calculated. While the calculated CPs are found to generally agree, they differ slightly from one another for small values of the Compton parameter q and are in good agreement for large q values. The expectation values within the three theories are also found to be comparable. The HS formalism is seen to mimic HF reasonably well in the momentum space, establishing the logical consistency of the former. Received: 11 December 1998 / Received in final form: 20 April 1999     

Pairwise entanglement in symmetric multi-qubit systems

For pairs of particles extracted from a symmetric state of N two-level systems, the two-particle density matrix is expressed in terms of expectation values of collective spin operators for the large system. Results are presented for experimentally relevant examples of pure states: Dicke states | S, M>, spin coherent, and spin squeezed states, where only the symmetric subspace, S = N/2 is populated, and for thermally entangled mixed states populating also lower S values. The entanglement of the extracted pair is then quantified by a calculation of the concurrence, which provides directly the entanglement of formation of the pair. Received 9 May 2001 and Received in final form 16 November 2001     

Coherent resonant transport through a mesoscopic system with quantum ac microwave field

The time-dependent transport through an ultrasmall quantum dot coupling to two electron reservoirs is investigated. The quantum dot is perturbed by a quantum microwave field (QMF) through gate. The tunneling current formulae are obtained by taking expectation values over coherent state (CS), and SU(1,1) CS. We derive the transport formulae at low temperature by employing the nonequilibrium Green function technique. The currents exhibit coherent behaviors which are strongly associated with the applied QMF. The time-dependent currents appear compound effects of resonant tunneling and time-oscillating evolution. The time-averaged current and differential conductance are calculated, which manifest photon-assisted behaviors. Numerical calculations reveal the similar properties as those in classical microwave field (CMF) perturbed system for the situations concerning CS and squeezed vacuum SU(1,1) CS. But for other squeezed SU(1,1) CS, the tunneling behavior is quite different from the system perturbed by a single CMF through gate. Due to the quantum signal perturbation, the measurable quantities fluctuate fiercely. Received 28 May 1998     

Well-defined Co clusters embedded in an Ag matrix: A model system for the giant magnetoresistance in granular films

Well-defined granular Co/Ag films have been prepared by the co-deposition of in-beam prepared Co clusters and Ag atoms. In this way we were able to study the giant magnetoresistance (GMR) as a function of mean Co cluster size for a fixed Co cluster volume fraction v_cl as well as a function of v_cl for a fixed . Mean Co cluster size has been varied between and 6.9 nm, Co cluster volume fraction between 5 and 43%. The GMR was measured in-situ at T=4.2 K in magnetic fields 1.2 T. The analysis of the GMR data obtained from these studies clearly shows that spin-dependent scattering at the Co-cluster/Ag-matrix interface is the only relevant scattering mechanism causing the GMR in our well-defined samples. Received: 21 April 1998 / Received in final form: 17 May 1998 / Accepted: 18 May 1998     

Elasticity of BaFCl single crystal under hydrostatic pressure

The sound velocities for longitudinal and transverse waves have been measured in single crystalline BaFCl at room temperature using ultrasonic pulse echo and Brillouin scattering techniques. The complete set of elastic constants is deduced and lead to the bulk moduli values of BaFCl at ambiant conditions (, , ) which are compared with those obtained by a shell model. Moreover, using the ultrasonic technique under pressure, the pressure derivatives of the second order elastic constants at 298 K have been determined up to 0.3 GPa. All moduli increase linearly with pressure in this pressure range, allowing to determine directly and separately the first derivative of the bulk modulus B'₀ = 5.8. These data are used to calculate a Murnaghan equation of state. A detailed comparison is given between our results with those recently obtained by X-ray diffraction on powder or calculated using the local density approximation method. Finally, the anisotropy of BaFCl under pressure is discussed. Received: 19 March 1998 / Revised: 15 May 1998 / Accepted: 19 May 1998     

Classical dynamical simulation of spontaneous alloying

“Spontaneous alloying” observed by Yasuda, Mori et al. for metallic small clusters is simulated using classical Hamiltonian dynamics. Very rapid alloying occurs homogeneously and cooperatively starting from the solid phase of the cluster if the heat of solution is negative and the size of cluster is less than a critical size. Analysis of 2D models reveals that the alloying rate obeys an Arrhenius-type law, which predicts the alloying time much less than second at room temperature. Evidences manifesting that the spontaneous alloying proceeds in the solid phase without melting are also presented. The simulation reproduces the essential features of the experiments. Received: 2 March 1998 / Revised: 21 May 1998 / Accepted: 28 May 1998     

Expansions for the eigenvalues of three-term recurrence relations. Two applications in molecular physics

Approximate expressions for the eigenvalue of a three-term recurrence relation with a general form describing various physical problems are proposed. Their range of availability is examined by comparison with exact values for two different problems: the bound and continuum states of monoelectronic diatomic ions and the Schr?dinger equation describing molecular alignment in intense laser fields. For each case, very good predictions have been obtained, which may be useful as initial values in iterative procedures for deriving exact solutions. Received: 30 January 1998 / Received in final form: 10 April 1998 / Accepted: 25 May 1998     

Photon statistics of a bad-cavity laser near threshold

A simple model of a bad-cavity laser is presented based on Haken's master equation for N pumped two-level atoms in a cavity. Via adiabatic elimination of fast variables the whole photon statistics is solved analytically near threshold. It is shown that the second order coherence function g ⁽²⁾ (0) has a very different behavior near threshold for a bad-cavity laser compared to a good-cavity laser. The power spectrum illustrates nicely the different time scales involved in the dynamics. Received: 13 November 1998 / Revised: 19 May 1998 / Accepted: 6 July 1998     

Density expansion of the energy of N close-to-boson excitons

Pauli exclusion between the carriers of N excitons induces novel many-body effects, quite different from the ones generated by Coulomb interaction. Using our commutation technique for interacting close-to-boson particles, we here calculate the Hamiltonian expectation value in the N-ground-state-exciton state. Coulomb interaction enters this quantity at first order only by construction; nevertheless, due to Pauli exclusion, subtle many-body effects take place, which give rise to terms in (Na _x ³/)ⁿ with n ≥ 2. An exact procedure to get these density dependent terms is given. Received 11 February 2002 / Received in final form 30 May 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: combescot@gps.jussieu.fr     

Dynamics of polymeric manifolds in melts: the Hartree approximation

The Martin-Siggia-Rose functional technique and the selfconsistent Hartree approximation is applied to the dynamics of a D-dimensional manifold in a melt of similar manifolds. The generalized Rouse equation is derived and its static and dynamic properties are studied. The static upper critical dimension, d _uc =2D/(2-D), discriminates between Gaussian (or screened) and non-Gaussian regimes, whereas its dynamical counterpart, , discriminates between Rouse- and renormalized-Rouse behavior. The Rouse modes correlation function in a stretched exponential form and the dynamical exponents are calculated explicitly. The special case of linear chains D=1 shows agreement with Monte-Carlo simulations. Received: 22 May 1998 / Received in final form: 31 August 1998 / Accepted: 8 September 1998     

A measurement of the QCD colour factors using event shape distributions at \sqrt{s}=14 to 189 GeV

Measurements of the QCD colour factors and and of the number of active quark flavours in the process at high energy are presented. They are based on fits of +NLLA QCD calculations to distributions of the event shape observables and measured at centre-of-mass energies from 14 GeV to 189 GeV. Hadronisation effects are approximated with power correction calculations which also depend on the QCD gauge structure. In this approach potential biases from hadronisation models are reduced. Our results for individually measured quantities obtained from and C are in good agreement with QCD based on the SU(3) symmetry group where for the energies considered here, and . From simultaneous fits of and with and C we find which is also in good agreement with the QCD expectation. Received: 3 May 2001 / Revised version: 22 June 2001 / Published online: 3 August 2001     

How popular is your paper? An empirical study of the citation distribution

Numerical data for the distribution of citations are examined for: (i) papers published in 1981 in journals which are catalogued by the Institute for Scientific Information (783,339 papers) and (ii) 20 years of publications in Physical Review D, vols. 11-50 (24,296 papers). A Zipf plot of the number of citations to a given paper versus its citation rank appears to be consistent with a power-law dependence for leading rank papers, with exponent close to -1/2. This, in turn, suggests that the number of papers with x citations, N(x), has a large-x power law decay , with . Received: 12 May 1998 / Accepted: 12 May 1998     

Invariable-profile wavefunctions and Brittingham's focus wave modes

A family of invariable-profile wavefunctions is constructed. The relations found describe both transient and steady-state waves. The Gauss and Bessel-Gauss focused waves of order m can be obtained from these steady-state waves via Bateman's transformation. Received: 14 May 1998 / Accepted: 22 August 1998     

Monocrystalline Si waffles for thin solar cells fabricated by the novel perforated-silicon process

2 for this waffle-shaped film when it is attached to glass substrates. Received: 15 May 1998/Accepted: 28 May 1998     

Two interacting particles in a disordered chain II: Critical statistics and maximum mixing of the one body states

For two particles in a disordered chain of length L with on-site interaction U, a duality transformation maps the behavior at weak interaction onto the behavior at strong interaction. Around the fixed point of this transformation, the interaction yields a maximum mixing of the one body states. When (the one particle localization length), this mixing results in weak chaos accompanied by multifractal wave functions and critical spectral statistics, as in the one particle problem at the mobility edge or in certain pseudo-integrable billiards. In one dimension, a local interaction can only yield this weak chaos but can never drive the two particle system to full chaos with Wigner-Dyson statistics. Received: 22 May 1998 / Received in final form: 24 August 1998 / Accepted: 4 September 1998     

High-temperature series analysis of the p-state Potts glass model on d-dimensional hypercubic lattices

We analyze recently extended high-temperature series expansions for the “Edwards-Anderson” spin-glass susceptibility of the p-state Potts glass model on d-dimensional hypercubic lattices for the case of a symmetric bimodal distribution of ferro- and antiferromagnetic nearest-neighbor couplings . In these star-graph expansions up to order 22 in the inverse temperature , the number of Potts states p and the dimension d are kept as free parameters which can take any value. By applying several series analysis techniques to the new series expansions, this enabled us to determine the critical coupling K_c and the critical exponent of the spin-glass susceptibility in a large region of the two-dimensional (p,d)-parameter space. We discuss the thus obtained information with emphasis on the lower and upper critical dimensions of the model and present a careful comparison with previous estimates for special values of p and d. Received: 25 May 1998 / Revised and Accepted: 11 August 1998     

Towards an universal classification of scale invariant processes

We consider fields which take random values over several decades. Starting from physical examples, we postulate that scale is not an absolute quantity. We then establish the equivalence between two existing approaches based on scale symmetry arguments as general as possible. This yields a classification of log-infinitely divisible laws, possibly universal. The physical significance of the parameters entering in the classification is discussed. Received: 7 November 1997 / Received in final form: 26 March 1998 / Accepted: 30 March 1998     

Island distance in one-dimensional epitaxial growth

The typical island distance in submonolayer epitaxial growth depends on the growth conditions via an exponent . This exponent is known to depend on the substrate dimensionality, the dimension of the islands, and the size i^* of the critical nucleus for island formation. In this paper we study the dependence of on i^* in one-dimensional epitaxial growth. We derive that for and confirm this result by computer simulations. Received: 26 May 1998 / Accepted: 23 June 1998