Spin correlations in electron liquids: Analytical results for the local-field correction in two and three dimensions

We study the spin correlations in two- and three-dimensional electron liquids within the sum-rule version of the self-consistent field approach of Singwi, Tosi, Land, and Sj?lander. Analytic expressions for the spin-antisymmetric static structure factor and the corresponding local-field correction are obtained with density dependent coefficients. We calculate the spin-dependent pair-correlation functions, paramagnon dispersion, and static spin-response function within the present model, and discuss the spin-density wave instabilities in double-layer electron systems. Received: 22 September 1997 / Revised: 1 December 1997 / Accepted: 4 December 1997     

Vesicle propulsion in haptotaxis: A local model

We study theoretically vesicle locomotion due to haptotaxis. Haptotaxis is referred to motion induced by an adhesion gradient on a substrate. The problem is solved within a local approximation where a Rayleigh-type dissipation is adopted. The dynamical model is akin to the Rousse model for polymers. An invariant formulation is used to solve a dynamical model which includes a kind of dissipation due to bond breaking/restoring with the substrate. For a stationary situation where the vesicle acquires a constant drift velocity, we formulate the propulsion problem in terms of a nonlinear eigenvalue (the a priori unknown drift velocity) one of Barenblat-Zeldovitch type. A counting argument shows that the velocity belongs to a discrete set. For a relatively tense vesicle, we provide an analytical expression for the drift velocity as a function of relevant parameters. We find good agreement with the full numerical solution. Despite the oversimplification of the model it allows the identification of a relevant quantity, namely the adhesion length, which turns out to be crucial also in the nonlocal model in the presence of hydrodynamics, a situation on which we have recently reported (I. Cantat and C. Misbah, Phys. Rev. Lett. 83, 235 (1999)) and which constitutes the subject of a forthcoming extensive study. Received 10 February 2000     

Scaling of hysteresis in a multi-dimensional all-optical bistable system

We analyse the hysteresis enlargements of an optical bistable system involving three dynamical variables. We investigate, both experimentally and numerically, the local dynamics of the up- and down-switching process versus the sweeping frequency of the control parameter. In particular, we delineate the domain of validity of the scaling law predicted for one-dimensional systems. At high sweeping frequency, we show the appearance of another asymptotic scaling low in . Thereafter, we analyse the global evolution of the hysteresis loop induced by these processes. At low frequency, a scaling law is retrieved, whereas at high frequency, the dynamical behaviour is shown to strongly depend on the particular shape of the bistability curve. Received: 14 September 1998 / Received in final form: 15 February 1999     

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     

Incoherent energy transfer within light-harvesting complexes

Rate equations are used to model spectroscopic observation of incoherent energy transfer in light-harvesting antenna systems based upon known structures. A two-parameter two-dimensional model is proposed. The transfer rates obtained, by matching the fluorescent decay, are self-consistent within our model. Received 29 May 1998     

Two-body density matrix for closed s-d shell nuclei

The two-body density matrix for ⁴He,¹⁶O and ⁴⁰Ca within the Low-order approximation of the Jastrow correlation method is considered. Closed analytical expressions for the two-body density matrix, the center of mass and relative local densities and momentum distributions are presented. The effects of the short-range correlations on the two-body nuclear characteristics are investigated. Received: 11 September 1999 / Revised version: 20 December 1999     

Unified quantum mechanical picture for confined spinons in dimerized and frustrated spin chains

A quantum mechanical picture is presented to describe the behavior of confined spinons in a variety of S =1/2 chains. The confinement is due to dimerization and frustration and it manifests itself as a nonlinear potential , centered at chain ends () or produced by modulation kinks (b > 1). The calculation extends to weak or zero frustration some previous ideas valid for spinons in strongly frustrated spin chains. The local magnetization patterns of the confined spinons are calculated. A (minimum) enhancement of the local moments of about 11/3 over a single S =1/2 is found. Estimates for excitation energies and binding lengths are obtained. Received: 8 May 1998 / Revised and Accepted: 12 August 1998     

Theory of EPR on a rotating sample: An illustration of Berry's phase

We describe the theory of EPR in a crystal field multiplet under sample spinning. Berry phases arise because the crystal field is of lower symmetry than the full rotation group. The formal development is limited to pure J multiplets, crystal field doublets, and field and rotation axes parallel to a principal axis. Received: 4 August 1997 / Received in final form: 19 December 1997 / Accepted: 28 January 1998     

Entropy and multi-particle correlations in two-dimensional lattice gases

We analyse the statistical entropy of two-dimensional lattice-gas models in terms of the contributions which arise from space correlations of increasing order. The “residual multiparticle entropy”, defined as the contribution to the excess entropy that is associated with correlations involving more than two particles, is calculated for the Ising and Coulomb lattice gases. The thermodynamic behaviour of the residual multiparticle entropy is then discussed in relation to the phase diagram of the model and the existence of underlying signatures of order-disorder phase transitions is also investigated. Received 31 December 1998 and Received in final form 8 March 1999     

wave superconductivity: Analysis of the electronic Raman data of and other cuprates

After briefly recalling the d + s model valid for some anisotropic high T c superconductors, we present a theory of electronic Raman spectra in that model and then compare it with new experimental data obtained for an overdoped Y123 single crystal. The d + s model appears to describe satisfactorily the experimental results, indicating a possible doping dependence of the mixing ratio. We note that the Raman spectrum of the overdoped Bi2212 could also be accounted for by the d + s superconductivity model. The case of Hg1212 (or Hg1223) is reexamined. It appears that the spontaneous breakdown of d-wave symmetry may be rather universal in high T c cuprates. Received: 3 March 1998 / Accepted: 30 April 1998     

Brownian rotation of classical spins: dynamical equations for non-bilinear spin-environment couplings

Given two strings X and Y of N and M characters respectively, the Longest Common Subsequence (LCS) Problem asks for the longest sequence of (non-contiguous) matches between X and Y. Using extensive Monte-Carlo simulations for this problem, we find a finite size scaling law of the form for the average LCS length of two random strings of size N over S letters. We provide precise estimates of for .We consider also a related Bernoulli Matching model where the different entries of an array are occupied with a match independently with probability 1/S. On the basis of a cavity-like analysis we find that the length of a longest sequence of matches in that case behaves as where r=M/N and . This formula agrees very well with our numerical computations. It provides a very good approximation for the Random String model, the approximation getting more accurate as S increases. The question of the “universality class” of the LCS problem is also considered. Our results for the Bernoulli Matching model show very good agreement with the scaling predictions of [#!HwaLassig96_PRL!#] for Needleman-Wunsch sequence alignment. We find however that the variance of the LCS length has a scaling different from Var in the Random String model, suggesting that long-ranged correlations among the matches are relevant in this model. We finally study the “ground state” properties of this problem. We find that the number of solutions typically grows exponentially with N. In other words, this system does not satisfy “Nernst's principle”. This is also reflected at the level of the overlap between two LCSs chosen at random, which is found to be self averaging and to approach a definite value q _S <1 as . Received: 23 April 1998 / Revised: 30 July 1998 / Accepted: 14 August 1998     

Finite-size scaling in the theory above the upper critical dimension

We derive exact results for several thermodynamic quantities of the O ( n ) symmetric field theory in the limit in a finite d-dimensional hypercubic geometry with periodic boundary conditions. Corresponding results are derived for an O ( n ) symmetric model on a finite d-dimensional lattice with a finite-range interaction. The leading finite-size effects near T_c of the field-theoretic model are compared with those of the lattice model. For 2 < d < 4, the finite-size scaling functions are verified to be universal. For d > 4, significant lattice effects are found. Finite-size scaling in its usual simple form does not hold for d > 4 but remains valid in a generalized form with two reference lengths. The finite-size scaling functions of the field theory turn out to be nonuniversal whereas those of the lattice model are independent of the nonuniversal model parameters. In particular, the field-theoretic model exhibits finite-size effects whose leading exponents differ from those of the lattice model. The widely accepted lowest-mode approach is shown to fail for both the field-theoretic and the lattice model above four dimensions. Received: 20 October 1997 / Accepted: 5 March 1998     

The finite-temperature photoluminescence correlation function in semiconductor heterostructures

We report the inclusion of temperature effects on the Mahan-Nozières-De Dominicis framework to study both many-body and temperature effects in photoluminescence spectra of doped semiconductors. The electronic part of the correlation function characterizes the photoluminescence spectra. We have treated the optical valence hole as a localized scattering potential center and studied effects of the electron-hole interaction enhancement on the photoluminescence spectra leading to the appearance of shake-up structures. We also have identified a term in the correlation function which represents the finite-temperature contribution to the intensities of the shake-up structures. The method is used to study the magnetophotoluminescence of modulation-doped quantum wells with a weak periodic lateral potential. Received 20 November 1998 and Received in final form 5 March 1999     

Mutual inductance effects in rf driven planar Josephson junctions arrays

In this paper we investigate the behavior of moderate size two-dimensional classical arrays of Josephson junctions in presence of an external oscillating field. We have included in the model the effects due to mutual inductance terms, and we have employed an explicit set of differential equations. We have found that the discretization parameter - i.e. the coupling term due to the inductance of the loops - is the most important parameter to determine the height of the Shapiro steps for a given amplitude and frequency of the rf-bias. The amplitude of the Shapiro steps in the case of zero frustration as a function of the coupling term shows a remarkable minimum for intermediate values when we retain all terms of the full model with mutual inductances, while the limits for very large and very small values of they are the same of the single Josephson junction. For the case of frustration 1/2 the Shapiro step becomes smaller in the rigid limit (i.e., small ) as expected for the XY model, and tends to the limit value of the single junctions for the decoupled case (i.e., large ). Received 9 November 1998 and Received in final form 6 April 1999     

Vortex lattice accommodation on twin boundaries in studied by neutron diffraction

An extensive study of small angle neutron scattering was performed in twinned YBa₂Cu₃O₇ crystals in its superconducting state as a function of the angle between the c-axis of the crystal and the magnetic field. The half of the twin boundaries are oriented in the horizontal plane, which also contains the neutron beam and the magnetic field. Two different diffraction patterns are studied as a function of at 5 K and B = 0.5 T, one along the c-axis of the crystal, the other one along the applied field. These variations are interpreted in the model of accommodation of the vortices on the twin planes by zigzagging from these planes to the ab-planes of the crystal, in order to minimize their energy. Received: 9 March 1998 / Revised and Accepted: 12 June 1998     

Spin correlations in the two-dimensional spin-5/2 Heisenberg antiferromagnet

We report a neutron scattering study of the instantaneous spin correlations in the two-dimensional spin S =5/2 square-lattice Heisenberg antiferromagnet Rb₂MnF₄. The measured correlation lengths are quantitatively described, with no adjustable parameters, by high-temperature series expansion results and by a theory based on the quantum self-consistent harmonic approximation. Conversely, we find that the data, which cover the range from about 1 to 50 lattice constants, are outside of the regime corresponding to renormalized classical behavior of the quantum non-linear model. In addition, we observe a crossover from Heisenberg to Ising critical behavior near the Néel temperature; this crossover is well described by a mean-field model with no adjustable parameters. Received: 3 March 1998 / Received in final form: 4 May 1998 / Accepted: 19 May 1998     

Thermoelectric transport properties in disordered systems near the Anderson transition

We study the thermoelectric transport properties in the three-dimensional Anderson model of localization near the metal-insulator transition (MIT). In particular, we investigate the dependence of the thermoelectric power S, the thermal conductivity K, and the Lorenz number L₀ on temperature T. We first calculate the T dependence of the chemical potential μ from the number density n of electrons at the MIT using an averaged density of states obtained by diagonalization. Without any additional approximation, we determine from the behavior of S, K and L₀ at low T as the MIT is approached. We find that and K decrease to zero at the MIT as and show that S does not diverge. Both S and L₀ become temperature independent at the MIT and depend only on the critical behavior of the conductivity. Received 5 February 1999     

Note on electron impact excitation for transition of Be-like isoelectronic sequence

Relativistic distorted-wave method was used to calculate the electron impact excitation collision strengths for transitions 2 s2 ¹ S0-2 s 2 p ³ P1 of Be-like isoelectronic ions. The target states were described, respectively, by 10-level, 46-level and 133-level MCDF configuration-expansion. The relativistic continuum orbitals were calculated in the potential field of frozen target-ion charge distribution with semi-classical exchange potential. The influence of the target states on this collision process along the isoelectronic sequence was investigated in the above three MCDF configuration-expansion modes. It was found that the configurations in the n =3 and the n =4 complexes have great influence on both the high and the low Z ions but the influence is relatively small for intermediate Z ions. The latter phenomenon was attributed to competition between opposing correlation and relativistic effects on the collision strengths. Received: 25 February 1998 / Received in final form: 18 June 1998     

A pseudopotential study of molecular spectroscopy in rare gas matrices: absorption of NO in argon

We present a pseudopotential method to study the absorption spectroscopy of NO in an argon matrix modeled by a large albeit finite cluster. The excited states of NO are described with the virtual orbitals of a NO⁺ Hartree-Fock calculation plus a core-polarization operator to account for the electron-NO⁺ correlation. The argon atoms of the matrix are replaced by pseudopotentials for the repulsive contributions and core-polarization operators to account for matrix polarization and correlation with the excited electron. The model is shown to account for the matrix-induced transition shifts and also for the cut-off of the Rydberg series for n >3 reported in absorption experiments from the ground state. Received: 6 March 1998 / Revised: 1st June 1998 / Accepted: 16 June 1998     

Bose-Einstein transition in a dilute interacting gas

We study the effects of repulsive interactions on the critical density for the Bose-Einstein transition in a homogeneous dilute gas of bosons. First, we point out that the simple mean field approximation produces no change in the critical density, or critical temperature, and discuss the inadequacies of various contradictory results in the literature. Then, both within the frameworks of Ursell operators and of Green's functions, we derive self-consistent equations that include correlations in the system and predict the change of the critical density. We argue that the dominant contribution to this change can be obtained within classical field theory and show that the lowest order correction introduced by interactions is linear in the scattering length, a, with a positive coefficient. Finally, we calculate this coefficient within various approximations, and compare with various recent numerical estimates. Received 15 July 2001