Correlated transport and non-Fermi-liquid behavior in single-wall carbon nanotubes

We derive the effective low-energy theory for single-wall carbon nanotubes including the Coulomb interactions among electrons. The generic model found here consists of two spin-fermion chains which are coupled by the interaction. We analyze the theory using bosonization, renormalization-group techniques, and Majorana refermionization. Several experimentally relevant consequences of the breakdown of Fermi liquid theory observed here are discussed in detail, e.g., magnetic instabilities, anomalous conductance laws, and impurity screening profiles. Received: 12 December 1997 / Revised: 9 March 1998 / Accepted: 12 March 1998     

Influence of hydrodynamics on the dynamics of a homopolymer

We present an analytical approach of the dynamics of a polymer when it is quenched from a solvent into a good or bad solvent. The dynamics is studied by means of a Langevin equation, first in the absence of hydrodynamic effect, then taking into account the hydrodynamic interactions with the solvent. The variation of the radius of gyration is studied as a function of time. In both cases, for the first stage of collapse or swelling, the evolution is described by a power law with a characteristic time proportional to N ^4/3 (N), where N is the number of monomers, without (with) hydrodynamic interactions. At larger times, scaling laws are derived for the diffusive relaxation time. Received: 10 March 1998 / Received in final form: 15 September 1998 / Accepted: 25 September 1998     

Low temperature thermodynamics of inverse square spin models in one dimension

We present a field-theoretic renormalization group calculation in two loop order for classical O(N)-models with an inverse square interaction in the vicinity of their lower critical dimensionality one. The magnetic susceptibility at low temperatures is shown to diverge like with a=(N-2)/(N-1) and . From a comparison with the exactly solvable Haldane-Shastry model we find that the same temperature dependence applies also to ferromagnetic quantum spin chains. Received: 20 February 1998 / Revised: 27 April 1998 / Accepted: 30 April 1998     

Three-body decay of a rubidium Bose–Einstein condensate

We have measured the three-body decay of a Bose–Einstein condensate of rubidium (⁸⁷Rb) atoms prepared in the doubly polarized ground state F=m _F =2. Our data are taken for a peak atomic density in the condensate varying between 2×10¹⁴ cm^-3 at initial time and 7×10¹³ cm^-3, 16 s later. Taking into account the influence of the uncondensed atoms on the decay of the condensate, we deduce a rate constant for condensed atoms L=1.8 (±0.5) ×10^-29 cm⁶ s^-1. For these densities we did not find a significant contribution of two-body processes such as spin dipole relaxation. Received: 24 November 1998 / Revised version: 26 June 1999 / Published online: 8 September 1999     

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     

Kinetics of shape equilibration for two dimensional islands

We study the relaxation to equilibrium of two dimensional islands containing up to 20 000 atoms by Kinetic Monte Carlo simulations. We find that the commonly assumed relaxation mechanism - curvature-driven relaxation via atom diffusion - cannot explain the results obtained at low temperatures, where the island edges consist in large facets. Specifically, our simulations show that the exponent characterizing the dependence of the equilibration time on the island size is different at high and low temperatures, in contradiction with the above cited assumptions. Instead, we propose that - at low temperatures - the relaxation is limited by the nucleation of new atomic rows on the large facets: this allows us to explain both the activation energy and the island size dependence of the equilibration time. Received 7 December 1998 and Received in final form 18 March 1999     

On charged mesoscopic metallic bubbles

We investigate the existence of stable charged metallic bubbles using the shell correction method. We find that for a given mesoscopic system of n atoms of a given metal and (positive) elementary charges, a metallic bubble turns out to have a lower total energy than a compact spherical cluster, whenever the charge number q is larger than a critical charge number q_c. For a magic number (n-q) of free electrons, the spherical metallic bubble may become stable against fission. Received: 17 November 1997 / Revised: 28 May 1998 / Accepted: 20 July 1998     

Time distribution and loss of scaling in granular flow

Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling p) and deterministic critical slope processes with internal correlation time t_c equal to the avalanche lifetime, in model A, and ,in model B. In both cases nonuniversal scaling properties of avalanche distributions are found for , where is related to directed percolation threshold in d=3. Distributions of avalanche durations for are studied in detail, exhibiting multifractal scaling behavior in model A, and finite size scaling behavior in model B, and scaling exponents are determined as a function of p. At a phase transition to noncritical steady state occurs. Due to difference in the relaxation mechanisms, avalanche statistics at approaches the parity conserving universality class in model A, and the mean-field universality class in model B. We also estimate roughness exponent at the transition. Received: 29 May 1998 / Revised: 8 September 1998 / Accepted: 10 September 1998     

Light-induced bistability in spin transition solids leading to thermal and optical hysteresis

We investigate the behaviour of photo-excitable, bistable systems, under permanent light irradiation, in presence of relaxation towards the non-excited state. Cooperativity causes bistability of the steady state, leading to light-induced thermal and optical hysteresis (LITH and LIOH). The light-induced instability is expected to induce demixtion, i.e. the coexistence of domains of the two stable steady states. Such effects are evidenced by magnetic and reflectivity measurements on the spin-crossover solid solution: , with x= 0.3, 0.5, 0.85. Experimental data are in quantitative agreement with a simple macroscopic model which includes a non-linear relaxation term in the master equation. Received: 5 June 1997 / Accepted: 17 July 1998     

Dissipation, decoherence and preparation effects in the spin-boson system

The dynamics of the reduced density matrix of the driven dissipative two-state system is studied for a general diagonal/off-diagonal initial state. We derive exact formal series expressions for the populations and coherences and show that they can be cast into the form of coupled nonconvolutive exact master equations and integral relations. We show that neither the asymptotic distributions, nor the transition temperature between coherent and incoherent motion, nor the dephasing rate and relaxation rate towards the equilibrium state depend on the particular initial state chosen. However, in the underdamped regime, effects of the particular initial preparation, e.g. in an off-diagonal state of the density matrix, strongly affect the transient dynamics. We find that an appropriately tuned external ac-field can slow down decoherence and thus allow preparation effects to persist for longer times than in the absence of driving. Received 23 October 1998 and Received in final form 26 February 1999     

Phase dynamics of Bose-Einstein condensates: Losses versus revivals

In the absence of losses the phase of a Bose-Einstein condensate undergoes collapses and revivals in time due to elastic atomic interactions. As experiments necessarily involve inelastic collisions, we develop a model to describe the phase dynamics of the condensates in presence of collisional losses. We find that a few inelastic processes are sufficient to damp the revivals of the phase. For this reason the observability of phase revivals for present experimental conditions is limited to condensates with a few hundreds of atoms. Received: 23 February 1998 / Revised: 21 July 1998 / Accepted: 23 July 1998     

Low temperature thermodynamical properties of the organic chain conductor (TMTSF)AsF

We report on specific heat measurements of the quasi-one-dimensional organic salt (TMTSF)₂AsF₆ in its spin density wave state between 75 mK and 7 K. Similarly to (TMTSF)₂PF₆, we find discontinuities in the lattice contribution at 1.9 K an d 3.5 K ascribed to sub-spin density wave phases. Time-dependent effects due to dynamics of low-energy excitations in metastable states occur only below 0.2 K which yields an activation energy for the equilibrium energy relaxation process of 0.34 K, 4-5 times smaller than found for (TMTSF)₂PF₆. Finally the reduction of the low-energy excitations contribution to the specific heat in comparison to PF₆ reveals an intermediate cubic-like regime between 0.25 and 0.5 K that we tentatively describe as the phason contribution of the incommensurate spin density wave modulation. Received: 17 March 1998 / Revised: 27 July 1998 / Accepted: 22 September 1998     

Mixed spin transverse Ising model with longitudinal random crystal field interactions

The effect of a longitudinal random crystal field interaction on the phase diagrams of the mixed spin transverse Ising model consisting of spin-1/2 and spin-1 is investigated within the finite cluster approximation based on a single-site cluster theory. In order to expand a cluster identity of spin-1, we transform the spin-1 to spin-1/2 representation containing Pauli operators. We derive the state equations applicable to structures with arbitrary coordination number N. The phase diagrams obtained in the case of a honeycomb lattice (N=3) and a simple-cubic lattice (N=6), are qualitatively different and examined in detail. We find that both systems exhibit a variety of interesting features resulting from the fluctuation of the crystal field interactions. Received: 13 February 1998 / Accepted: 17 March 1998     

Strain relaxation at cleaved surfaces studied by atomic force microscopy

Atomic force microscopy (AFM) in air is used to study the (110) cleaved surface of strained (100) In_xGa_1-xAs/ InP heterostructures for different compositions and thicknesses of the ternary compound layers. We find that the elastic strain relaxation induces a surface undulation of a few ? amplitude, even for very small misfits, provided the layers are thick enough. Using finite-element calculations of the strain relaxation near the cleaved edge, we reproduce quantitatively the AFM observations for compressive- as well as for tensile-strained layers with an accuracy better than 0.1 nm. This demonstrates the ability of AFM to quantify strain distributions by making use of surface profile measurements. Received: 9 November 1998 / Accepted: 11 March 1999 / Published online: 7 July 1999     

Instabilities of an electron cloud in a Penning trap

We have measured the storage instabilities of electrons in a Penning trap at low magnetic fields. These measurements are carried out as a function of the trapping voltage, for different magnetic fields. It is seen that these instabilities occur at the same positions when the trapping voltage is expressed as a percentage of the maximum voltage, given by the stability limit. The characteristic frequencies at which these instabilities occur, obey a relation that is given by n _zω _z + n ₊ω ₊ + n _-ω _- = 0, where ω _z, ω ₊ and ω _- are the axial, perturbed cyclotron and the magnetron frequencies of the trapped electrons respectively, and the n's are integers. The reason for these instabilities are attributed to higher order static perturbations in the trapping potential. Received 5 August 2002 / Received in final form 14 October 2002 Published online 17 December 2002 RID="a" ID="a"Present address: Dept. of Physics, Rampurhat College, Rampurhat, Birbhum, West Bengal, India. RID="b" ID="b"e-mail: werth@mail.uni-mainz.de     

Elliptic curves from finite order recursions or non-involutive permutations for discrete dynamical systems and lattice statistical mechanics

We study birational mappings generated by matrix inversion and permutations of the entries of matrices. For q=3 we have performed a systematic examination of all the birational mappings associated with permutations of matrices in order to find integrable mappings and some finite order recursions. This exhaustive analysis gives, among 30 462 classes of mappings, 20 classes of integrable birational mappings, 8 classes associated with integrable recursions and 44 classes yielding finite order recursions. An exhaustive analysis (with a constraint on the diagonal entries) has also been performed for matrices: we have found 880 new classes of mappings associated with integrable recursions. We have visualized the orbits of the birational mappings corresponding to these 880 classes. Most correspond to elliptic curves and very few to surfaces or higher dimensional algebraic varieties. All these new examples show that integrability can actually correspond to non-involutive permutations. The analysis of the integrable cases specific of a particular size of the matrix and a careful examination of the non-involutive permutations, shed some light on the integrability of such birational mappings. Received: 9 February 1998 / Revised: 13 March 1998 / Accepted: 17 March 1998     

Comparison of tunneling through molecules with Mott-Hubbard and with dimerization gaps

In order to study the tunneling of electrons through an interacting, 1D, dimerized molecule connected to leads, we consider the persistent current in a ring embedding this molecule. We find numerically that, for spinless fermions, a molecule with a gap mostly due to interactions, i.e. a Mott-Hubbard gap, gives rise to a larger persistent current than a molecule with the same gap, but due only to the dimerization. In both cases, the tunneling current decreases exponentially with the size of the molecule, but more slowly in the interacting case. Implications for molecular electronic are briefly discussed. Received: 17 November 1997 / Revised: 16 January 1998 / Accepted: 16 January 1998     

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     

Specific heat jump in non-Fermi superconductors

We derive the jump in the specific heat at T=T _c for a superconductor in a non-Fermi liquid model. We took into consideration the two possible limits in this problem: the spin-charge separation model for a Fermi liquid and the usual non-Fermi liquid model which satisfies the homogeneity relation for the spectral function , ). We also derive the order parameter behavior for these two cases in the vecinity of the critical temperature. Received: 25 January 1998 / Revised: 25 March 1998 / Accepted: 25 March 1998