The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

We present numerical and analytical results for the thermodynamical properties of the spin-1/2 Heisenberg chain at arbitrary external magnetic field. Special emphasis is placed on logarithmic corrections in the susceptibility and specific heat at very low temperatures (T/J=10^-24) and small fields. A longstanding controversy about the specific heat is resolved. At zero temperature the spin-Peierls exponent is calculated in dependence on the external magnetic field. This describes the energy response of the system to commensurate and incommensurate modulations of the lattice. The exponent for the spin gap in the incommensurate phase is given. Received: 12 February 1998 / Received in final form: 15 March 1998 / Accepted: 17 March 1998     

Electrostatics of DNA-cationic lipid complexes: isoelectric instability

We propose a Poisson-Boltzmann electrostatic theory for DNA/cationic lipid complexes modeled as a stack of aligned DNA chains intercalated with lipid bilayers, a structure suggested by the recent X-ray synchrotron studies of Radler et al. Poisson-Boltzmann theory is shown to predict that the isoelectric point - where the DNA and cationic lipid charges are in balance - is unstable against absorption of extra DNA or lipid material. The instability is caused by the entropy gain obtained following the release of small ions inside the complex and is manifested by singular behavior of the rod-rod spacing near the isoelectric point. We apply the theory to a discussion of the results of Radler et al. Received: 21 July 1997 / Received in final form: 19 January 1998 /Accepted: 5 March 1998     

Field theoretical calculation of the specific heat exponent for a classical N-vector model in a random external field

We calculate using diagrammatic perturbation theory in the two-loop approximation, the specific heat exponent for the classical N-vector model in a random external field for spatial dimension (D) lying between four and six. The calculation supports the modified hyperscaling , where is the correlation length exponent. Received: 18 March 1998 / Revised: 17 April 1998 / Accepted: 21 April 1998     

Self organization of interacting polya urns

We introduce a simple model which shows non-trivial self organized critical properties. The model describes a system of interacting units, modelled by Polya urns, subject to perturbations and which occasionally break down. Three equivalent formulations - stochastic, quenched and deterministic - are shown to reproduce the same dynamics. Among the novel features of the model are a non-homogeneous stationary state, the presence of a non-stationary critical phase and non-trivial exponents even in mean field. We discuss simple interpretations in term of biological evolution and earthquake dynamics and we report on extensive numerical simulations in dimensions d=1,2 as well as in the random neighbors limit. Received: 18 February 1998 / Revised: 20 March 1998 / Accepted: 29 March 1998     

Transition from small to big charged unilamellar vesicles

The transition from small to big unilamellar vesicles predicted by a Poisson-Boltzmann Cell Model for the thermodynamics of a dilute phase of unilamellar charged vesicles is characterized. The radius as a function of experimental parameters is calculated and the coexistence region of small and big vesicles is identified. We further investigate the physical meaning in terms of simplified models, which allow for an identification of the role of parameters like the surface charge density or the Debye-length. Connections to experiments are discussed. Received: 20 October 1997 / Received in final form: 9 February 1998 / Accepted: 9 March 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     

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     

The new identity for the scattering matrix of exactly solvable models

We discovered a simple quadratic equation, which relates scattering phases of particles on Fermi surface. We consider one-dimensional Bose gas and XXZ Heisenberg quantum spin chain. Received: 4 December 1997 / Accepted: 17 March 1998     

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     

Optical conductivity of the Bechgaard salts: the sum rules revisited

The validity of the optical sum rules has been addressed eversince and was always matter of debate. Particularly controversial is the proof that the partial sum rules can be extended to both optical conductivity and energy loss function. We show in this paper that for both transverse (optical conductivity) and longitudinal (energy loss function) absorption processes the corresponding sum rule can be theoretically established and through appropriate conditions for the integration limits exactly verified. We also focus our attention on the one-dimensional case within the microscopic Hubbard model. An application of these concepts to the quasi one-dimensional systems, for which we have chosen the organic (TMTSF)₂PF₆ material, will also be presented. Received: 19 December 1997 / Received in final form: 9 March 1998 / Accepted: 23 March 1998     

Some remarks on Yang-Baxter algebras

We point out the existence of an alternative algebraic structure in Yang-Baxter algebra with trigonometric R-matrix, which appears to be the generalization of the Yangian in Yang-Baxter algebras with rational R-matrix and which is described most naturally by q-commutators. Some properties are presented, in particular in the case of the well-known symmetric six-vertex model. Received: 13 February 1998 / Revised: 16 March 1998 / Accepted: 17 April 1998     

Magnetothermal instabilities in an organic superconductor

We have studied the occurrence of magnetothermal instabilities in a single crystal during field sweep magnetization experiments, equivalent to short time relaxation studies. We find instability behaviour in good agreement with a recent model by Mints, for a non-linear E(J) characteristic. In particular, we find that a decrease of the dynamic relaxation rate, characterizing the effective activation energy, precedes the unstable regime. We point out formal analogies between such instabilities and the general predictions for flux avalanches. Received: 11 December 1997 / Revised: 15 January 1998 / Accepted: 31 March 1998     

Squeezed two-mode lasers without and with inversion

On the basis of the nondegenerate quantum-beat laser model, we introduce a coherent field which drives the transition between the upper lasing level and an auxiliary level. We demonstrate that such a four-level system can produce squeezed two-mode laser without and with inversion. When the laser is operated well above threshold, the intensity fluctuation in the average mode is reduced below the shot noise with an optimum Mandel parameter Q=- 1/2. At the same time, the noises in the relative amplitude and the relative phase drop to their vaccum noise levels. Furthermore, regardless of inversion, noninversion, and transition between inversion and noninversion, the optimum Mandel Q parameter of Q=- 1/2 is retained when the system operates well above threshold. A simple physical explanation of the squeezing mechanism for two-mode squeezing is given. Received: 22 December 1997 / Revised: 25 March 1998 / Accepted: 9 September 1998     

Ascending air bubbles in protein solutions

We report measurements of the ascending velocity of air bubbles in protein (bovine serum albumin) solutions. We show that, because of the protein molecules adsorbed on their surface, the terminal ascending velocity of bubbles is strongly reduced compared to the terminal velocity in pure water: protein- covered bubbles behave hydrodynamically as solid spheres. From the evolution of the ascending velocity with time, we can derive the amount of protein needed to immobilize the bubble interface which is 0.5 mg m^-2, i.e. only one fifth of the amount adsorbed at equilibrium in the range of used bulk concentrations. Received: 6 March 1998 / Revised and accepted: 6 May 1998     

Crystallized vortex crystals

Numerical simulations of the equations of motion of 300 charged particles confined to a plane with an additional magnetic field orthogonal to the plane reproduce recently observed self-organization of non-neutral plasmas into a small number of interacting vortices. In the presence of damping we observe crystallized vortices, i.e. vortices with regular internal structure. We also observe crystallized vortex crystals, i.e. geometric patterns of crystallized vortices. Fractal vortex arrangements are investigated and found to be stable. Our results are relevant for quantum dots and artificial atoms. Received: 24 February 1998 / Revised: 4 March 1998 / Accepted: 4 May 1998     

Off-diagonal long-range order in a supersymmetric integrable model of correlated electrons

A new model for correlated electrons is presented which is integrable in one-dimension. The symmetry algebra of the model is the Lie superalgebra gl(2|1) which depends on a continuous free parameter. This symmetry algebra contains the pairing algebra as a subalgebra which is used to show that the model exhibits Off-Diagonal Long-Range Order in any number of dimensions. Received: 9 December 1997 / Revised: 12 February 1998 / Accepted: 17 March 1998     

Universal conductance in quantum wires in the presence of Umklapp scattering

The effects of Umklapp scattering on the zero-temperature conductance in one-dimensional quantum wires are reexamined by taking into account both the screening of external potential and the non-uniform chemical potential shift due to electron-electron interaction. It is shown that in the case away from half-filling the conductance is given by the universal value, 2e ² /h, even in the presence of Umklapp scattering, owing to these renormalization effects of external potential. The conclusion is in accordance with the recent claim obtained for the system with non-interacting leads being attached to a quantum wire. Received: 5 February 1998 / Received in final form: 16 March 1998 / Accepted: 17 April 1998     

Charge density wave transport in submicron antidot arrays in NbSe3

We demonstrate for the first time that a periodic array of submicrometer holes (antidots) can be patterned into thin single NbSe₃ crystals. We report on the study of Charge Density Wave (CDW) transport of the network of mesoscopic units between antidots. Size of the elementary unit can be as small as 0.5 μm along the chain axis and in cross-section. We observe size effects for Ohmic residual resistance and in CDW transport current-voltage characteristics in submicronic networks. Received: 25 November 1997 / Received in final form: 30 March 1998 / Accepted: 6 April 1998     

Critical behavior of interacting surfaces with tension

Wetting phenomena, molecular protrusions of lipid bilayers and membrane stacks under lateral tension provide physical examples for interacting surfaces with tension. Such surfaces are studied theoretically using functional renormalization and Monte-Carlo simulations. The critical behavior arising from thermally-excited shape fluctuations is determined both for global quantities such as the mean separation of these surfaces and for local quantities such as the probabilities for local contacts. Received: 30 January 1998 / Accepted: 17 March 1998     

Spherical averaged jellium model with norm-conserving pseudopotentials

The effect of non-local norm-conserving pseudo-potentials on the static and dynamic properties of Na_n and Li_n cluster with n=6,8 is investigated in the frame of self-consistent LDA calculations with spherically averaged ionic density (SAPS model). A comparison with previous calculations which use local pseudo-potentials as well with uniform averaged non-local pseudo-jellium calculation has been carried out. A better quantitative agreement with experiments has been found in the calculation of the photoresponse cross-section with respect to either simple jellium or pseudo-jellium model, even in very small clusters, where deviations from sphericity are not negligible. Received: 3 March 1998 / Received in final form and Accepted: 2 June 1998