Distinct critical fluctuations and molecular motions manifest in a model biomembrane

Lattice dynamics in bis-(n-C₁₆H₃₇NH₃)₂SnCl₆, where the hydrocarbon part is analogous to lipid membrane, was investigated by means of 200 MHz ¹H nuclear magnetic resonance. As a result, critical fluctuations and molecular dynamics associated with the phase transitions, an order-disorder and a conformational phase transition, were distinguished in a wide temperature range. The dynamical origin of the critical fluctuations, observed in the long-chain compounds but not in the short-chain compounds, by the laboratory frame spin-lattice relaxation measurements, is revealed and discussed in this work.     

Ladders in a magnetic field: a strong coupling approach

We show that non-frustrated and frustrated ladders in a magnetic field can be systematically mapped onto an XXZ Heisenberg model in a longitudinal magnetic field in the limit where the rung coupling is the dominant one. This mapping is valid in the critical region where the magnetization goes from zero to saturation. It allows one to relate the properties of the critical phase (H _c ¹, H _c ², the critical exponents) to the exchange integrals and provide quantitative estimates of the frustration needed to create a plateau at half the saturation value for different models of frustration. Received: 7 May 1998 / Revised and Accepted: 10 July 1998     

Model glasses coupled to two different heat baths

In a p-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change with time. The spins are coupled to a heat bath with temperature T, while the coupling constants are coupled to a bath having temperature T_J. In an adiabatic limit (where relaxation time of the couplings is much larger that of the spins) we construct a generalized two-temperature thermodynamics. It involves entropies of the spins and the coupling constants. The application for spin-glass systems leads to a standard replica theory with a non-vanishing number of replicas, n=T/T _J . For p>2 there occur at low temperatures two different glassy phases, depending on the value of n. The obtained first-order transitions have positive latent heat, and positive discontinuity of the total entropy. This is an essentially non-equilibrium effect. The dynamical phase transition exists only for n<1. For p=2 correlation of the disorder (leading to a non-zero n) removes the known marginal stability of the spin glass phase. If the observation time is very large there occurs no finite-temperature spin glass phase. In this case there are analogies with the non-equilibrium (aging) dynamics. A generalized fluctuation-dissipation relation is derived. Received 12 July 1999 and Received in final form 8 December 1999     

Pore size distribution in porous glass: fractal dimension obtained by calorimetry

By differential Scanning Calorimetry (DSC), at low heating rate and using a technique of fractionation, we have measured the equilibrium DSC signal (heat flow) J _q ⁰ of two families of porous glass saturated with water. The shape of the DSC peak obtained by these techniques is dependent on the sizes distribution of the pores. For porous glass with large pore size distribution, obtained by sol-gel technology, we show that in the domain of ice melting, the heat flow J_q is related to the melting temperature depression of the solvent, ΔT _m , by the scaling law: J _q ⁰∼ΔT _m ^{- (1 + D)}. We suggest that the exponent D is of the order of the fractal dimension of the backbone of the pore network and we discuss the influence of the variation of the melting enthalpy with the temperature on the value of this exponent. Similar D values were obtained from small angle neutron scattering and electronic energy transfer measurements on similar porous glass. The proposed scaling law is explained if one assumes that the pore size distribution is self similar. In porous glass obtained from mesomorphic copolymers, the pore size distribution is very sharp and therefore this law is not observed. One concludes that DSC, at low heating rate ( q? 2^°C/min) is the most rapid and less expensive method for determining the pore distribution and the fractal exponent of a porous material. Received 23 July 1999 and Received in final form 16 February 2001     

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     

Subleading long-range interactions and violations of finite size scaling

We study the behavior of systems in which the interaction contains a long-range component that does not dominate the critical behavior. Such a component is exemplified by the van der Waals force between molecules in a simple liquid-vapor system. In the context of the mean spherical model with periodic boundary conditions we are able to identify, for temperatures close above T _c, finite-size contributions due to the subleading term in the interaction that are dominant in this region decaying algebraically as a function of L. This mechanism goes beyond the standard formulation of the finite-size scaling but is to be expected in real physical systems. We also discuss other ways in which critical point behavior is modified that are of relevance for analysis of Monte Carlo simulations of such systems. Received 21 November 2000 and Received in final form 28 February 2001     

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     

Characteristic variations in the effect of diluents on polymer crystallization and melting observed for a sample of poly(ethylene-co-octene)

Melting points in mixtures of a crystallizable polymer with a low-molar-mass diluent depend on both, the diluent fraction and the crystal thickness. A differentiation of the two factors can be achieved by temperature-dependent SAXS experiments. A corresponding study, complemented by DSC, dilatometry, microscopy and AFM-imaging, was carried out for mixtures of a poly(ethylene-co-octene) with n-C₁₆H₃₄, c-C₁₆H₃₂ and methyl-anthracene, respectively. All diluents lead for a constant crystal thickness to melting point depressions in agreement with Raoult's law. On the other hand, the effect of the diluents on the thickness of the crystals formed at a fixed crystallization temperature varies. While in the presence of the two alkanes thicker crystals form, no effect arises for the methyl-anthracene—as was previously found for the octene-co-units. We consider these observations as a further support for our view that polymer crystallization follows a multi-stage route which includes a passage through an intermediate mesomorphic phase. Under such conditions crystal thicknesses would only be affected if the diluent is still present in the mesomorphic phase and stay invariant if the diluent molecules are already rejected when this intermediate phase forms.     

Charge transfer between alkali cluster ions and atoms in the 1 to 10 keV collisional energy range

The cross-sections for collisional charge transfer between singly charged free clusters M _n ⁺ (M = Li, Na; n=1...50) and atomic targets A (cesium, potassium) have been measured as a function of collisional relative velocity in laboratory energy range 1–10 keV. For each cluster size, the experimental values of the charge transfer cross-section are fitted with an universal parametric curve with two independent parameters and v_m, the maximum cross-section and the corresponding velocity. For small size clusters (), the characteristic parameters show strong variations with the number of atoms in the cluster. Abrupt dips observed for n=10 and n=22 are attributed to electronic properties. Charge transfer patterns observed for various collisional systems present similarities, which appear more sensitive to cluster quantum size effects than to collision energy defects. In their whole, the and v_m parameters show differences in both their size evolution and their absolute values discussed in term of projectile and target electronic structures. Received 13 April 2000 and Received in final form 29 June 2000     

Optical properties of natural quantum-well compounds (C6H5-CnH2n-NH3)2PbBr4 (n=1-4)

This paper describes the synthesis and characterization of self-assembled organic-inorganic layered perovskite compounds, (C₆H₅-C_nH_2n-NH₃)₂PbBr₄ (n=1-4). the effect of the number of carbon atoms of the alkyl chain length (n) on optical properties has been studied. (C₆H₅-C_nH_2n-NH₃)₂PbBr₄ films fabricated by spin-coating are microcrystalline form, single phase and oriented with the c-axis. Crystallinity, the maximum PL intensity and the lifetime of exciton emissions varied with the number of carbon atoms. the lowest-energy exciton splits into a few fine-structure levels at low temperatures. Time-resolved photoluminescence spectra reveal that (C₆H₅-C_nH_2n-NH₃)₂PbBr₄ shows both singlet and triplet excitons. with decreasing temperature, triplet exciton emissions become dominant for (C₆H₅-C_nH_2n-NH₃)₂PbBr₄ (n=1-3), while (C₆H₅-C₄H₈-NH₃)₂PbBr₄ shows mainly singlet exciton emissions. The intersystem crossing from excited singlet state to triplet state plays an important role in the relaxation process of excitons.     

Scaling and infrared divergences in the replica field theory of the Ising spin glass

Replica field theory for the Ising spin glass in zero magnetic field is studied around the upper critical dimension d=6. A scaling theory of the spin glass phase, based on Parisi's ultrametrically organised order parameter, is proposed. We argue that this infinite step replica symmetry broken (RSB) phase is nonperturbative in the sense that amplitudes of scaling forms cannot be expanded in term of the coupling constant w². Infrared divergent integrals inevitably appear when we try to compute amplitudes perturbatively, nevertheless the -expansion of critical exponents seems to be well-behaved. The origin of these problems can be traced back to the unusual behaviour of the free propagator having two mass scales, the smaller one being proportional to the perturbation parameter w² and providing a natural infrared cutoff. Keeping the free propagator unexpanded makes it possible to avoid producing infrared divergent integrals. The role of Ward-identities and the problem of the lower critical dimension are also discussed. Received 23 December 1998 and Received in final form 23 March 1999     

UV excimer laser photochemistry of hybrid organometallic compounds of gallium

The gas phase ultraviolet (UV) excimer laser induced photolysis of the gallium-alkyls Ga(t-C₄H₉) _n ^– (CH₃)_3–n (n=0, 1, 2, 3) was studied, using photolysis wavelengths of 308, 248, and 193 nm. The photofragments Ga, GaH, and GaCH₃ were detected by laser ionization time-of-flight mass spectroscopy, while the hydrocarbon products CH₄, C₂H₆, HC(CH₃)₃ and H₂C=C(CH₃)₂ were identified using Fourier transform infrared (FTIR) spectroscopy. The formation of the GaH photofragment, and a high olefin-to-alkane product ratio, for Ga(t-C₄H₉)₂(CH₃) and Ga(t-C₄H₉)₃ are interpreted to indicate a -hydrogen elimination process. However, -hydrogen elimination only occurs after fission of the weakest Ga-C bond, thus no -hydride elimination is observed for Ga(t-C₄H₉)(CH₃)₂. Detection of C₂H₆ for Ga(CH₃)₃ and Ga(t-C₄H₉)(CH₃)₂, but not for Ga(t-C₄H₉)₂(CH₃), shows that under our experimental conditions the formation of ethane is as a result of the reductive elimination of the methyl groups, and is not due to the recombination of two free methyl radicals.     

Frustrated Blume-Emery-Griffiths model

A generalised integer S Ising spin glass model is analysed using the replica formalism. The bilinear couplings are assumed to have a Gaussian distribution with ferromagnetic mean . Incorporation of a quadrupolar interaction term and a chemical potential leads to a richer phase diagram with transitions of first and second order. The first order transition may be interpreted as a phase separation, and contrary to what has been argued previously, it persists in the presence of disorder. Finally, the stability of the replica symmetric solution with respect to fluctuations in replica space is analysed, and the transition lines are obtained both analytically and numerically. Received 13 January 1997     

Phase Transitions in Dynamical Random Graphs

We study a large-time limit of a Markov process whose states are finite graphs. The number of the vertices is described by a supercritical branching process, and the dynamics of edges is determined by the rates of appending and deleting. We find a phase transition in our model similar to the one in the random graph model G _n,p . We derive a formula for the line of critical parameters which separates two different phases: one is where the size of the largest component is proportional to the size of the entire graph, and another one, where the size of the largest component is at most logarithmic with respect to the size of the entire graph. In the supercritical phase we find the asymptotics for the size of the largest component.     

Stretched exponential relaxation on the hypercube and the glass transition

We study random walks on the dilute hypercube using an exact enumeration Master equation technique, which is much more efficient than Monte Carlo methods for this problem. For each dilution p the form of the relaxation of the memory function q(t) can be accurately parametrized by a stretched exponential over several orders of magnitude in q(t). As the critical dilution for percolation is approached, the time constant tends to diverge and the stretching exponent drops towards 1/3. As the same pattern of relaxation is observed in a wide class of glass formers, the fractal like morphology of the giant cluster in the dilute hypercube appears to be a good representation of the coarse grained phase space in these systems. For these glass formers the glass transition may be pictured as a percolation transition in phase space. Received 16 June 2000 and Received in final form 13 October 2000     

Electronic and magnetic structure of the undoped two and three-leg ladder cuprates in an itinerant electrons model

We study the electronic and magnetic structure of the undoped ideal two and three-leg ladder cuprates by assuming a moderate on site coulombic repulsion. This analysis is an extension of the Fermi liquids studies proposed for the CuO₂ plane in view to explain the high T_c superconductivity and the competition with the antiferromagnetic phase. At zero doping, the quasi-one-dimensionality of the structure results in SDW correlations with different (commensurate) vectors according to the number of legs, which contrasts with the predictions made from the Heisenberg model. At mean field, and for n = 3 (Sr₂Cu₃O₅), we predict a magnetic ordered state, detected by μSr and NMR measurements with critical temperatures consistent with our assumptions on the physical parameters, the modulation vector being .The presence of several bands at the Fermi level explains why there is no observable gap in the static susceptibility measurements. For n = 2, we predict a gap consistent with experimental Curie susceptibility. But the expected magnetic instability is detected only in La₂Cu₂O₅, where the interladder coupling is stronger. In every case the one-dimensional van Hove singularities are far from the Fermi level, making difficult the obtaining of high T_c superconductivity. Received 3 June 1998     

Persistent spectral hole-burning in a -doped aluminosilicate glass from 8 to 295 K: Study of the burning and refilling kinetics, and of optical dephasing

High-temperature persistent spectral hole-burning (PSHB), up to room temperature, has been observed in a Eu ³⁺ -doped aluminosilicate glass using a high peak-power nanosecond dye laser. Spontaneous refilling as well as thermal cycling measurements show that at least two mechanisms, a fast and a slow one, are involved in our sample. We suggest that the fast or “easy” component may correspond to a non-photochemical local rearrangement of the host or to photoreduction of the Eu ³⁺ ions and that the second one leading to very stable photoproducts may correspond to transfer of an electron over a sizable distance through a several-step process. The mechanisms we suggest agree with light-induced hole refilling measurements. Line broadening mechanisms are discussed and the temperature-dependent part of the homogeneous width and of the spectral shift is interpreted in terms of a two-phonon (Raman) process involving pseudo-local phonons. Received 28 July 1999     

Quantum fluctuations in a single electron box

Recent experiments have demonstrated that the numbern of additional electrons on a small metallic island is a staircase function of a continuous external chargen _x for temperaturesT small compared to the single electron charging energyU. We show that the finite conductanceg of the tunnel barrier connecting the island to the external gate gives rise to quantum fluctuations inn which lead to a smearing of the staircase even at zero temperature. In the experimentally relevant case of wide junctions and in the limit of small conductanceg1 the slope <n>/n _x at the turning point between two plateaus saturates at a finite value of order 1/g asT0 instead of diverging likeU/T as predicted with thermal fluctuations only. The experimentally observed broadening however is still much larger which is probably due to extrinsic effects.     

Fermi liquid theory: a renormalization group approach

We show how Fermi liquid theory results can be systematically recovered using a renormalization group (RG) approach. Considering a two-dimensional system with a circular Fermi surface, we derive RG equations at one-loop order for the two-particle vertex function in the limit of small momentum () and energy () transfer and obtain the equation which determines the collective modes of a Fermi liquid. The density-density response function is also calculated. The Landau function (or, equivalently, the Landau parameters F _l ^s and F _l ^a ) is determined by the fixed point value of the -limit of the two-particle vertex function (). We show how the results obtained at one-loop order can be extended to all orders in a loop expansion. Calculating the quasi-particle life-time and renormalization factor at two-loop order, we reproduce the results obtained from two-dimensional bosonization or Ward Identities. We discuss the zero-temperature limit of the RG equations and the difference between the Field Theory and the Kadanoff-Wilson formulations of the RG. We point out the importance of n-body () interactions in the latter. Received: 27 June 1997 / Received in final form: 17 December 1997 / Accepted: 26 January 1998