On the validity of pre-equilibrium model assumptions

The Hartree-Fock calculation is performed for nuclear matter using the Skyrme interaction. It is shown that a stable density wave periodic in only one direction exists at densities below about one-third of the normal nuclear density. The critical densityρ _c below which the energy of the density wave is lower than that of the Fermi gas is determined for Skyrme interactions SKI to SKVI. It is further shown that even at densities slightly higher thanρ _c the density wave still exists as ametastable state in the sense that its energy is a local minimum in the variation parameter space. The density wave solution suddenly disappears at a higher density, since there the local minimum changes to an inflection point.     

Critical behaviour at the displacive limit of structural phase transitions

For a special critical point at zero temperature,T _c =0, which is called the displacive limit of a classical or of a quantum-mechanical model showing displacive phase transitions, we derive a set of static critical exponents in the large-n limit. Due to zero-point motions and quantum fluctuations at low temperatures, the exponents of the quantum model are different from those of the classical model. Moreover, we report results on scaling functions, corrections to scaling, and logarithmic factors which appear ford=2 in the classical case and ford=3 in the quantum-mechanical case. Zero-point motions cause a decrease of the critical temperature of the quantum model with respect to the classicalT _c , which implies a difference between the classical and the quantum displacive limit. However, finite critical temperatures are found in both cases ford>2, while critical fluctuations still occur atT _c =0 for 0<d≦2 in the classical case and for 1 <d≦2 in the quantum model. Further we derive the slope of the critical curve at the classical displacive limit exactly. The absence of 1/n-corrections to the exponents of the classical model is also discussed.     

Structural instability and superconductivity in niobium-titanium alloys

Niobium-titanium is the most widely used technical superconductor. Titaniumrich transition metal alloys, quenched from high temperatures, can generally be retained in the bccβ phase. This phase is metastable and the instability is relieved by a variety of low temperature structural transformations. This aspect has been investigated using x-ray, TEM, low temperature resistivity,T _c and dH _c2/dT studies, in a series of Nb-Ti alloys. The instability has been characterized by the normal state resistivityρ _n and dρ/dT. The commercially used Nb-Ti alloys are Ti rich per atom-wise. This stems basically from the anomalous increase in the normal state resistivityρ _n as the Ti concentration is increased. This is a consequence of a dynamical process through which theβ phase instability tends to be relieved leading to athermal ω precipitation. The resulting anomalous resistivity behaviour can be understood in terms of a ‘two-level system’ model generally invoked for amorphous materials. It has also been possible to induce instability towards athermal ω precipitation in a system spontaneously undergoing a martensitic transformation to become stable. Thus in an alloy of Nb-83 at % Ti, addition of 1% nitrogen has suppressed the martensitic transformation, giving a three-fold increase inρ _n (about 150µΘ cm), the highest known in Nb-Ti so far. The increase in the normal state resistivity has beneficial effects on the upper critical field. From studies on several Nb-Ti alloys, it is inferred that a peak inH _c2(0) occurs at 17–18 tesla at aρ _n value of 100µΘ cm. It is pointed out that in the present commercial alloys, the sequence of thermo-mechanical treatments given to optimizeJ _c, restrictsρ _n, perhaps owing to the partial relieving of the metastability of theβ phase. They are therefore non-optimized with respect toH _c2.     

Electronic and superconducting properties of a superlattice of quantum stripes at the atomic limit

The superconducting gap, the critical temperature and the isotope coefficient in a superlattice of metallic quantum stripes is calculated as a function of the electron number density. We show that it is possible to design a particular artificial superlattice of quantum stripes that exhibits the curves of T _c and of the isotope coefficient as a function of the charge density as in cuprate superconductors. The shape of the superlattice is designed in order to tune the chemical potential near the bottom of the third subband for an electron number density of ρ ～ 5:810-²Å^-2. The superconducting critical temperature shows a resonant amplification as a function of electron number density ρ with a maximum at a critical value ρ _c. The isotope coefficient shows a sharp drop from a regime where α > 0:5 at ρ < ρ _c to a regime where α < 0:2 at ρ ≥ ρ _c. The underdoped and overdoped regime in cuprate superconductors is associated with a transition from a quasi 1D behavior for ρ > ρ _c to quasi 2D behavior for ρ < ρ _c with opening of a pseudogap at ρ ～ ρ _c.     

Resistivity variation near the critical temperature in some Ni-Fe base amorphous alloys

Accurate measurements of the electrical resistivity of three Ni_80?xFe_xP₁₄B₆ alloys (with x=10, 20 and 30) were performed in the temperature interval 1.5–500 K. Resistivity (ρ) and dρ/dT behaviours near T_c for the alloys with different x values are mutually very different. In particular $\text{dρ}\text{dT}$ variation near T_c for the alloys with x=10 and 20 is Ornstein-Zernicke like while for the alloy with x=30 is of more usual energy like type. A tentative explanation of this behaviour in terms of the influence of the percolation limit on the nature of the magnetic transition is offered.     

The speed of sound in hadronic matter

We calculate the speed of sound c _s in an ideal gas of resonances, whose mass spectrum is assumed to have the Hagedorn form ρ(m)～m ^?a exp?{bm}, which leads to singular behavior at the critical temperature T _c =1/b. With a=4 the pressure and the energy density remain finite at T _c , while the specific heat diverges there. As a function of the temperature, the corresponding speed of sound initially increases similarly to that of an ideal pion gas, until near T _c resonance effects dominate, which causes c _s to vanish as (T _c ?T)^1/4. In order to compare this result to the physical resonance gas models, we introduce an upper cut-off M in the resonance mass integration. Although the truncated form still decreases somewhat in the region around T _c , the actual critical behavior in these models is no longer present.     

Spin-0 and spin-1/2 particles in a constant scalar-curvature background

We study the Klein-Gordon and Dirac equations in the presence of a background metric ds²=−dt²+dx²+e^−2gx(dy²+dz²) in a semi-infinite lab (x>0). This metric has a constant scalar-curvature R=6g² and is produced by a perfect fluid with equation of state p=−ρ/3. The eigenfunctions of spin-0 and spin-1/2 particles are obtained exactly, and the quantized energy eigenvalues are compared. It is shown that both of these particles must have nonzero transverse momentum in this background. We show that there is a minimum energy E²_min=m²c⁴+g²c²?² for bosons (E_KG>E_min), while the fermions have no specific ground state (E_Dirac>mc²).     

Height-height correlations for surface growth on percolation networks

The height-height correlations of the surface growth for equilibrium and nonequilibrium restricted solid-on-solid (RSOS) model were investigated on randomly diluted lattices, i.e., on infinite percolation networks. It was found that the correlation function calculated over the chemical distances reflected the dynamics better than that calculated over the geometrical distances. For the equilibrium growth on a critical percolation network, the correlation function for the evolution time t?1 yielded a power-law behavior with the power ζ^′, associated with the roughness exponent ζ via the relation ζ=ζ^′d_f/d_l, with d_f and d_l being, respectively, the fractal dimension and the chemical dimension of the substrate. For the nonequilibrium growth, on the other hand, the correlation functions did not yield power-law behaviors for the concentration of diluted sites x less than or equal to the critical concentration x_c.     

Analysis of experiments on the measurement of the pion electromagnetic formfactor

We analyse the experiments [1–3] on the measurement of the pion electromagnetic formfactor in the time-like and space-like region using an expression with correct analytical properties and with the asymptotics predicted by QCD. The best fit values for the physical quantities (1) electromagnetic radius of the pion:r _π ² =0.466±0.002 fm², (2) the mass and width of the ρ (770) and the ρ′ (1600) meson:m _ρ=768±1 MeV,Г _ρ=138±1 MeV,m _ρ′=1546±26 MeV,Г _ρ'=620±60 MeV; (3) the residuesg _ρ m _ρ ² =0.676±0.003,g _ρ′ m _ρ′ ² =?(0.644±0.009); (4) the ππ-scattering lengtha ₁ ¹ =(0.1±0.01)m _π ^?3 .     

Scaling of pseudorapidity distributions at c.m. energies up to 0.9 TeV

New data are presented on charged particle pseudorapidity distributions for inelastic events produced at c.m. energies \(\sqrt s \) =200 and 900 GeV. The data were obtained at the CERN antiproton-proton Collider operated in a new pulsed mode. The rise of the central density ρ(0) at energies up to \(\sqrt s \) =900 GeV has been studied. A new form of central region scaling is found involving the densityρ _n (0) for charged multiplicityn, namely that the scaled central densityρ _n (0)/ρ(0) expressed as a function ofz=n/〈n〉 is independent ofs. Scaling in the fragmentation region holds to 10–20%, and the small amount of scalebreaking observed here could be accommodated within the framework suggested by Wdowcyk and Wolfendale to account for both accelerator and cosmic ray data.     

Field theoretic approach to unstable critical dynamics: Initial stage renormalization

The formalism of initial stage renormalization is constructed and used to study the spinodal decomposition of time-dependent Ginzburg-Landau models. Scaling relations of correlation functions are derived and new critical exponents describing the effects of initial order parameters and external fields are identified. At early stages, the structure function satisfies the usual dynamic scaling ansatz and exponents for characteristic length scales are nothing but the inverse of the dynamic critical exponent. Critical exponents and the structure function are calculated explicitly to first order in ϵ=d_c−d.     

Modeling of the out-of-plane resistivity of cuprate superconductors

The out-of-plane (c-axis) resistivity, ρ_c(T), of high-T_c cuprates have been modeled in this study. The non-Fermi liquid like temperature dependence of ρ_c(T) has been described by considering (i) the full impact of the pseudogap (PG) in the electronic density of states (EDOS) and (ii) the presence of a quantum critical point (QCP) beneath the superconducting dome at slightly overdoped region. This simple phenomenological model describes the experimental ρ_c(T) data over a wide range of hole content (from the underdoped to slightly overdoped regions) remarkably well. The PG energy scale, ε_g (dominated by the anti-nodal parts of the Brillouin zone) extracted from the analysis of ρ_c(T) data was found to decrease almost linearly with increasing hole concentration, p, in the CuO₂ planes. We have also discussed about the possible origin of more conventional behavior of ρ_c(T) observed in the deeply overdoped side of the T–p phase diagram in this paper.     

Simulation studies of gas-liquid transitions in two dimensions via a subsystem-block-density distribution analysis

The finite-size scaling analysis of the density distribution function of subsystems of a system studied at constant total density is studied by a comparative investigation of two models: (i) the nearest-neighbor lattice gas model on the square lattice, choosing a total lattice size of 64×64 sites. (ii) The two-dimensional off-lattice Lennard-Jones system (truncated at a distance of 2.5 σ, σ being the range parameter of the interaction) withN=4096 particles, applying the NVT ensemble. In both models, the density distribution functionP _L (ρ) is obtained forL×L subsystems for a wide range of temperaturesT, subblock linear dimensionsL and average densities <ρ>. Particular attention is paid to the question whether accurate estimates of critical temperatureT _c and critical density ρ _c can be obtained. In the lattice gas model these critical parameters are known exactly and the limitations of the approach can thus be definitively asserted. The final estimates for the Lennard Jones problem areT _c =0.47±0.01 (in units of the Lennard Jones energy ε) and ρ _c (in units of σ²), a comparison with previous estimates is made.     

Study of the three-dimensional Ising model on film geometry with the cluster Monte Carlo method

Topological properties of clusters are used to extract critical parameters. This method is tested for the bulk properties ofd=2 percolation and thed=2, 3 Ising model. For the latter we obtain an accurate value of the critical temperatureJ/k _B T _c=0.221617(18). In the case of thed=3 Ising model with film geometry the critical value of the surface coupling at the special transitions is determined as J_1c/J=1.5004(20) together with the critical exponents ₁ ^m =0.237(5) and=0.461(15).     

Transport properties of the disordered charged bose condensate in two dimensions

Analytical results for the frequency-dependent conductivity of a disordered two-dimensional interacting Bose condensate are presented. Charged and uncharged impurities are considered. We find that for weak disorder the condensate is a superfluid while for strong disorder it is an insulator (a Bose glass). At the superfluid-insulator transition point (at the critical boson densityN _c) the condensate exhibits metallic tranport properties. An loffe-Regel criterion for the transition point is derived. The conductivity at the transition point is of ordere ²/h (h is Planck's constant) and depends on the kind of disorder. For charged impurities (with impurity densityN _i) the conductivity (for a condensate of particles with charge 2e and forN _i=2N _c) at the transition point is given by _c =0.26x(2e)²/h. We discuss recent experiments on superconducting ultra-thin films and on high-T _c superconductors.     

Are CKM andW,Z phenomenology consistent withA=p=1 and δ≃π/3?

The expectation of the geometrical catamorphic representation of the quark-lepton families is that the parameters of the CKM matrix, in the Wolfenstein substitution, have the valuesA=p=1 and δ?π/3. No conflict is found with the geometrical expectation which, furthermore, requires 107<m _t<165 GeV/c², consistent withW, Z phenomenology.     

Crossover from high-temperature vortex-liquid to low-temperature vortex-glass behavior in single phase HgBa2Ca2Cu3O8+δ superconductor

The ρ-T curves in our single phase HgBa₂Ca₂Cu₃O_8+δ superconductor were measured as a function of temperature and magnetic field, ρ=ρ₀exp(−U_eff/κ_BT). It can be transformed to another form d(lnρ)/d(1/T)=−U_eff+TdU_eff/dT, then this becomes a plot of the activation energy U_eff as a function of temperature. Our data plotted in these ways show a clear crossover from high-temperature two-dimensional vortex-liquid to a critical region associated with the low-temperature three-dimensional vortex-glass phase transition. The critical exponents v(z−1)=3.9±1.9 in this system are little different with previous measurements in BSCCO and YBCO systems.     

Stochastic dynamics and Parrondo’s paradox

The Spanish physicist Juan Parrondo has provided two stochastic losing games such that for certain stochastic combinations one may obtain a winning game. If a large number of players are involved and if they try to play such that their gain in the next round is maximized one arrives at the problem of investigating a random walk on a certain space of measures.The appropriate abstract setting is as follows. There is given a compact metric space (M,d), and M is written as the union of certain closed subsets A₁,…,A_r. For every ρ=1,…,r there is prescribed a strict contraction Γ_ρ:A_ρ→M. A random walk (X_m)_m∈N0 on M is then defined as follows. The starting position is X₀=x₀, where x₀∈M is fixed, and if the walk at the m’th step is at position X_m∈M, then one chooses a ρ among the ρ with X_m∈A_ρ (with equal probability, say) and defines X_m+1 as Γ_ρ(X_m). Associated with the walk is a gainφ(X_m) in every round, where φ:M→R is a continuous function.The aim of the present investigations is the study of the expectation G_m of φ(X_m) as a function of m. Our main result states that the sequence (G_m) is “eventually approximately periodic” provided that all A_ρ are not only closed but also open in M: for every ε there is an l₀∈N such that (G_m) is l₀-periodic up to an error of at most ε for sufficiently large m. In fact it turns out that the behaviour of our process can be described well with a finite Markov chain.In the general case, however, the process might behave rather chaotically. We give an example where M is the unit interval. M is written as the union of two closed subsets A₁,A₂, the contractions Γ₁,Γ₂ are rather simple, but the expectations of the gains are not even Cesáro convergent.     

Finite width effect on the upper critical field Hc2 of superconducting networks

A recent prediction for the continuum limit of the upper critical field of infinite superconducting networks H_c2(T)= dH^(bulk)_c2 (d=spatial dimension of the network) is checked experimentally. A direct comparison of the measured critical fields on both samples: film and infinite 2D regular networks, made of the same material, support strongly this theoretical prediction. The deviation of the proportionality coefficient from d=2 is attributed to the finite width of wires. Wires of finite width are shown to be responsible for a renormalization of the diffusion coefficient of Cooper pairs. The expression so obtained for H_c2 as a function of the filling factor is consistent with the measured value.     

Fluid–fluid phase equilibria in disordered porous media. Nonadditive hard sphere mixture

We report a computer simulation and integral equation study of fluid–fluid phase equilibria of nonadditive hard sphere binary mixture adsorbed in disordered hard sphere matrix. The mixture exhibits phase separation with critical density ρ_c^f lower than its bulk counterpart. It is found that ρ_c^f decreases with increasing both porosity and nonadditivity parameter.