Defect production in nonlinear quench across a quantum critical point

We show that the defect density n, for a slow nonlinear power-law quench with a rate tau(-1) and an exponent alpha>0, which takes the system through a critical point characterized by correlation length and dynamical critical exponents nu and z, scales as n approximately tau(-alphanud/(alphaznu+1)) [n approximately (alphag((alpha-1)/alpha)/tau)(nud/(znu+1))] if the quench takes the system across the critical point at time t=0 [t=t(0) not = 0], where g is a nonuniversal constant and d is the system dimension. These scaling laws constitute the first theoretical results for defect production in nonlinear quenches across quantum critical points and reproduce their well-known counterpart for a linear quench (alpha=1) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.     

Effect of Polydispersity on the Phase Behavior of Polystyrene (PS)/Poly (Vinyl Methyl Ether) (PVME)

The thermodynamics and kinetics of phase separation in partially miscible blends of poly (vinyl methyl ether) (PVME) and two kinds of polystyrene (PS) with the same weight average molecular weight but different polydispersity were studied. The miscibility of PS/PVME with the monodisperse PS was better than that of PS/PVME with the polydisperse PS. Different morphology was observed for the two kinds of PS/PVME (10/90) blends during the nonisothermal phase separation process. The blend with monodisperse PS presented a co-continuous structure while the blend with polydisperse PS presented a viscoelastic phase separated network structure at a quench depth of 29°C. With increase of the heating rate, the increase of cloud point of PS/PVME (30/70) with polydisperse PS was smaller than that of PS/PVME (30/70) with monodisperse PS. During the isothermal phase separation of the critical composition (20/80) of PS/PVME with a quench depth of 30°C, it was found that the phase morphology of the two kinds of blends was nearly the same at the early stage of phase separation. However, as the dispersed phase, an approximately spherical droplet structure was observed in the blend with monodisperse PS at the late stage of phase separation, which did not appear in the blend with polydisperse PS.     

Theorem on the origin of phase transitions

For physical systems described by smooth, finite-range, and confining microscopic interaction potentials V with continuously varying coordinates, we announce and outline the proof of a theorem that establishes that, unless the equipotential hypersurfaces of configuration space Sum(v)=[(q(1),...,q(N)) subset R(N)/V(q(1),...,q(N))=v], v subset R, change topology at some v(c) in a given interval [v(0),v(1)] of values v of V, the Helmoltz free energy must be at least twice differentiable in the corresponding interval of inverse temperature (beta(v(0)),beta(v(1))) also in the N--> infinity limit. Thus, the occurrence of a phase transition at some beta(c)=beta(v(c)) is necessarily the consequence of the loss of diffeomorphicity among the [Sigma(v)](vv(c)), which is the consequence of the existence of critical points of V on Sigma(v=v(c)), that is, points where inverted Delta V=0.     

Griffiths-McCoy singularities in random quantum spin chains: exact results through renormalization

The Ma-Dasgupta-Hu renormalization group (RG) scheme is used to study singular quantities in the Griffiths phase of random quantum spin chains. For the random transverse-field Ising spin chain we have extended Fisher's analytical solution to the off-critical region and calculated the dynamical exponent exactly. Concerning other random chains we argue by scaling considerations that the RG method generally becomes asymptotically exact for large times, both at the critical point and in the whole Griffiths phase. This statement is checked via numerical calculations on the random Heisenberg and quantum Potts models by the density matrix renormalization group method.     

Comparative study of the critical behavior in one-dimensional random and aperiodic environments

We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents . At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as . Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of , whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities. Received: 5 February 1998 / Accepted: 17 April 1998     

Critical amplitude ratios of the Baxter–Wu model

A Monte Carlo simulation study of the critical and off-critical behavior of the Baxter–Wu model, which belongs to the universality class of the 4-state Potts model, was performed. We estimate the critical temperature window using known analytical results for the specific heat and magnetization. This helps us to extract reliable values of universal combinations of critical amplitudes with reasonable accuracy. Comparisons with approximate analytical predictions and other numerical results are discussed.     

Equilibrium Pure States and Nonequilibrium Chaos

We consider nonequilibrium systems such as the Edwards–Anderson Ising spin glass at a temperature where, in equilibrium, there are presumed to be (two or many) broken-symmetry pure states. Following a deep quench, we argue that as time t, although the system is usually in some pure state locally, either it never settles permanently on a fixed length scale into a single pure state, or it does, but then the pure state depends on both the initial spin configuration and the realization of the stochastic dynamics. But this latter case can occur only if there exists an uncountable number of pure states (for each coupling realization) with almost every pair having zero overlap. In both cases, almost no initial spin configuration is in the basin of attraction of a single pure state; that is, the configuration space (resulting from a deep quench) is all boundary (except for a set of measure zero). We prove that the former case holds for deeply quenched 2D ferromagnets. Our results raise the possibility that even if more than one pure state exists for an infinite system, time averages do not necessarily disagree with Boltzmann averages.     

Der Einfluss der Metallbedeckung auf die Supraleitenden Eigenschaften von Dünnen Zylindern

The critical parameters (upper critical field, critical temperature) of a thin type II superconducting cylinders are considerably changed by coating with normal metal. Below a minimum cylinder radius, the superconductivity can no longer exist. The oscillations of the critical temperature with magnetic field are also modified. For good conductive metals, only an aperiodic effect appears. The decrease of the critical temperature produced by coating is given. The thin-film quantization effects the existence of jumps in the field dependence of the critical temperature.     

Unusual Phase Separation Kinetics in Poly(Methyl Methacrylate)/Poly(Styrene-co-Acrylonitrile) (PMMA/SAN) Blends with PMMA of Different Molecular Weights

The influence of molecular weight of poly (methyl methacrylate) (PMMA) on the thermodynamics and dynamics of phase separation in PMMA/poly (styrene-co-acrylonitrile) (SAN) blends was investigated via optical microscopy, time-resolved small-angle light scattering (SALS), and dynamic rheological measurements. It was found that the cloud point temperature of the blends decreased with an increase in the molecular weight of the PMMA. The phase separation rates of PMMA 48K/SAN and PMMA 85K/SAN blends with the near-critical composition were almost the same at small quench depths due to the limited mobility of molecular chains at low temperatures. However, an unexpected phase separation dynamics was observed at larger quench depths. Not only the morphology evolution but also the apparent diffusion coefficient D_app calculated from SALS revealed that the phase separation rate was faster in the PMMA 85K/SAN blend than in the PMMA 48K/SAN blend. The possible reasons for this unusual rapid kinetics of phase separation observed in the higher molecular weight blend were discussed in terms of molecular mobility and viscoelasticity.     

Criticality in a non-equilibrium,driven system: Charged colloidal rods (fd-viruses) in electric fields

Experiments on suspensions of charged colloidal rods (fd-virus particles) in external electric fields are performed, which show that a non-equilibrium critical point can be identified. Several transition lines of field-induced phases and states meet at this point and it is shown that there is a length- and time-scale which diverge at the non-equilibrium critical point. The off-critical and critical behavior is characterized, with both power law and logarithmic divergencies. These experiments show that analogous features of the classical, critical divergence of correlation lengths and relaxation times in equilibrium systems are also exhibited by driven systems that are far out of equilibrium, related to phases/states that do not exist in the absence of the external field.     

Growth kinetics in multicomponent fluids

The hydrodynamic effects on the late-stage kinetics in spinodal decomposition of multicomponent fluids are examined using a lattice Boltzmann scheme with stochastic fluctuations in the fluid and at the interface. In two dimensions, the three- and four-component immiscible fluid mixture (with a 1024² lattice) behaves like an off-critical binary fluid with an estimated domain growth oft ^0.4±0.03 rather thant ^1/3 as previously estimated, showing the significant influence of hydrodynamics. In three dimensions (with a 256³ lattice), we estimate the growth ast ^0.96±0.05 for both critical and off-critical quenches, in agreement with phenomenological theory.     

Black-hole singularities: a new critical phenomenon

The singularity inside a spherical charged black hole, coupled to a spherical, massless scalar field is studied numerically. The profile of the characteristic scalar field was taken to be a power of advanced time with an exponent alpha>0. A critical exponent alpha(crit) exists. For exponents below the critical one (alphaalpha(crit)) an all-encompassing, spacelike singularity evolves, which completely blocks the "tunnel" inside the black hole, preventing the use of the black hole as a portal for hyperspace travel.     

Speckle correlations in the light scattered from a weakly rough one-dimensional random metal surface

Perturbation theory is used to compute the angular-intensity correlation function C(q, k|q(?), k(?)) = ?[I(q|k) - ?I(q|k)?][I(q(?)|k(?)) - ?I(q(?)|k(?))]? for p-polarized light scattered from a weakly rough, one-dimensional random metal surface. I(q|k) is the squared modulus of the scattering matrix for the system, and q , q(?) and k , k(?) are the projections on the mean scattering surface of the wave vectors of the scattered and the incident light, respectively. Contributions to C include (a) short-range memory effect and time-reversed memory effect terms, C((1)) ; (b) an additional short-range term of comparable magnitude C((10)) ; (c) a long-range term C((2)) ; (d) an infinite-range term C((3)) ; and (e) a new term C((1.5)) that along with C((2)) displays peaks associated with the excitation of surface polaritons. These new features arise when the factorization approximation is not made in calculating the correlation function C .     

Flat FRW models with variableG and Λ

We consider Einstein's equations with variable gravitational couplingG and cosmological term . For a power-law time-dependence ofG, the cosmological term varies in proportion to the inverse square of the time, provided the equation of state is not that of vacuum. There is then no dimensional constant associated with . For a vacuum equation of state the model is compatible with classical inflation for a wide class of functionsG(t) and (t). For non-power-law behaviour ofG(t), it is possible to have a scale factor that increases exponentially without a vacuum equation of state. For this case the energy density associated with decreases exponentially, while at time zero it is equal with opposite sign to the regular energy density, so there is zero total energy initially.     

Fields,particles and universality in two dimensions

We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical case, considering systems both on the whole plane and in presence of boundaries. The topics we discuss include magnetism, percolation, phase separation, interfaces, wetting.     

Influence of a continuous quenching procedure on the initial stages of spinodal decomposition

Instead of the standard assumption in the theory of phase separation where an instantaneous quench from an initial equilibrium state to the final state in the two-phase region is assumed, we consider the more realistic situation that the change of the external control parameter (e.g. temperature) can only be performed with finite rates. During the initial stages of spinodal decomposition the system then has some memory of the states intermediate between the initial and the final one. This influence of the finite quench rate in continuous quenching procedures is studied within the linearized theory of spinodal decomposition, with the Langer-Baron-Miller decoupling, and with Monte Carlo simulations. Both the case of thermally activated mobilities (applicable to solid metallic alloys) and the case of nearly temperature-independent mobilities (applicable to fluid polymer mixtures) are treated, and possible experimental applications are discussed. We find drastic deviations from the standard instantaneous quench situations in all cases of experimental interest.     

Pattern guided structure formation in polymer films of asymmetric blends

Two off-critical blends of poly(2-vinylpyridine) and polystyrene, 2:3 and 3:2 (w:w) PVP:PS, were spin-cast (with varied domain scale R) onto periodically (λ = 4 μm) patterned substrate. The pattern consisted of two alternating symmetric stripes: Au attracting PVP and neutral self-assembled monolayer. The resulting droplet-type morphologies were recorded with Scanning Force Microscopy and examined with integral geometry approach. PVP-rich islands of the 2:3 PVP:PS films form, for a wide R/λ range, strongly anisotropic morphologies. They show up, for R/λ ∼ 0.5, a weak λ/2-substructure of smaller PVP droplets in addition to the domains periodic with λ. The 3:2 blend exhibits morphologies with dominant λ-structure of PVP ribbons, which encircle PS droplets. For R/λ ∼ 0.5, smaller PS domains are also present but no λ/2-substructure is formed. The |χ_E|-values of droplet surface density are reduced, as compared to homogeneous substrate, for the 3:2 blend (with |χ_E| → 0 for R ∼ λ). This effect is absent for the 2:3 mixture.     

Continuously Varying Exponents in a Sandpile Model with Dissipation Near Surface

We consider the directed Abelian sandpile model in the presence of sink sites whose density f_t at depth t below the top surface varies as ct^–. For >1 the disorder is irrelevant. For <1, it is relevant and the model is no longer critical for any nonzero c. For =1 the exponents of the avalanche distributions depend continuously on the amplitude c of the disorder. We calculate this dependence exactly, and verify the results with simulations.     

Generation of suprathermal electrons during magnetic reconnection at the sawtooth crash and disruption instability in the T-10 tokamak

Evidence for excitation of suprathermal electrons ( E(gamma) approximately 20-100 keV) during magnetic reconnection in the T-10 tokamak is presented through analysis of the x-ray measurements with enhanced spatial and time resolution. A toroidally viewing x-ray imaging system and a fast hard x-ray detector placed inside the tokamak vessel allow identification of bursts of the nonthermal x-ray radiation around X points of the m = 1 and m = 2 magnetic islands during the sawtooth crash and prior to the energy quench at the density limit disruption.