Ghost points in inverse scattering constructions of stationary Einstein metrics

We prove a removable singularities theorem for stationary Einstein equations, with useful implications for constructions of stationary solutions using soliton methods

Doping effect on the anomalous behavior of the Hall effect in electron-doped superconductor Nd2−x_{2-x}Cex_xCuO4+δ_{4+\delta}

Transport properties of Nd$_{2-x}$Ce$_x$CuO$_{4+\delta}$ single crystal films are investigated in magnetic fields $B$ up to 9T at $T$=(0.4-4.2)K. An analysis of normal state (at $B>B_{c2}$) Hall coefficient $R_H$$^n$ dependence on Ce doping takes us to a conclusion about the existence both of electron-like and hole-like contributions to transport in nominally electron-doped system. In accordance with $R_H$$^n$(x) analysis an anomalous sign reversal of Hall effect in mixed state at $B<B_{c2}$ may be ascribed to a flux-flow regime for two types of carriers with opposite charges.Comment: 14 pages, 5 figure

Transformation of in-plane ρ(T)\rho (T) in YBa2Cu3O7−δYBa_{2}Cu_{3}O_{7-\delta} at fixed oxygen content

This paper reveals the origin of variation in the magnitude and temperature dependence of the normal state resistivity frequently observed in different YBCO single crystal or thin film samples with the same $T_{c}$. We investigated temperature dependence of resistivity in $YBa_{2}Cu_{3}O_{7-\delta}$ thin films with 7- $\delta = 6.95$ and 6.90, which were subjected to annealing in argon at 400-420 K ($120-140^{o}C$). Before annealing these films exhibited a non-linear $\rho_{ab}(T)$, with a flattening below 230 K, similar to $\rho_{b}(T)$ and $\rho_{ab}(T)$ observed in untwinned and twinned YBCO crystals, respectively. For all films the annealing causes an increase of resistivity and a transformation of $\rho_{ab}(T)$ from a non-linear dependence towards a more linear one (less flattening). In films with 7- $\delta = 6.90$ the increase of resistivity is also associated with an increase in $T_{c}$. We proposed the model that provides an explanation of these phenomena in terms of thermally activated redistribution of residual O(5) oxygens in the chain-layer of YBCO. Good agreement between the experimental data for $\rho_{ab}(t,T)$, where t is the annealing time, and numerical calculations was obtained.Comment: 8 pages, 9 figures, submitted to PR

Anisotropic Scaling in Threshold Critical Dynamics of Driven Directed Lines

The dynamical critical behavior of a single directed line driven in a random medium near the depinning threshold is studied both analytically (by renormalization group) and numerically, in the context of a Flux Line in a Type-II superconductor with a bulk current $\vec J$. In the absence of transverse fluctuations, the system reduces to recently studied models of interface depinning. In most cases, the presence of transverse fluctuations are found not to influence the critical exponents that describe longitudinal correlations. For a manifold with $d=4-\epsilon$ internal dimensions, longitudinal fluctuations in an isotropic medium are described by a roughness exponent $\zeta_\parallel=\epsilon/3$ to all orders in $\epsilon$, and a dynamical exponent $z_\parallel=2-2\epsilon/9+O(\epsilon^2)$. Transverse fluctuations have a distinct and smaller roughness exponent $\zeta_\perp=\zeta_\parallel-d/2$ for an isotropic medium. Furthermore, their relaxation is much slower, characterized by a dynamical exponent $z_\perp=z_\parallel+1/\nu$, where $\nu=1/(2-\zeta_\parallel)$ is the correlation length exponent. The predicted exponents agree well with numerical results for a flux line in three dimensions. As in the case of interface depinning models, anisotropy leads to additional universality classes. A nonzero Hall angle, which has no analogue in the interface models, also affects the critical behavior.Comment: 26 pages, 8 Postscript figures packed together with RevTeX 3.0 manuscript using uufiles, uses multicol.sty and epsf.sty, e-mail [email protected] in case of problem

Superconducting fluctuations and the Nernst effect: A diagrammatic approach

We calculate the contribution of superconducting fluctuations above the critical temperature $T_c$ to the transverse thermoelectric response $\alpha_{xy}$, the quantity central to the analysis of the Nernst effect. The calculation is carried out within the microscopic picture of BCS, and to linear order in magnetic field. We find that as $T \to T_c$, the dominant contribution to $\alpha_{xy}$ arises from the Aslamazov-Larkin diagrams, and is equal to the result previously obtained from a stochastic time-dependent Ginzburg-Landau equation [Ussishkin, Sondhi, and Huse, arXiv:cond-mat/0204484]. We present an argument which establishes this correspondence for the heat current. Other microscopic contributions, which generalize the Maki-Thompson and density of states terms for the conductivity, are less divergent as $T \to T_c$.Comment: 11 pages, 5 figure

Meissner effect, Spin Meissner effect and charge expulsion in superconductors

The Meissner effect and the Spin Meissner effect are the spontaneous generation of charge and spin current respectively near the surface of a metal making a transition to the superconducting state. The Meissner effect is well known but, I argue, not explained by the conventional theory, the Spin Meissner effect has yet to be detected. I propose that both effects take place in all superconductors, the first one in the presence of an applied magnetostatic field, the second one even in the absence of applied external fields. Both effects can be understood under the assumption that electrons expand their orbits and thereby lower their quantum kinetic energy in the transition to superconductivity. Associated with this process, the metal expels negative charge from the interior to the surface and an electric field is generated in the interior. The resulting charge current can be understood as arising from the magnetic Lorentz force on radially outgoing electrons, and the resulting spin current can be understood as arising from a spin Hall effect originating in the Rashba-like coupling of the electron magnetic moment to the internal electric field. The associated electrodynamics is qualitatively different from London electrodynamics, yet can be described by a small modification of the conventional London equations. The stability of the superconducting state and its macroscopic phase coherence hinge on the fact that the orbital angular momentum of the carriers of the spin current is found to be exactly $\hbar/2$, indicating a topological origin. The simplicity and universality of our theory argue for its validity, and the occurrence of superconductivity in many classes of materials can be understood within our theory.Comment: Submitted to SLAFES XX Proceeding

Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory

We study quartic matrix models with partition function Z[E,J]=\int dM \exp(trace(JM-EM^2-(\lambda/4)M^4)). The integral is over the space of Hermitean NxN-matrices, the external matrix E encodes the dynamics, \lambda>0 is a scalar coupling constant and the matrix J is used to generate correlation functions. For E not a multiple of the identity matrix, we prove a universal algebraic recursion formula which gives all higher correlation functions in terms of the 2-point function and the distinct eigenvalues of E. The 2-point function itself satisfies a closed non-linear equation which must be solved case by case for given E. These results imply that if the 2-point function of a quartic matrix model is renormalisable by mass and wavefunction renormalisation, then the entire model is renormalisable and has vanishing \beta-function. As main application we prove that Euclidean \phi^4-quantum field theory on four-dimensional Moyal space with harmonic propagation, taken at its self-duality point and in the infinite volume limit, is exactly solvable and non-trivial. This model is a quartic matrix model, where E has for N->\infty the same spectrum as the Laplace operator in 4 dimensions. Using the theory of singular integral equations of Carleman type we compute (for N->\infty and after renormalisation of E,\lambda) the free energy density (1/volume)\log(Z[E,J]/Z[E,0]) exactly in terms of the solution of a non-linear integral equation. Existence of a solution is proved via the Schauder fixed point theorem. The derivation of the non-linear integral equation relies on an assumption which we verified numerically for coupling constants 0<\lambda\leq (1/\pi).Comment: LaTeX, 64 pages, xypic figures. v4: We prove that recursion formulae and vanishing of \beta-function hold for general quartic matrix models. v3: We add the existence proof for a solution of the non-linear integral equation. A rescaling of matrix indices was necessary. v2: We provide Schwinger-Dyson equations for all correlation functions and prove an algebraic recursion formula for their solutio

Theoretical description of phase coexistence in model C60

We have investigated the phase diagram of the Girifalco model of C60 fullerene in the framework provided by the MHNC and the SCOZA liquid state theories, and by a Perturbation Theory (PT), for the free energy of the solid phase. We present an extended assessment of such theories as set against a recent Monte Carlo study of the same model [D. Costa et al, J. Chem. Phys. 118:304 (2003)]. We have compared the theoretical predictions with the corresponding simulation results for several thermodynamic properties. Then we have determined the phase diagram of the model, by using either the SCOZA, or the MHNC, or the PT predictions for one of the coexisting phases, and the simulation data for the other phase, in order to separately ascertain the accuracy of each theory. It turns out that the overall appearance of the phase portrait is reproduced fairly well by all theories, with remarkable accuracy as for the melting line and the solid-vapor equilibrium. The MHNC and SCOZA results for the liquid-vapor coexistence, as well as for the corresponding critical points, are quite accurate. All results are discussed in terms of the basic assumptions underlying each theory. We have selected the MHNC for the fluid and the first-order PT for the solid phase, as the most accurate tools to investigate the phase behavior of the model in terms of purely theoretical approaches. The overall results appear as a robust benchmark for further theoretical investigations on higher order C(n>60) fullerenes, as well as on other fullerene-related materials, whose description can be based on a modelization similar to that adopted in this work.Comment: RevTeX4, 15 pages, 7 figures; submitted to Phys. Rev.

Non-monotonic variation with salt concentration of the second virial coefficient in protein solutions

The osmotic virial coefficient $B_2$ of globular protein solutions is calculated as a function of added salt concentration at fixed pH by computer simulations of the ``primitive model''. The salt and counter-ions as well as a discrete charge pattern on the protein surface are explicitly incorporated. For parameters roughly corresponding to lysozyme, we find that $B_2$ first decreases with added salt concentration up to a threshold concentration, then increases to a maximum, and then decreases again upon further raising the ionic strength. Our studies demonstrate that the existence of a discrete charge pattern on the protein surface profoundly influences the effective interactions and that non-linear Poisson Boltzmann and Derjaguin-Landau-Verwey-Overbeek (DLVO) theory fail for large ionic strength. The observed non-monotonicity of $B_2$ is compared to experiments. Implications for protein crystallization are discussed.Comment: 43 pages, including 17 figure

From dynamical scaling to local scale-invariance: a tutorial

Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced. Schr\"odinger-invariance, the most simple example of local scale-invariance, will be introduced as a dynamical symmetry in the Edwards-Wilkinson universality class of interface growth. The Lie algebra construction, its representations and the Bargman superselection rules will be combined with non-equilibrium Janssen-de Dominicis field-theory to produce explicit predictions for responses and correlators, which can be compared to the results of explicit model studies. At the next level, the study of non-stationary states requires to go over, from Schr\"odinger-invariance, to ageing-invariance. The ageing algebra admits new representations, which acts as dynamical symmetries on more general equations, and imply that each non-equilibrium scaling operator is characterised by two distinct, independent scaling dimensions. Tests of ageing-invariance are described, in the Glauber-Ising and spherical models of a phase-ordering ferromagnet and the Arcetri model of interface growth.Comment: 1+ 23 pages, 2 figures, final for