Stability of Transonic Shock Solutions for One-Dimensional Euler-Poisson Equations

In this paper, both structural and dynamical stabilities of steady transonic shock solutions for one-dimensional Euler-Poission system are investigated. First, a steady transonic shock solution with supersonic backgroumd charge is shown to be structurally stable with respect to small perturbations of the background charge, provided that the electric field is positive at the shock location. Second, any steady transonic shock solution with the supersonic background charge is proved to be dynamically and exponentially stable with respect to small perturbation of the initial data, provided the electric field is not too negative at the shock location. The proof of the first stability result relies on a monotonicity argument for the shock position and the downstream density, and a stability analysis for subsonic and supersonic solutions. The dynamical stability of the steady transonic shock for the Euler-Poisson equations can be transformed to the global well-posedness of a free boundary problem for a quasilinear second order equation with nonlinear boundary conditions. The analysis for the associated linearized problem plays an essential role

A Hybrid Monte Carlo Method for Surface Growth Simulations

We introduce an algorithm for treating growth on surfaces which combines important features of continuum methods (such as the level-set method) and Kinetic Monte Carlo (KMC) simulations. We treat the motion of adatoms in continuum theory, but attach them to islands one atom at a time. The technique is borrowed from the Dielectric Breakdown Model. Our method allows us to give a realistic account of fluctuations in island shape, which is lacking in deterministic continuum treatments and which is an important physical effect. Our method should be most important for problems close to equilibrium where KMC becomes impractically slow.Comment: 4 pages, 5 figure

Doping dependence of the superconducting gap in Bi2Sr2CaCu2O{8 + delta}

Bi2Sr2CaCu2O{8 + \delta} crystals with varying hole concentrations (0.12 < p < 0.23) were studied to investigate the effects of doping on the symmetry and magnitude of the superconducting gap. Electronic Raman scattering experiments that sample regions of the Fermi surface near the diagonal (B_{2g}) and principal axes (B_{1g}) of the Brillouin Zone have been utilized. The frequency dependence of the Raman response function at low energies is found to be linear for B_{2g} and cubic for B_{1g} (T< T_c). The latter observations have led us to conclude that the doping dependence of the superconducting gap is consistent with d_{x^2-y^2} symmetry, for slightly underdoped and overdoped crystals. Studies of the pair-breaking peak found in the B_{1g} spectra demonstrate that the magnitude of the maximum gap decreases monotonically with increasing hole doping, for p > 0.12. Based on the magnitude of the B_{1g} renormalization, it is found that the number of quasiparticles participating in pairing increases monotonically with increased doping. On the other hand, the B_{2g} spectra show a weak "pair-breaking peak" that follows a parabolic-like dependence on hole concentration, for 0.12 < p < 0.23.Comment: 9 pages REvTex document including 8 eps figures; new table II; changes to Fig. 5 and tex

Raman Scattering versus Infrared Conductivity: Evidence for one-dimensional Conduction in La_{2-x}Sr_{x}CuO_{4}

Raman and Infrared (IR) spectra of an underdoped La_{1.90}Sr_{0.10}CuO_{4} single crystal have been measured as a function of temperature. Both techniques provide unconventional low-energy spectra. The IR conductivity exhibits features peaked at finite frequencies which do not have a counterpart in the Raman response. Below approximately 100 K a transfer of both Raman and IR spectral weight towards lower energies is found and a new component in the Raman response builds up being characterized by a very long lifetime of electrons propagating along the Cu-O bonds.Comment: 4 pages, 3 eps figure

Cosmological perturbations in a healthy extension of Horava gravity

In Horava's theory of gravity, Lorentz symmetry is broken in exchange for renormalizability, but the original theory has been argued to be plagued with problems associated with a new scalar mode stemming from the very breaking of Lorentz symmetry. Recently, Blas, Pujolas, and Sibiryakov have proposed a healthy extension of Horava gravity, in which the behavior of the scalar mode is improved. In this paper, we study scalar modes of cosmological perturbations in extended Horava gravity. The evolution of metric and density perturbations is addressed analytically and numerically. It is shown that for vanishing non-adiabatic pressure of matter the large scale evolution of cosmological perturbations converges to that described by a single constant, $\zeta$, which is an analog of a curvature perturbation on the uniform-density slicing commonly used in usual gravitational theories. The subsequent evolution is thus determined completely by the value of $\zeta$.Comment: 10 pages, 4 figures; v2: published versio

Extremal black holes in the Ho\v{r}ava-Lifshitz gravity

We study the near-horizon geometry of extremal black holes in the $z=3$ Ho\v{r}ava-Lifshitz gravity with a flow parameter $\lambda$. For $\lambda>1/2$, near-horizon geometry of extremal black holes are AdS$_2 \times S^2$ with different radii, depending on the (modified) Ho\v{r}ava-Lifshitz gravity. For $1/3\le \lambda \le 1/2$, the radius $v_2$ of $S^2$ is negative, which means that the near-horizon geometry is ill-defined and the corresponding Bekenstein-Hawking entropy is zero. We show explicitly that the entropy function approach does not work for obtaining the Bekenstein-Hawking entropy of extremal black holes.Comment: 18 pages, v2:some points on Lifshitz black holes claified, v3: version to appear in EJP

Interplay of structural and electronic phase separation in single crystalline La(2)CuO(4.05) studied by neutron and Raman scattering

We report a neutron and Raman scattering study of a single-crystal of La(2)CuO(4.05) prepared by high temperature electrochemical oxidation. Elastic neutron scattering measurements show the presence of two phases, corresponding to the two edges of the first miscibility gap, all the way up to 300 K. An additional oxygen redistribution, driven by electronic energies, is identified at 250 K in Raman scattering (RS) experiments by the simultaneous onset of two-phonon and two-magnon scattering, which are fingerprints of the insulating phase. Elastic neutron scattering measurements show directly an antiferromagnetic ordering below a N\'eel temperature of T_N =210K. The opening of the superconducting gap manifests itself as a redistribution of electronic Raman scattering below the superconducting transition temperature, T_c = 24K. A pronounced temperature-dependent suppression of the intensity of the (100) magnetic Bragg peak has been detected below T_c. We ascribe this phenomenon to a change of relative volume fraction of superconducting and antiferromagnetic phases with decreasing temperature caused by a form of a superconducting proximity effect.Comment: 9 pages, including 9 eps figures, submitted to PR

Electrochemical capacitance of a leaky nano-capacitor

We report a detailed theoretical investigation on electrochemical capacitance of a nanoscale capacitor where there is a DC coupling between the two conductors. For this ``leaky'' quantum capacitor, we have derived general analytic expressions of the linear and second order nonlinear electrochemical capacitance within a first principles quantum theory in the discrete potential approximation. Linear and nonlinear capacitance coefficients are also derived in a self-consistent manner without the latter approximation and the self-consistent analysis is suitable for numerical calculations. At linear order, the full quantum formula improves the semiclassical analysis in the tunneling regime. At nonlinear order which has not been studied before for leaky capacitors, the nonlinear capacitance and nonlinear nonequilibrium charge show interesting behavior. Our theory allows the investigation of crossover of capacitance from a full quantum to classical regimes as the distance between the two conductors is changed

Raman light scattering study and microstructural analysis of epitaxial films of the electron-doped superconductor La_{2-x}Ce_{x}CuO_{4}

We present a detailed temperature-dependent Raman light scattering study of optical phonons in molecular-beam-epitaxy-grown films of the electron-doped superconductor La_{2-x}Ce_{x}CuO_{4} close to optimal doping (x ~ 0.08, T_c = 29 K and x ~ 0.1, T_c = 27 K). The main focus of this work is a detailed characterization and microstructural analysis of the films. Based on micro-Raman spectroscopy in combination with x-ray diffraction, energy-dispersive x-ray analysis, and scanning electron microscopy, some of the observed phonon modes can be attributed to micron-sized inclusions of Cu_{2}O. In the slightly underdoped film (x ~ 0.08), both the Cu_{2}O modes and others that can be assigned to the La_{2-x}Ce_{x}CuO_{4} matrix show pronounced softening and narrowing upon cooling below T ~ T_c. Based on control measurements on commercial Cu_{2}O powders and on a comparison to prior Raman scattering studies of other high-temperature superconductors, we speculate that proximity effects at La_{2-x}Ce_{x}CuO_{4}/Cu_{2}O interfaces may be responsible for these anomalies. Experiments on the slightly overdoped La_{2-x}Ce_{x}CuO_{4} film (x ~ 0.1) did not reveal comparable phonon anomalies.Comment: 7 pages, 8 figure

Anomalous Self-Energy Effects of the B_1g Phonon in Y_{1-x}(Pr,Ca)_xBa_2Cu_3O_7 Films

In Raman spectra of cuprate superconductors the gap shows up both directly, via a redistribution of the electronic background, the so-called "2Delta peaks", and indirectly, e.g. via the renormalization of phononic excitations. We use a model that allows us to study the redistribution and the related phonon self-energy effects simultaneously. We apply this model to the B_1g phonon of Y_{1-x}(Pr,Ca)_xBa_2Cu_3O_7 films, where Pr or Ca substitution enables us to investigate under- and overdoped samples. While various self-energy effects can be explained by the strength and energy of the 2\Delta peaks, anomalies remain. We discuss possible origins of these anomalies.Comment: 6 pages including 4 figure