A Simple Passive Scalar Advection-Diffusion Model

This paper presents a simple, one-dimensional model of a randomly advected passive scalar. The model exhibits anomalous inertial range scaling for the structure functions constructed from scalar differences. The model provides a simple computational test for recent ideas regarding closure and scaling for randomly advected passive scalars. Results suggest that high order structure function scaling depends on the largest velocity eddy size, and hence scaling exponents may be geometry-dependent and non-universal.Comment: 30 pages, 11 figure

Dynamics of Scalar Fields in the Background of Rotating Black Holes

A numerical study of the evolution of a massless scalar field in the background of rotating black holes is presented. First, solutions to the wave equation are obtained for slowly rotating black holes. In this approximation, the background geometry is treated as a perturbed Schwarzschild spacetime with the angular momentum per unit mass playing the role of a perturbative parameter. To first order in the angular momentum of the black hole, the scalar wave equation yields two coupled one-dimensional evolution equations for a function representing the scalar field in the Schwarzschild background and a second field that accounts for the rotation. Solutions to the wave equation are also obtained for rapidly rotating black holes. In this case, the wave equation does not admit complete separation of variables and yields a two-dimensional evolution equation. The study shows that, for rotating black holes, the late time dynamics of a massless scalar field exhibit the same power-law behavior as in the case of a Schwarzschild background independently of the angular momentum of the black hole.Comment: 14 pages, RevTex, 6 Figure

Wave Propagation in Gravitational Systems: Completeness of Quasinormal Modes

The dynamics of relativistic stars and black holes are often studied in terms of the quasinormal modes (QNM's) of the Klein-Gordon (KG) equation with different effective potentials $V(x)$. In this paper we present a systematic study of the relation between the structure of the QNM's of the KG equation and the form of $V(x)$. In particular, we determine the requirements on $V(x)$ in order for the QNM's to form complete sets, and discuss in what sense they form complete sets. Among other implications, this study opens up the possibility of using QNM expansions to analyse the behavior of waves in relativistic systems, even for systems whose QNM's do {\it not} form a complete set. For such systems, we show that a complete set of QNM's can often be obtained by introducing an infinitesimal change in the effective potential

High-temperature phase transitions in SrBi_2Ta_2O_9 film: a study by THz spectroscopy

Time-domain THz transmission experiment was performed on a $\rm SrBi_2Ta_2O_9$ film deposited on sapphire substrate. Temperatures between 300 and 923 K were investigated and complex permittivity spectra of the film were determined. The lowest frequency optic phonon near 28 cm$^{-1}$ reveals a slow monotonic decrease in frequency on heating with no significant anomaly near the phase transitions. We show that the dielectric anomaly near the ferroelectric phase transition can be explained by slowing down of a relaxational mode, observed in the THz spectra. A second harmonic generation signal observed in a single crystal confirms a loss of center of symmetry in the ferroelectric phase and a presence of polar clusters in the intermediate ferroelastic phase.Comment: subm. to J. Phys.: Condens. Matte

Quasi-Normal Mode Expansion for Linearized Waves in Gravitational Systems

The quasinormal modes (QNM's) of gravitational systems modeled by the Klein-Gordon equation with effective potentials are studied in analogy to the QNM's of optical cavities. Conditions are given for the QNM's to form a complete set, i.e., for the Green's function to be expressible as a sum over QNM's, answering a conjecture by Price and Husain [Phys. Rev. Lett. {\bf 68}, 1973 (1992)]. In the cases where the QNM sum is divergent, procedures for regularization are given. The crucial condition for completeness is the existence of spatial discontinuities in the system, e.g., the discontinuity at the stellar surface in the model of Price and Husain.Comment: 12 pages, WUGRAV-94-

Pressure-induced polarization reversal in multiferroic YMn2O5YMn_2O_5

The low-temperature ferroelectric polarization of multiferroic $YMn_2O_5$ is completely reversed at a critical pressure of 10 kbar and the phase transition from the incommensurate to the commensurate magnetic phase is induced by pressures above 14 kbar. The high-pressure data correlate with thermal expansion measurements indicating a significant lattice strain at the low-temperature transition into the incommensurate phase. The results support the exchange striction model for the ferroelectricity in multiferroic $RMn_2O_5$ compounds and they show the importance of magnetic frustration as well as the spin-lattice coupling

Wave Propagation in Gravitational Systems: Late Time Behavior

It is well-known that the dominant late time behavior of waves propagating on a Schwarzschild spacetime is a power-law tail; tails for other spacetimes have also been studied. This paper presents a systematic treatment of the tail phenomenon for a broad class of models via a Green's function formalism and establishes the following. (i) The tail is governed by a cut of the frequency Green's function $\tilde G(\omega)$ along the $-$~Im~$\omega$ axis, generalizing the Schwarzschild result. (ii) The $\omega$ dependence of the cut is determined by the asymptotic but not the local structure of space. In particular it is independent of the presence of a horizon, and has the same form for the case of a star as well. (iii) Depending on the spatial asymptotics, the late time decay is not necessarily a power law in time. The Schwarzschild case with a power-law tail is exceptional among the class of the potentials having a logarithmic spatial dependence. (iv) Both the amplitude and the time dependence of the tail for a broad class of models are obtained analytically. (v) The analytical results are in perfect agreement with numerical calculations

Perturbative Approach to the Quasinormal Modes of Dirty Black Holes

Using a recently developed perturbation theory for uasinormal modes (QNM's), we evaluate the shifts in the real and imaginary parts of the QNM frequencies due to a quasi-static perturbation of the black hole spacetime. We show the perturbed QNM spectrum of a black hole can have interesting features using a simple model based on the scalar wave equation.Comment: Published in PR

Dispersion Interactions between Optically Anisotropic Cylinders at all Separations: Retardation Effects for Insulating and Semiconducting Single Wall Carbon Nanotubes

We derive the complete form of the van der Waals dispersion interaction between two infinitely long anisotropic semiconducting/insulating thin cylinders at all separations. The derivation is based on the general theory of dispersion interactions between anisotropic media as formulated in [J. N. Munday, D. Iannuzzi, Yu. S. Barash and F. Capasso, {\sl Phys. Rev. A} {\bf 71}, 042102 (2005)]. This formulation is then used to calculate the dispersion interactions between a pair of single walled carbon nanotubes at all separations and all angles. Non-retarded and retarded forms of the interactions are developed separately. The possibility of repulsive dispersion interactions and non-monotonic dispersion interactions is discussed within the framework of the new formulation

Exactly solvable path integral for open cavities in terms of quasinormal modes

We evaluate the finite-temperature Euclidean phase-space path integral for the generating functional of a scalar field inside a leaky cavity. Provided the source is confined to the cavity, one can first of all integrate out the fields on the outside to obtain an effective action for the cavity alone. Subsequently, one uses an expansion of the cavity field in terms of its quasinormal modes (QNMs)-the exact, exponentially damped eigenstates of the classical evolution operator, which previously have been shown to be complete for a large class of models. Dissipation causes the effective cavity action to be nondiagonal in the QNM basis. The inversion of this action matrix inherent in the Gaussian path integral to obtain the generating functional is therefore nontrivial, but can be accomplished by invoking a novel QNM sum rule. The results are consistent with those obtained previously using canonical quantization.Comment: REVTeX, 26 pages, submitted to Phys. Rev.