Evolution of nonlinear cosmological perturbations

We define fully nonperturbative generalizations of the uniform density and comoving curvature perturbations, which are known, in the linear theory, to be conserved on sufficiently large scales for adiabatic perturbations. Our nonlinear generalizations are defined geometrically, independently of any coordinate system. We give the equations governing their evolution on all scales. Also, in order to make contact with previous works on first- and second-order perturbations, we introduce a coordinate system and show that previous results can be recovered, on large scales, in a remarkably simple way, after restricting our definitions to first and second orders in a perturbative expansion.     

Gravitational perturbations of spherically symmetric systems. II. Perfect fluid interiors

Methods developed in a previous paper on perturbations of the Schwarzschild metric are here extended to the treatment of perturbations of perfect fluid stellar models. The perturbations of a perfect fluid sphere are explicitly decomposed into their gauge invariant and gauge dependent parts and a variational principle for the perturbation equations is derived. The Hamiltonian for the perturbations is constructed and a sufficient condition for stability against nonradial, radiative perturbations is derived from it. The stability criterion is applied to two interesting classes of stellar models, polytropic white dwarf models and high-density neutron star cores with pressure proportional to energy density.     

Maintenance and suppression of chaos by weak harmonic perturbations: a unified view

General results concerning maintenance or enhancement of chaos are presented for dissipative systems subjected to two harmonic perturbations (one chaos inducing and the other chaos enhancing). The connection with previous results on chaos suppression is also discussed in a general setting. It is demonstrated that, in general, a second harmonic perturbation can reliably play an enhancer or inhibitor role by solely adjusting its initial phase. Numerical results indicate that general theoretical findings concerning periodic chaos-inducing perturbations also work for aperiodic chaos-inducing perturbations, and in arrays of identical chaotic coupled oscillators.     

A planar perturbation of the Bianchi type I metric

The standard procedure for finding analytic perturbations in General Relativity suffers from the drawback that it is cumbersome to use beyond linear order perturbations. Following up on our previous work, we continue to use an alternate method of finding perturbations. We find a plane symmetric perturbation of the cosmological Bianchi type I metric. The perturbation corresponds to a fluid with heat flow moving perpendicularly to a singular plane in a region which can be made to be either overdense or underdense relative to the background spacetime. The fluid satisfies both the Strong and Dominant energy conditions everywhere except the region close to the singularity.     

Analysis of forward scattering of diffuse photon-density waves in turbid media: a diffraction tomography approach to an analytic solution

We present a model of the forward problem for diffuse photon-density waves in a turbid medium containing a spherical inhomogeneity, using diffraction tomographic (DT) methods. Recently, by use of DT methods, the forward problem was investigated [Opt. Express 1, 6 (1997); www.osa.org] assuming weak perturbations from the background medium but an arbitrary inhomogeneity structure. We apply DT concepts to a forward problem solution that permits strong perturbations but requires a spherical inhomogeneity. We show that this model is consistent with previous DT results and discuss the application of this new model.     

Low-temperature spin-relaxation time in normal liquid 3He

We calculate the low-temperature (T ? T_F) spin-relaxation time T₁ in normal liquid ³He, expressed in terms of the perturbations of the scattering amplitudes due to nuclear dipole-dipole interactions. These perturbations are obtained using the induced interaction model, yielding good agreement with experiment, as well as with previous calculations.     

Adaptive auditory feedback control of the production of formant trajectories in the Mandarin triphthong /iau/ and its pattern of generalization

In order to test whether auditory feedback is involved in the planning of complex articulatory gestures in time-varying phonemes, the current study examined native Mandarin speakers' responses to auditory perturbations of their auditory feedback of the trajectory of the first formant frequency during their production of the triphthong /iau/. On average, subjects adaptively adjusted their productions to partially compensate for the perturbations in auditory feedback. This result indicates that auditory feedback control of speech movements is not restricted to quasi-static gestures in monophthongs as found in previous studies, but also extends to time-varying gestures. To probe the internal structure of the mechanisms of auditory-motor transformations, the pattern of generalization of the adaptation learned on the triphthong /iau/ to other vowels with different temporal and spatial characteristics (produced only under masking noise) was tested. A broad but weak pattern of generalization was observed; the strength of the generalization diminished with increasing dissimilarity from /iau/. The details and implications of the pattern of generalization are examined and discussed in light of previous sensorimotor adaptation studies of both speech and limb motor control and a neurocomputational model of speech motor control.     

A Non-Variational Approach to Nonlinear Stability in Stellar Dynamics Applied to the King Model

In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in stellar dynamics, i.e., of steady states of the Vlasov-Poisson system, was accessed by variational techniques. Here we propose a different, non-variational technique and use it to prove nonlinear stability of the King model against a class of spherically symmetric, dynamically accessible perturbations. This model is very important in astrophysics and was out of reach of the previous techniques.     

Dimensionally hybrid Green's functions for impurity scattering in the presence of interfaces

A previous calculation of Green's function (E-H)^-1 for an interface Hamiltonian which interpolates between two and three dimensions is generalized to include scattering from perturbations both on and off the interface.     

Global stability of large solutions to the 3D Navier-Stokes equations

We prove the stability of mildly decaying global strong solutions to the Navier-Stokes equations in three space dimensions. Combined with previous results on the global existence of large solutions with various symmetries, this gives the first global existence theorem for large solutions with approximately symmetric initial data. The stability of unforced 2D flow under 3D perturbations is also obtained.     

Excitation cross sections of the <Superscript>1</Superscript><Emphasis Type="Italic">S</Emphasis>and <Superscript>1</Superscript><Emphasis Type="Italic">P</Emphasis>° Levels of a Sr atom in electron-Sr atom collisions

The excitation of the singlet S and P° levels of a Sr atom from the ground state by slow electrons was studied by the method of extended crossing beams. It was ascertained that perturbations manifest themselves in the behavior of the excitation cross sections in the spectral series arising as a result of the transitions from these levels. The perturbations affect to a larger extent the form of the optical excitation functions rather than the absolute values of the cross sections. The results obtained are compared with previous data.     

Does quasi-long-range order in the two-dimensional XY model really survive weak random phase fluctuations?

Effective theories for random critical points are usually non-unitary, and thus may contain relevant operators with negative scaling dimensions. To study the consequences of the existence of negative-dimensional operators, we consider the random-bond XY model. It has been argued that the XY model on a square lattice, when weakly perturbed by random phases, has a quasi-long-range ordered phase (the random spin wave phase) at sufficiently low temperatures. We show that infinitely many relevant perturbations to the proposed critical action for the random spin wave phase were omitted in all previous treatments. The physical origin of these perturbations is intimately related to the existence of broadly distributed correlation functions. We find that those relevant perturbations do enter the Renormalization Group equations, and affect critical behavior. This raises the possibility that the random XY model has no quasi-long-range ordered phase and no Kosterlitz-Thouless (KT) phase transition.     

PERTURBED SPATIAL DARK SOLITONS

Effect of perturbations on spatial dark optical solitons is studied analytically with a novel direct perturbation approach for dark solitons. The problems of two-photon absorption and gain with saturation are reconsidered. The corresponding shifts of the soliton centers which have never been obtained by previous theories are given.     

Relaxation mechanisms of multi-quantum coherences in the Zeeman structure of atomic Cs trapped in solid He

This paper extends our previous work on near-degenerate magnetic resonance transitions in alkali ground states involving the simultaneous absorption of multiple radio-frequency quanta. New experimental results with an improved spectral resolution were obtained with cesium atoms trapped in the cubic phase of a helium crystal. The main objective of the paper is a theoretical study of the influence of stochastic perturbations of given multipole orders on the various multi-photon coherences. Algebraic and numerical results for perturbations of both dipolar and quadrupolar symmetry are presented. The present experimental resolution does not yet allow us to distinguish between these two most likely relaxation mechanisms. Nonetheless, the experimental spectra are very well described when allowing in the calculations for a magnetic field inhomogeneity of 2×10^-5. PACS 76.70.Hb; 32.80.Wr; 32.30.Dx; 32.60.+i     

Intrinsic Entropy of Squeezed Quantum Fields and Nonequilibrium Quantum Dynamics of Cosmological Perturbations

Density contrasts in the universe are governed by scalar cosmological perturbations which, when expressed in terms of gauge-invariant variables, contain a classical component from scalar metric perturbations and a quantum component from inflaton field fluctuations. It has long been known that the effect of cosmological expansion on a quantum field amounts to squeezing. Thus, the entropy of cosmological perturbations can be studied by treating them in the framework of squeezed quantum systems. Entropy of a free quantum field is a seemingly simple yet subtle issue. In this paper, different from previous treatments, we tackle this issue with a fully developed nonequilibrium quantum field theory formalism for such systems. We compute the covariance matrix elements of the parametric quantum field and solve for the evolution of the density matrix elements and the Wigner functions, and, from them, derive the von Neumann entropy. We then show explicitly why the entropy for the squeezed yet closed system is zero, but is proportional to the particle number produced upon coarse-graining out the correlation between the particle pairs. We also construct the bridge between our quantum field-theoretic results and those using the probability distribution of classical stochastic fields by earlier authors, preserving some important quantum properties, such as entanglement and coherence, of the quantum field.     

The Evolution for Various Matter Perturbations in the Expanding Universe

We present a systematic treatment of the linear theory of scalar gravitational perturbations of various matter (including baryons, cold dark matter, photons, massless neutrinos,and massive neutrino) for the flat, open and close universes, concentrating on the treatment of the massive neutrino component which has been either ignored or approximated crudely for the nonflat universe in previous literatures.     

Compensatory responses to loudness-shifted voice feedback during production of Mandarin speech

Previous studies have demonstrated that perturbations in voice pitch or loudness feedback lead to compensatory changes in voice F(0) or amplitude during production of sustained vowels. Responses to pitch-shifted auditory feedback have also been observed during English and Mandarin speech. The present study investigated whether Mandarin speakers would respond to amplitude-shifted feedback during meaningful speech production. Native speakers of Mandarin produced two-syllable utterances with focus on the first syllable, the second syllable, or none of the syllables, as prompted by corresponding questions. Their acoustic speech signal was fed back to them with loudness shifted by +/-3 dB for 200 ms durations. The responses to the feedback perturbations had mean latencies of approximately 142 ms and magnitudes of approximately 0.86 dB. Response magnitudes were greater and latencies were longer when emphasis was placed on the first syllable than when there was no emphasis. Since amplitude is not known for being highly effective in encoding linguistic contrasts, the fact that subjects reacted to amplitude perturbation just as fast as they reacted to F(0) perturbations in previous studies provides clear evidence that a highly automatic feedback mechanism is active in controlling both F(0) and amplitude of speech production.     

Solitonic gravitational waves in Bianchi II cosmologies. 2. One solitonic perturbations

This paper is a continuation of a previous one, in which the general framework for constructing solitonic perturbations on Bianchi II background was described. Here we calculate the exact solitonic perturbation corresponding to one (real) pole and we investigate in detail some of its main features. Its asymptotic behavior in time is discussed with the aid of a modified oscillatory approach to the singularity.     

Electron-capture aftereffects: The case of CdCl2

The compound CdCl₂ was investigated by TDPAC searching for aftereffects at¹¹¹Cd probes. In opposition to previous results, we do not find such effects. This confirms that, as previously suggested, the probe must be a non-isovalent impurity in the compound, so that the atomic disturbances following electron-capture persist long enough to produce detectable perturbations in the angular correlation.     

Theory of intercollisional interference effects: V. Pressure shift of the interference minimum in the Q branch of H2-rare gas mixtures

We extend our previous kinetic theory of intercollisional interference effects to include vibrational perturbations in collisions, and so obtain expressions for the pressure shifts of the interference minima in H₂-rare gas mixtures. These shifts are found to be different from those of the isotropic Raman Q lines in the same systems. The use of phase space averages for the analysis of Raman line shifting is discussed.