The Erpenbeck high frequency instability theorem for ZND detonations

The rigorous study of spectral stability for strong detonations was begun by J.J. Erpenbeck in [Er1]. Working with the Zeldovitch-von Neumann-D\"oring (ZND) model, which assumes a finite reaction rate but ignores effects like viscosity corresponding to second order derivatives, he used a normal mode analysis to define a stability function V(\tau,\eps) whose zeros in $\Re \tau>0$ correspond to multidimensional perturbations of a steady detonation profile that grow exponentially in time. Later in a remarkable paper [Er3] he provided strong evidence, by a combination of formal and rigorous arguments, that for certain classes of steady ZND profiles, unstable zeros of $V$ exist for perturbations of sufficiently large transverse wavenumber \eps, even when the von Neumann shock, regarded as a gas dynamical shock, is uniformly stable in the sense defined (nearly twenty years later) by Majda. In spite of a great deal of later numerical work devoted to computing the zeros of V(\tau,\eps), the paper \cite{Er3} remains the only work we know of that presents a detailed and convincing theoretical argument for detecting them. The analysis in [Er3] points the way toward, but does not constitute, a mathematical proof that such unstable zeros exist. In this paper we identify the mathematical issues left unresolved in [Er3] and provide proofs, together with certain simplifications and extensions, of the main conclusions about stability and instability of detonations contained in that paper. The main mathematical problem, and our principal focus here, is to determine the precise asymptotic behavior as \eps\to \infty of solutions to a linear system of ODEs in $x$, depending on \eps and a complex frequency $\tau$ as parameters, with turning points $x_*$ on the half-line $[0,\infty)$

Replica Symmetry Breaking in Attractor Neural Network Models

The phenomenon of replica symmetry breaking is investigated for the retrieval phases of Hopfield-type network models. The basic calculation is done for the generalized version of the standard model introduced by Horner [1] and by Perez-Vicente and Amit [2] which can exhibit low mean levels of neural activity. For a mean activity $\bar a =1/2$ the Hopfield model is recovered. In this case, surprisingly enough, we cannot confirm the well known one step replica symmetry breaking (1RSB) result for the storage capacity which was presented by Crisanti, Amit and Gutfreund [3] (\alpha_c^{\hbox{\mf 1RSB}}\simeq 0.144). Rather, we find that 1RSB- and 2RSB-Ans\"atze yield only slightly increased capacities as compared to the replica symmetric value (\alpha_c^{\hbox{\mf 1RSB}}\simeq 0.138\,186 and \alpha_c^{\hbox{\mf 2RSB}}\simeq 0.138\,187 compared to \alpha_c^{\hbox{\mf RS}}\simeq 0.137\,905), significantly smaller also than the value \alpha_c^{\hbox{\mf sim}} = 0.145\pm 0.009 reported from simulation studies. These values still lie within the recently discovered reentrant phase [4]. We conjecture that in the infinite Parisi-scheme the reentrant behaviour disappears as is the case in the SK-spin-glass model (Parisi--Toulouse-hypothesis). The same qualitative results are obtained in the low activity range.Comment: Latex file, 20 pages, 8 Figures available from the authors upon request, HD-TVP-94-

Electron Spin Resonance Above Tc In Layered Manganites

We have performed electron spin resonance (ESR) and dc magnetization measurements on single crystals of La2(1-x)Sr1+2xMn2O7 up to 800 K with special emphasis on the x = 0.4 composition. The ESR linewidth shows behavior similar to that observed in the three-dimensional perovskites and above ∼500 K can be described by a universal expression ΔHpp(T)=[C/Tχ(T)]ΔHpp (∞). The linewidth and the resonance field become anisotropic below ∼500 K. The anisotropy in the resonance field is proportional to the magnetization M, and we concluded that it is intrinsic to the system. We show that demagnetization effects can explain only part of the anisotropy. The remainder arises from short-range uniaxial terms in the Hamiltonian that are associated with the crystal field and Dzialozhinsky-Moriya interactions. The anisotropy in the linewidth is attributed to the easy-plane ferromagnetic ordering, which also arises from the short-range anisotropy.631717441311744136Ruddlesden, S.N., Popper, P., (1958) Acta Crystallogr., 11, p. 54Moritomo, Y., Asamitsu, A., Kuwahara, H., Tokura, Y., (1996) Nature (London), 380, p. 141Causa, M.T., Tovar, M., Caneiro, A., Prado, F., Ibanez, G., Ramos, C.A., Butera, A., Oseroff, S.B., (1998) Phys. Rev. B, 58, p. 3233Causa, M.T., Alejandro, G., Tovar, M., Pagliuso, P.G., Rettori, C., Oseroff, S.B., Subramanian, M.A., (1999) J. Appl. Phys., 85, p. 5408Huber, D.L., Alejandro, G., Caneiro, A., Causa, M.T., Prado, F., Tovar, M., Oseroff, S.B., (1999) Phys. Rev. B, 60, p. 12155Oseroff, S.B., Moreno, N.O., Pagliuso, P.G., Rettori, C., Huber, D.L., Gardner, J.S., Sarrao, J.L., Alascio, B.R., (2000) J. Appl. Phys., 87, p. 5810Seehra, M.S., Ibrahim, M.M., Babu, V.S., Srinivasan, G., (1996) J. Phys.: Condens. Matter, 8, p. 11283Dominguez, M., Lofland, S.E., Bhagat, S.M., Raychaudhuri, A.K., Ju, H.L., Venkates, T., Greene, R.L., (1996) Solid State Commun., 97, p. 193Lofland, S.E., Kim, P., Dahiroc, P., Bhagat, S.M., Tyagi, S.D., Karabashev, S.G., Shultyatev, D.A., Mukovskii, Y., (1997) Phys. Lett. A, 233, p. 476Kimura, T., Tomioka, Y., Kuwahara, H., Asamitsu, A., Tamura, M., Tokura, Y., (1996) Science, 274, p. 1698Perring, T.G., Aeppli, G., Moritomo, Y., Tokura, Y., (1997) Phys. Rev. Lett., 78, p. 3197Zhou, J.-S., Goodenough, J.B., Mitchell, J.F., (1998) Phys. Rev. B, 58, p. 579Zhou, J.-S., Goodenough, J.B., (1998) Phys. Rev. Lett., 80, p. 2665Kelley, T.M., Argyriou, D.N., Robinson, R.A., Nakotte, H., Mitchell, J.F., Osbron, R., Jorgensen, J.D., (1998) Physica B, 241-243, p. 439Heffner, R.H., MacLaughlin, D.E., Nieuwenhuys, G.J., Kimura, T., Luke, G.M., Tokura, Y., Uemura, Y.J., (1998) Phys. Rev. Lett., 81, p. 1706Potter, C.D., Swiatek, M., Bader, S.D., Argyriou, D.N., Mitchell, J.F., Miller, D.J., Hinks, D.G., Jorgensen, J.D., (1998) Phys. Rev. B, 57, p. 72Chauvet, O., Goglio, G., Molinie, P., Corraze, B., Brohan, L., (1998) Phys. Rev. Lett., 81, p. 1102Hirota, K., Moritomo, Y., Fujioka, H., Kubota, M., Yoshizawa, H., Endoh, Y., (1998) J. Phys. Soc. Jpn., 67, p. 3380Li, J.Q., Matsui, Y., Kimura, T., Tokura, Y., (1998) Phys. Rev. B, 57, pp. R3205Kimura, T., Kumai, R., Tokura, Y., Li, J.Q., Matsui, Y., (1998) Phys. Rev. B, 58, p. 11081Hayashi, T., Miura, N., Tokunaga, M., Kimura, T., Tokura, Y., (1998) J. Phys.: Condens. Matter, 10, p. 11525Suryanarayanan, R., Dhalenne, G., Revcolevschi, A., Prellier, W., Renard, J.P., Dupas, C., Caliebe, W., Chatterji, T., (2000) Solid State Commun., 113, p. 267Kubota, M., Fujioka, H., Ohoyama, K., Hirota, K., Moritomo, Y., Yoshizawa, H., Endoh, Y., (1999) J. Phys. Chem. Solids, 60, p. 116Bhagat, S.M., Lofland, S.E., Mitchell, J.F., (1999) Phys. Lett. A, 259, p. 326Kittel, C., (1997) Introduction to Solid State Physics, , Wiley, New YorkOkochi, M., (1970) J. Phys. Soc. Jpn., 28, p. 897Victoria, C., Barker, R.C., Yelon, A., (1967) Phys. Rev. Lett., 19, p. 792Nagata, K., (1976) J. Phys. Soc. Jpn., 40, p. 1209Nagata, K., Yamamoto, I., Takano, H., Yokozawa, Y., (1977) J. Phys. Soc. Jpn., 43, p. 857. , and references thereinHuber, D.L., Seehra, M.S., (1976) Phys. Status Solidi B, 74, p. 145Stanger, J.-L., Andre, J.-J., Turek, P., Hosokoshi, Y., Tamura, M., Kinoshita, M., Rey, P., Veciana, J., (1997) Phys. Rev. B, 55, p. 8398Van Vleck, J.H., (1950) Phys. Rev., 78, p. 266Kittel, C., (1948) Phys. Rev., 73, p. 15

Quasifree kaon-photoproduction from nuclei in a relativistic approach

We compute the recoil polarization of the lambda-hyperon and the photon asymmetry for the quasifree photoproduction of kaons in a relativistic impulse-approximation approach. Our motivation for studying polarization observables is threefold. First, polarization observables are more effective discriminators of subtle dynamics than the unpolarized cross section. Second, earlier nonrelativistic calculations suggest an almost complete insensitivity of polarization observables to distortions effects. Finally, this insensitivity entails an enormous simplification in the theoretical treatment. Indeed, by introducing the notion of a ``bound-nucleon propagator'' we exploit Feynman's trace techniques to develop closed-form, analytic expressions for all photoproduction observables. Moreover, our results indicate that polarization observables are also insensitive to relativistic effects and to the nuclear target. Yet, they are sensitive to the model parameters, making them ideal tools for the study of modifications to the elementary amplitude --- such as in the production, propagation, and decay of nucleon resonances --- in the nuclear medium.Comment: 15 pages and 6 figures - submitted to PR

All-Optical Broadband Excitation of the Motional State of Trapped Ions

We have developed a novel all-optical broadband scheme for exciting, amplifying and measuring the secular motion of ions in a radio frequency trap. Oscillation induced by optical excitation has been coherently amplified to precisely control and measure the ion's secular motion. Requiring only laser line-of-sight, we have shown that the ion's oscillation amplitude can be precisely controlled. Our excitation scheme can generate coherent motion which is robust against variations in the secular frequency. Therefore, our scheme is ideal to excite the desired level of oscillatory motion under conditions where the secular frequency is evolving in time. Measuring the oscillation amplitude through Doppler velocimetry, we have characterized the experimental parameters and compared them with a molecular dynamics simulation which provides a complete description of the system.Comment: 8 pages, 10 figure

Isospin-Violating Meson-Nucleon Vertices as an Alternate Mechanism of Charge-Symmetry Breaking

We compute isospin-violating meson-nucleon coupling constants and their consequent charge-symmetry-breaking nucleon-nucleon potentials. The couplings result from evaluating matrix elements of quark currents between nucleon states in a nonrelativistic constituent quark model; the isospin violations arise from the difference in the up and down constituent quark masses. We find, in particular, that isospin violation in the omega-meson--nucleon vertex dominates the class IV CSB potential obtained from these considerations. We evaluate the resulting spin-singlet--triplet mixing angles, the quantities germane to the difference of neutron and proton analyzing powers measured in elastic $\vec{n}-\vec{p}$ scattering, and find them commensurate to those computed originally using the on-shell value of the $\rho$-$\omega$ mixing amplitude. The use of the on-shell $\rho$-$\omega$ mixing amplitude at $q^2=0$ has been called into question; rather, the amplitude is zero in a wide class of models. Our model possesses no contribution from $\rho$-$\omega$ mixing at $q^2=0$, and we find that omega-meson exchange suffices to explain the measured $n-p$ analyzing power difference~at~183 MeV.Comment: 20 pages, revtex, 3 uuencoded PostScript figure

Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles

The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comparatively fast time scale, the main dynamical property of (strongly) monotone systems, convergence to steady states, is still valid. An application is worked out to a double-phosphorylation ``futile cycle'' motif which plays a central role in eukaryotic cell signaling.Comment: 21 pages, 3 figures, corrected typos, references remove

Phase variance of squeezed vacuum states

We consider the problem of estimating the phase of squeezed vacuum states within a Bayesian framework. We derive bounds on the average Holevo variance for an arbitrary number $N$ of uncorrelated copies. We find that it scales with the mean photon number, $n$, as dictated by the Heisenberg limit, i.e., as $n^{-2}$, only for $N>4$. For $N\leq 4$ this fundamental scaling breaks down and it becomes $n^{-N/2}$. Thus, a single squeezed vacuum state performs worse than a single coherent state with the same energy. We find the optimal splitting of a fixed given energy among various copies. We also compute the variance for repeated individual measurements (without classical communication or adaptivity) and find that the standard Heisenberg-limited scaling $n^{-2}$ is recovered for large samples.Comment: Minor changes, version to appear in PRA, 8 pages, 2 figure

Equation of State of Oscillating Brans-Dicke Scalar and Extra Dimensions

We consider a Brans-Dicke scalar field stabilized by a general power law potential with power index $n$ at a finite equilibrium value. Redshifting matter induces oscillations of the scalar field around its equilibrium due to the scalar field coupling to the trace of the energy momentum tensor. If the stabilizing potential is sufficiently steep these high frequency oscillations are consistent with observational and experimental constraints for arbitrary value of the Brans-Dicke parameter $\omega$. We study analytically and numerically the equation of state of these high frequency oscillations in terms of the parameters $\omega$ and $n$ and find the corresponding evolution of the universe scale factor. We find that the equation of state parameter can be negative and less than -1 but it is not related to the evolution of the scale factor in the usual way. Nevertheless, accelerating expansion is found for a certain parameter range. Our analysis applies also to oscillations of the size of extra dimensions (the radion field) around an equilibrium value. This duality between self-coupled Brans-Dicke and radion dynamics is applicable for $\omega= -1 + 1/D$ where D is the number of extra dimensions.Comment: 10 two-column pages, RevTex4, 8 figures. Added clarifying discussions, new references. Accepted in Phys. Rev. D (to appear

Tri-meson-mixing of π\pi-η\eta-η′\eta' and ρ\rho-ω\omega-ϕ\phi in the light-cone quark model

The radiative transition form factors of the pseudoscalar mesons {$\pi$, $\eta$, $\eta'$} and the vector mesons {$\rho$, $\omega$, $\phi$} are restudied with $\pi$-$\eta$-$\eta'$ and $\rho$-$\omega$-$\phi$ in tri-meson-mixing pattern, which is described by tri-mixing matrices in the light-cone constituent quark model. The experimental transition decay widths are better reproduced with tri-meson-mixing than previous results in a two-mixing-angle scenario of only two-meson $\eta$-$\eta'$ mixing and $\omega$-$\phi$ mixing.Comment: 8 pages, 6 figures, final version to appear in EPJ