Peter F. Meier

Vibrationally averaged spin densities on muons and protons in the hydroxyl and ethyl radicals

The observations of the residual isotope effect for muonated radicals are discussed using calculations on the hydroxyl and ethyl radicals. The origins are partly due to the non-linear increase of the hyperfine coupling constants with increase in bond length, although a significant contribution comes from the anharmonicity of the molecular vibrations.

Green’s function approach to phonon hydrodynamics in solids

In the first part the Green’s function approach developed byKadanoff andBaym is used to derive a transport equation for phonons in a dielectric anharmonic crystal. The approximations which reduce this generalized equation to the Peierls equation are exhibited. In the second part, neglecting Umklapp processes, the linearized equation is applied to hydrodynamic phenomena. In a system close to local thermal equilibrium second sound and Poiseuille flow may exist. The damping through normal processes is approximately calculated by a momentum-dependent relaxation time. The coupling between the phonon and the dilatation fields is discussed.RésuméDans la première partie la méthode des fonctions de Green, qui a été développée parKadanoff etBaym, est appliquée à dériver une equation de transport pour des phonons dans un cristal diélectrique anharmonique. Les approximations qui réduisent cette équation généralisée à celle de Peierls sont indiquées. En négligeant les processus Umklapp, dans la seconde partie on applique l’équation linéarisée à l’étude des phénomènes hydrodynamiques. Dans un système au voisinage de l’équilibre thermique locale le second son et le flux de Poiseuille peuvent exister. L’atténuation par des processus normaux est calculée approximativement à l’aide d’un temps de relaxation qui dépend du nombre d’onde. On discute le couplage entre les champs de phonons et de dilatation.ZusammenfassungIm ersten Teil wird die vonKadanoff undBaym entwickelte Methode der Greenschen Funktionen verwendet, um eine Transportgleichung für Phononen in einem dielektrischen anharmonischen Kristall herzuleiten. Die Näherungen, welche diese verallgemeinerte Gleichung auf die Peierls-Gleichung zurückführen, werden aufgezeigt. Unter Vernachlässigung von Umklapp-Prozessen wird im zweiten Teil die linearisierte Gleichung auf hydrodynamische Phänomene angewendet. In einem System, welches beinahe im lokalen thermischen Gleichgewicht ist, können zweiter Schall und Poiseuille-Strömung auftreten. Die Dämpfung durch Normalprozesse wird mittels einer Relaxationszeit, die von der Wellenzahl abhängt, näherungsweise berechnet. Die Kopplung zwischen Phonon- und Dilatationsfeld wird diskutiert.

Non-equilibrium approach to transport phenomena in quantum crystals

A pure dielectric quantum crystal subjected to an external mechanical force is described by non-equilibrium Green’s functions. In equilibrium the leading approximation leads to the definition of elementary excitations, the phonons in the renormalized harmonic approximation. Their temperature dependent energies are to be determined as solutions of an integral equation. For hydrodynamic disturbances a generalized transport equation for a phonon number density is derived. A similar approximation for the spectral function yields an integral equation for space and time dependent quasiparticle energies which are expressed as functionals of the displacement field and the phonon distribution. The Boltzmann equation for the latter includes the quasi-particle interaction.ZusammenfassungEin reiner dielektrischer Kristall, auf den eine äußere mechanische Kraft wirkt, wird durch Nichtgleichgewichts-Greenfunktionen beschrieben. Im Gleichgewicht werden durch die führende Approximation Elementaranregungen definiert: Phononen in der sog. renormierten harmonischen Approximation. Eine Integralgleichung bestimmt die temperaturabhängigen Phononenergien. Für hydrodynamische Störungen wird eine verallgemeinerte Transportgleichung für eine Phonondichte hergeleitet. Ähnliche Näherungen für die Spektralfunktion führen zu einer Integralgleichung für orts- und zeitabhängige Quasiteilchen-Energien, welche Funktionale des Verschiebungsfeldes und der Phononverteilung sind. Die Boltzmann-Gleichung für letztere umfaßt die Quasiteilchen-Wechselwirkung.RésuméUn cristal quantique diélectrique pur dans un champ de force mécanique extérieur est décrit par des fonctions de Green pour des systèmes hors d’équilibre. A l’équilibre la contribution principale mène à la définition d’excitations élémentaires, les phonons dans l’approximation harmonique rénormalisée. Leurs énergies qui dépendent de la température se déterminent comme solution d’une équation intégrale. Pour des perturbations hydrodynamiques une équation de transport généralisée pour une densité de phonons est dérivée. Après une approximation analogue pour la fonction spectrale il résulte une équation intégrale pour les énergies des quasi-particules. Ces énergies, dépendant du temps et du lieu, sont des fonctionnels du champ de dilatation et de la distribution des phonons. L’équation de Boltzmann pour la dernière comprend l’interaction des quasi-particules.

Numerical analysis of moments expansions

Abstract We present numerical results for the estimate of the ground state energy for two quantum many-body systems using the connected moments expansion (CMX) and a newly developed alternate moments expansion (AMX). Comparisons are made with an equivalent Lanczos scheme which yields a variational upper bound for the ground state energy. For each system, the utility of both expansions is evaluated as they pertain to relevant regions of parameter space. A brief description of the (numerical) nature of the singularities which may arise in the series expansions is also given.

Temporal patterns of human behaviour: are there signs of deterministic 1/f scaling?

Temporal patterns apparently exhibiting scaling properties may originate either from fractal stochastic processes or from causal (i.e., deterministic) dynamics. In general, the distinction between the possible two origins remains a non-trivial task. This holds especially for the interpretation of properties derived from temporal patterns of various types of human behaviour, which were reported repeatedly. We propose here a computational scheme based on a generic intermittency model to test predictability (thus determinism) of a part of a time series with knowledge gathered from another part. The method is applied onto psychodynamic time series related to turns from non-psychosis to psychosis. A nonrandom correlation (ρ=0.76) between prediction and real outcome is found. Our scheme thus provides a particular kind of fractal risk-assessment for this possibly deterministic process. We briefly discuss possible implications of these findings to evaluate the risk to undergo a state transition, in our case a patients risk to enter a next psychotic state. We further point to some problems concerning data sample pecularities and equivalence between data and model setup.

Muon level-crossing resonance in Si∶Al

AbstractμLCR spectra from single-crystal Si∶Al have been taken at 30 K with the field along the 〈111〉 direction. The spectra show strong resonances near 12 and 50 mT, and weaker resonances near 38 and 42 mT. There is also indication of lines near 15 and 21 mT. The strong signals are due to the well-known zero crossings for Mu* in Si, and the weak signals may be associated with the quadrupole interaction of27Al, as predicted byab initio electronic structure calculations.

Self-energy of phonons in anharmonic one-dimensional crystals

Using the expression obtained by Greens function methods the self-energy of phonons, interacting through anharmonic terms of third and fourth order in the expansion of the potential energy, is calculated for a linear chain without further approximations. The phonon energy shift and width show strong dependence on the frequency and the wave-vector.ZusammenfassungAusgehend von einem Ausdruck, der mittels Greenscher Funktionen erhalten wurde, wird die Selbstenergie von Phononen, welche miteinander in Wechselwirkung stehen, durch anharmonische Glieder dritter und vierter Ordnung in der Entwicklung der potentiellen Energie, ohne weitere Näherungen für eine lineare Kette berechnet. Die Energieverschiebung und die Dämpfung der Phononen hängen stark von der Frequenz und der Wellenzahl ab.RésuméUtilisant une expression qui a été obtenue par la méthode des fonctions de Green, lénergie propre des phonons, qui sont en interaction par des termes de troisième et quatrième ordre dans le développement de lénergie potentielle, est calculée pour une chaine linéaire sans faire dautres approximations. Le déplacement de lénergie et la durée de vie du phonon dépendent fortement de la fréquence et du nombre donde.

First Principles Investigation of Local Distortions in Doped La2CuO4

We present the results of first-principles cluster calculations of local distortions in doped La2CuO4. Local deformations of the CuO6 octahedra associated with the presence of an additional extrinsic hole were determined using the density-functional (DF) method on various cluster models. The results indicate that a localized hole induces a contraction of the CuO(apical) distance from 2.40 to 2.28 Å. The contracted distance is in very good agreement with the anomalous, short CuO(apical) distance of 2.3 Å, observed recently by polarized Cu K-edge extended x-ray absorption fine structure (EXAFS) in La1.85Sr0.15CuO4 and associated with the hole-rich stripe region.

Ground-state of a two dimensional Heisenberg antiferromagnet

Abstract The Lanczos tridiagonal formalism is employed in the study of the ground-state of the s = 1 2 anisotropic Heisenberg antiferromagnet for the honeycomb, simple cubic and body-centered cubic lattices. Using the connected moments of Lee and Lo, we are able to generate, in a straightforward manner, an equivalent 6 × 6 Lanczos matrix and in turn, evaluate the ground-state energy and the singlet-triplet energy for all values of the anisotropy parameter.

Ordered and Chaotic Response of a Modulated or Driven NMR Laser

The Feature Issue on Instabilities in Active Optical Media of the Journal of the Optical Society of America B [1]shows the increasing interest in nonlinear phenomena in laser systems. The ruby nuclear-magnetic-resonance (NMR) laser [2], among others, is an excellent test system with which to study the nature of instabilities and the routes to chaos of lasing systems. In our contribution [3] we reviewed theoretical and experimental investigations of the ruby NMR laser that operates in the rf regime and has its counterpart in the homogeneously broadened single-mode ring laser. Two topics were stressed in particular: the transition from ordered to chaotic response of the parametrically modulated laser (PML), and the transition to injection-locking of a laser with an injected signal (LIS). In both cases a control parameter of the system was slowly swept in time. For the PML it was either the amplitude or the frequency of the parametric modulation signal Apsinωpt; for the LIS it was the amplitude of the injected signal V0sinωt which was detuned by Δωa=ωa−ω from the NMR frequency ωa. In scanning the control parameter we observed in both cases sequences of instabilities leading to either regular or irregular response.