Näherungsweise Bestimmung von Phononenfrequenzen und Kraftkonstanten aus der Temperaturabhängigkeit der Spezifischen Wärmekapazität

Zusammenfassung Die vorliegende Arbeit hat gezeigt, daß sich aus Messungen der spezifischen Wärmekapazität eine Reihe gitterdynamischer Daten mit einer Genauigkeit ermitteln lassen, die eine weitergehende festkörperphysikalische Interpretation erlaubt. Mit den beschriebenen Verfahren eröffnet sich daher auch für andere Strukturen die Möglichkeit, brauchbare gitterdynamische Größen für eine große von Materialien zu bestimmen, für die die inelastische Neutronenbeugung bzw. Ramanmessungen wegen zu großen Aufwandes, unzureichender Probenbeschaffenheit oder aus anderen Gründen nicht optimal eingesetzt werden können.

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Estimation of phonon frequencies and force constants by means of the temperature dependence of the specific heat

From specific heat data several lattice dynamical quantities can be estimated as shown for binary and ternary semiconducting compounds with sphalerite and chalcopyrite structure, respectively. Low temperature C_V-measurements yield an approximation of the acoustic phonon dispersion relations. In addition, for ternary compounds the force constants and the zone centered phonon frequencies may be calculated. The reliability of the procedures described, which, on principle, may be extended to other structures too, is shown by comparison with independent lattice dynamical data.

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Die Autoren danken Prof. Dr. J. Monecke und Prof. Dr. H. A. Schneider für wertvolle Anregungen und Diskussionen sowie O. Bílek, Dr. K. Bohmhammel und Dr. W. Cordts für die gemeinsamen Arbeiten, die zu den beschriebenen Ergebnissen führten.     

Three-body interaction and phonon dispersion relations in aluminium

Based on an ab initio cohesive energy calculation and a model of three-body interaction, the pair potential can be calculated using the Möbius inversion theorem in the theory of numbers. Then the atomic force constants and the phonon dispersion for A1 are evaluated both with and without three-body interaction. Compared with experiments, the results show that taking the three-body interaction into account considerably improves the dispersions. Contrary to previous work, the method for calculating the atomic force constants and phonon dispersions presented here is simple, with only two adjustable parameters.     

A quantum model of option pricing: When Black-Scholes meets Schrödinger and its semi-classical limit

The Black-Scholes equation can be interpreted from the point of view of quantum mechanics, as the imaginary time Schrödinger equation of a free particle. When deviations of this state of equilibrium are considered, as a product of some market imperfection, such as: Transaction cost, asymmetric information issues, short-term volatility, extreme discontinuities, or serial correlations; the classical non-arbitrage assumption of the Black-Scholes model is violated, implying a non-risk-free portfolio. From Haven (2002) [1] we know that an arbitrage environment is a necessary condition to embedding the Black-Scholes option pricing model in a more general quantum physics setting. The aim of this paper is to propose a new Black-Scholes-Schrödinger model based on the endogenous arbitrage option pricing formulation introduced by Contreras et al. (2010) [2]. Hence, we derive a more general quantum model of option pricing, that incorporates arbitrage as an external time dependent force, which has an associated potential related to the random dynamic of the underlying asset price. This new resultant model can be interpreted as a Schrödinger equation in imaginary time for a particle of mass 1/σ² with a wave function in an external field force generated by the arbitrage potential. As pointed out above, this new model can be seen as a more general formulation, where the perfect market equilibrium state postulated by the Black-Scholes model represent a particular case. Finally, since the Schrödinger equation is in place, we can apply semiclassical methods, of common use in theoretical physics, to find an approximate analytical solution of the Black-Scholes equation in the presence of market imperfections, as it is the case of an arbitrage bubble. Here, as a numerical illustration of the potential of this Schrödinger equation analogy, the semiclassical approximation is performed for different arbitrage bubble forms (step, linear and parabolic) and compare with the exact solution of our general quantum model of option pricing.     

Spin Transport in the Presence of Rashba Interaction

A Gaussian type spin-polarized electronic wave packet is constructed to investigate the spin transport behaviour in an infinite two-dimensional electron gas system with Rashba spin--orbit (SO) interaction by solving the Schrödinger equation exactly. In the presence of Rashba SO interaction, the spin-dependent force induces a momentum dependent splitting of the two spin directions, the average spin current indicates the corresponding spin accumulation clearly. Furthermore, the coherence of the injected spin-polarized wave packet, as well as the transverse force, decays during the motion in the Rashba SO regime.     

Satellite test of intermediate-range deviation from Newton's law of gravity

A recent reanalysis of the original Eotvos experiment suggests the existence of a repulsive intermdiate-range deviation from Newtonian gravity with coupling strength on the order of 7.2×10^–3 and a range on the order of 200 m. If such a force exists it would induce a test mass in the interior of a laboratory-scale spherical mass shell in the earth's orbit to undergo linear harmonic oscillation about the shell center. If the non-Newtonian force couples to baryon number, two such test masses of different composition would oscillate at different frequencies. The fractional change in oscillation frequency is more than one million times the fractional change in acceleration incurred by the same test masses in an Eötvös experiment at the earth's surface.This essay received an honourable mention from the Gravity Reseach Foundation for the year 1986—Ed.     

Synchronization defect lines in complex-oscillatory target waves

It is well known that one of key features of spiral waves in complex-oscillatory media is the appearance of synchronization defect lines, across which the phase of the oscillation changes by multiplies of 2π. In this Letter, we report the appearance of synchronization defect lines in target waves in complex-oscillatory media by studying a model of two-dimensional Rössler reaction-diffusion system subject to an appropriate periodic force in a small region of the center of domain. The geometric structure and stability of the defect lines are studied.     

A deterministic solver for a hybrid quantum-classical transport model in nanoMOSFETs

We model a nanoMOSFET by a mesoscopic, time-dependent, coupled quantum-classical system based on a sub-band decomposition and a simple scattering operator. We first compute the sub-band decomposition and electrostatic force field described by a Schrödinger–Poisson coupled system solved by a Newton–Raphson iteration using the eigenvalue/eigenfunction decomposition. The transport in the classical direction for each sub-band modeled by semiclassical Boltzmann-type equations is solved by conservative semi-lagrangian characteristic-based methods. Numerical results are shown for both the thermodynamical equilibrium and time-dependent simulations in typical nowadays nanoMOSFETs.     

Mössbauer-effect study of Mg-Al ferrites having a rectangular hysteresis loop

A Mössbauer-effect study was made of Mg-Al ferrites having a rectangular hysteresis loop. The replacement of Fe³⁺ ions by A1³⁺ ions produces an additional component in the Mössbauer spectra, due to second-phase inclusions. The phase composition of the Mg-Al ferrite has a marked effect on the shape of the hysteresis loop. As the second-phase inclusions increase in relative importance, rectangularity coefficient D decreases. Local lattice distortion has a lesser effect on D. At high Al₂O₃ concentrations (above 15 mole%) in the Mg ferrite there is a sharp increase in the coercive force with increasing Al₂O₃ content. This increase is also due to second-phase inclusions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 2, pp. 105–109, February, 1971.In conclusion the authors thank I. I. Sil'vestrovich and B. A. Pavel'ev for furnishing the samples.     

On the quantum motion of a generalized time-dependent forced harmonic oscillator

In this work, we use linear invariants and the dynamical invariant method to obtain exact solutions of the Schrödinger equation for the generalized time-dependent forced harmonic oscillator in terms of solutions of a second order ordinary differential equation that describes the amplitude of the classical unforced damped oscillator. In addition, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum as well as the quantum correlations between coordinate and momentum. It is shown that the width of the Gaussian packet, fluctuations and correlations do not depend on the external force. As a particular case, we consider the forced Caldirola-Kanai oscillator.     

Solutions of the Fokker-Planck equation describing the thermalization of neutrons in a heavy gas moderator

The thermalization of neutrons is described by a transport equation with a second order differential operator with respect to the energy. First this equation is transformed to an one-variable Fokker-Planck equation. Next an eigenfunction expansion and a polynomial expansion are used to solve the time-dependent Fokker-Planck equation. The eigenvalues are obtained either by solving a Schrödinger equation or by calculating 2×2 matrix continued fractions. Explicit results for the approach to equilibrium of a pulse of neutrons as well as the stationary distribution for 1/v absorption are presented. It is shown that the theory of the photoelectromotive force in semiconductors also leads to the same problem.     

Approach to the quantum evolution for underdamped, critically damped, and overdamped driven harmonic oscillators using unitary transformation

Exact solution of the Schrödinger equation is derived for underdamped, critically damped, and overdamped harmonic oscillators with a driving force. A unitary operator transforming Hamiltonian into a simple form is introduced. The transformed Hamiltonian, represented in terms of a modified frequency ω, is identical with the Hamiltonian of the standard harmonic oscillator for the underdamped oscillator, with the Hamiltonian of a free particle for the critically damped oscillator, and with the Hamiltonian of a system with a harmonic parabolic potential for the overdamped oscillator. The eigenvalues of underdamped oscillator are discrete while those of the critically damped and the overdamped oscillators are continuous.     

Cylindrical molecular brushes under poor solvent conditions: microscopic observation and scaling analysis

Axial contraction of cylindrical molecular brushes of polymethylmethacrylate was observed by static light scattering and scanning force microscopy. Single brush molecules were visualized as worm-like particles whose length was almost three times shorter than the contour length of the backbone. A somewhat larger length was measured by light scattering in a good solvent. A scaling approach has been used to analyze the driving forces for the axial contraction and the conformation of the molecular brushes.Received: 27 November 2003, Published online: 25 March 2004PACS: 36.20.-r Macromolecules and polymer molecules - 36.20.Ey Conformation (statistics and dynamics) - 61.16.Ch Scanning probe microscopy: scanning tunneling, atomic force, scanning optical, magnetic force, etc.S.S. Sheiko: Current address: Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599-3290, USAS.A. Prokhorova: Current address: University of Freiburg, IMTEK - Institute for Microsystem Technology, Georges-Koehler-Allee 103,S.A. Prokhorova: 79110 Freiburg, GermanyM. Möller: Present adress: Institut für Technische Chemie und Makromolekulare Chemie, Rhein-Westfälische Technische Hochschule Aachen, Veltmanplatz 8, 52062 Aachen, Germany     

Lagrangian submanifolds and an application to the reduced Schrödinger equation in central force problems

In this Letter, a Lagrangian foliation of the zero energy level is constructed for a family of planar central force problems. The dynamics on the leaves are explicitly computed and these dynamics are given a simple interpretation in terms of the dynamics near the singularity of the potential. Lagrangian submanifolds also arise when seeking asymptotic solutions to certain partial differential equations with a large parameter. In determining such solutions, an operator between half densities on the Lagrangian submanifold and half densities on the configuration space is computed. This operator is derived for the given example, and the corresponding first order asymptotic solution to the reduced Schrödinger equation is given.     

Aerosol Fe Nanoparticles with the Passivating Oxide Shell

Structure, state, transformations and interactions of iron oxide shell with the iron metallic core in aerosol Fe nano-particles has been studied by X-ray and electron diffraction, TEM, Mössbauer spectroscopy and magnetization measurements. A strong influence of the state of nanoparticles oxide shell has been revealed on their magnetization, coercive force and hysteresis loop shift. A long-term passivation of the particles has been shown to be caused by the primary amorphous oxide. The passivation ability of the oxide shell becomes essentially worse after heat treatment of powder, resulting in its crystallization. Basing on the obtained results, a qualitative mechanism of passivation for nanoparticles covered with amorphous oxide shell has been suggested.     

Study of interaction between protein and main active components in Citrus aurantium L. by optical spectroscopy

The interaction between flavonoids and proteins was investigated by fluorescence and absorption spectroscopy. The binding parameters of drugs with proteins were obtained according to the corrected fluorescence data by an improved calculation method. The ΔH, ΔS and ΔG obtained indicate that the van der Waals or hydrogen bond, electrostatic force and hydrophobic forces all play a role in the interaction of drugs with proteins. Based on Förster's theory, the binding average distance r between the protein and drug was evaluated and found to be less than 3 nm. The interaction of drug-metal ion complexes and proteins was also investigated.     

The influence of Cr content in Fe-Cr-Co alloys on the magnetic properties and Mössbauer effect

Fe-xCr-8Co (x=24, 25, 27, 29 and 32 wt%) permanent magnetic alloys have been studied bv Mössbauer effect, magnetic balance and vibrating-sample magnetometer. It is indicated that the optimum permanent magnetic properties obtained for the composition of the alloys at about x=27. The value of Cr content in these alloys sigificantly influences the average hyperfine field, the saturation magnetic moment, the proportion of paramagnetic phase and orientation of magnetic moment in these alloys. The intrinsic coercive force is gradually reduced with the temperature decreasing from 290 to 77k. The paramagnetic peak in the spectrum disappars at about 125k. The certain mechanism has been suggested to explain the experimental results.     

Quantum mechanics derived from stochastic electrodynamics

The connection between stochastic electrodynamics (SED) and the quantum theory of matter is further explored. The main result is that the Fokker-Planck-like equation of SED can be recast into the form of a Schrödinger equation with radiative corrections, when the system is close to a state of equilibrium. The phase-space distribution can be written as Wigner's pseudo-distribution plus corrections due to the nonlinearity of the external force and to radiative effects. The radiative corrections predicted by the theory, namely the Lamb shift and the decay of excited atomic states, coincide with those predicted by QED. Moreover, the theory offers a clear physical interpretation of these phenomena as due to the coupling of the electric dipole of the system with the zero-point radiation field and to radiation reaction, respectively.     

Spectral studies of Co substituted Ni-Zn ferrites

The spinel ferrites Zn_0.35Ni_0.65−xCo_xFe₂O₄, 0≤x≤1, have been prepared using the standard ceramic technique. Room temperature Mössbauer, X-ray and infrared IR spectra were used for carrying out this study. X-ray patterns reveal that all the samples have single-phase cubic spinel structure. The Mössbauer spectra of the samples show a paramagnetic phase for x=0 and a six-line magnetic pattern and a central paramagnetic phase for x≥0.1. They are analyzed and attributed to two magnetic subpatterns and two quadrupole doublets due to Fe³⁺ ions at the tetrahedral A-sites and octahedral B-sites. Four absorption bands are observed in IR spectra. They confirm the spinel structure of the samples and existence of Fe³⁺ ions in the sample sublattices. The deduced hyperfine interactions, lattice parameters, absorption band positions and intensities and force constant are found to be dependent on the substitution factor x, where the cation distribution is estimated. The hyperfine magnetic fields, magnetization and lattice resonant frequency are found to be dependent on the interionic distance.     

Quantum treatment of the time-dependent coupled oscillators under the action of a random force

In this communication we introduce the problem of time-dependent frequency converter under the action of external random force. We have assumed that the coupling parameter and the phase pump are explicitly time dependent. Using the equations of motion in the Heisenberg picture the dynamical operators are obtained, however, under a certain integrability condition. When the system is initially prepared in the even coherent states the squeezing phenomenon is discussed. The correlation function is also considered and it has been shown that the nonclassical properties are apparent and sensitive to any variation in the integrability parameter. Furthermore, the wave function in Schrödinger picture is calculated and used it to derive the wave function in the coherent states. The accurate definition of the creation and annihilation operators are also introduced and employed to diagonalize the Hamiltonian system.