Collection Of Oscillators Research Articles

Stability mechanism of crystalline CO2 and Xe.

We explore the phase behaviors of simple molecular crystals in order to investigate the molecular basis of the stability mechanism relative to their liquid counterparts. The free energies of the face centered cubic crystals of Xe and CO2 are calculated as a collection of oscillators, and those of the liquids are from an equation of state via molecular dynamics simulations. The vibrational free energy in the solid is separated into the harmonic and anharmonic terms. The harmonic free energies decrease harshly with the expansion of the volume manifested as the large positive Grüneisen parameters, but the anharmonic free energies are positive and increase with volume, both of which originate from the deviation of the potential surface from the parabolic curve. The anharmonic free energies, though less significant in magnitude and destabilize the solids thermodynamically, serve to enhance their mechanical stability. The solid-liquid phase boundaries cannot be settled correctly without the exquisite balance between the two opposing contributions. A sharp contrast regarding the solid free energy is found in low-pressure ice, where the harmonic free energy does not decrease monotonically with volume and its anharmonic free energy is negative.

Role of cilia activity and surrounding viscous fluid in properties of metachronal waves.

Large groups of active cilia collectively beat in a fluid medium as metachronal waves, essential for some microorganisms motility and for flow generation in mucociliary clearance. Several models can predict the emergence of metachronal waves, but what controls the properties of metachronal waves is still unclear. Here, we numerically investigate the respective impacts of active beating and viscous dissipation on the properties of metachronal waves in a collection of oscillators, using a simple model for cilia in the presence of noise on regular lattices in one and two dimensions. We characterize the wave using spatial correlation and the frequency of collective beating. Our results clearly show that the viscosity of the fluid medium does not affect the wavelength; the activity of the cilia does. These numerical results are supported by a dimensional analysis, which shows that the result of wavelength invariance is robust against the model taken for sustained beating and the structure of hydrodynamic coupling. Interestingly, the enhancement of cilia activity increases the wavelength and decreases the beating frequency, keeping the wave velocity almost unchanged. These results might have significance in understanding paramecium locomotion and mucociliary clearance diseases.

Time correlation functions for quantum systems: Validating Bayesian approaches for harmonic oscillators and beyond

The quantum harmonic oscillator is the fundamental building block to compute thermal properties of virtually any dielectric crystal at low temperatures in terms of phonons, extended further to cases with anharmonic couplings, or even disordered solids. In general, Path Integral Monte Carlo or Path Integral Molecular Dynamics methods are powerful tools to determine stochastically thermodynamic quantities without systematic bias, not relying on perturbative schemes. Addressing transport properties, for instance calculating thermal conductivity from PIMC, however, is substantially more difficult. Although correlation functions of current operators can be determined by PIMC from analytic continuation on the imaginary time axis, Bayesian methods are usually employed for the numerical inversion back to real time response functions. This task not only strongly relies on the accuracy of the PIMC data but also introduces noticeable dependence on the model used for the inversion. Here, we address both difficulties with care. In particular, we first devise improved estimators for current correlations, which substantially reduce the variance of the PIMC data. Next, we provide a neat statistical approach to the inversion problem, blending into a fresh workflow the classical stochastic maximum entropy method together with recent notions borrowed from statistical learning theory. We test our ideas on a single harmonic oscillator and a collection of oscillators with a continuous distribution of frequencies and provide indications of the performance of our method in the case of a particle in a double well potential. This work establishes solid grounds for an unbiased, fully quantum mechanical calculation of transport properties in solids.

Exploring the Optical Properties of Hg1−x Cd x Se Films Using IR-Spectroscopic Ellipsometry

We have used infrared spectroscopic ellipsometry to interrogate the dielectric response of a series of Hg1−xCdxSe samples in a spectral range between 2000 and 40000 nm. Using a standard inversion technique, the experimental data obtained at multiple angles of incidence were modeled to deduce the dielectric function of each sample. The dielectric functions obtained for Hg1−xCdxSe samples allowed us to predict the band gaps for the samples, which increase as a function of the Cd concentration. Next, we modeled the dielectric function as a collection of oscillators, each of which represented a particular transition manifested in the spectrum. The most significant result obtained from this work is the recovery of their doping characteristics from the ellipsometric data. Specifically, two Hg1−xCdxSe samples with x = 0.21 and 0.28, grown on GaSb substrates, show a carrier concentration of 1.6 × 1017 and 1.8 × 1018 cm−3, respectively. These results are particularly helpful because conventional Hall measurements cannot be used for these specific samples due to the substrates (i.e., GaSb) used to grow them being highly conductive.

Quantum mechanical averaging over fluctuating rates

Quantum transport in a fluctuating medium is often described using phenomenological time-dependent model Hamiltonians. Fitting the spectrum of the time-dependent forces onto a collection of oscillators, medium fluctuations can be mapped onto an interaction with a harmonic bath. In this framework, classical as well as quantum mechanical schemes can be applied to estimate averaged transport rates. Considering a generic two state model, a classical approach which relates a transfer rate to each fluctuation, and the total rate to an ensemble average, is shown to reproduce a standard rate expression. This expression turns out to be the high temperature limit of a quantum averaging scheme, which deviates from the classical result at finite temperature. The quantum averaging over fluctuating parameters is proposed here as an efficient and general approach to estimate the validity of quantum-classical simulations which treat quantum transport within an ensemble of molecular configurations generated by classical molecular dynamics.

Electromagnetic energy, absorption, and Casimir forces: Uniform dielectric media in thermal equilibrium

The derivation of Casimir forces between dielectrics can be simplified by ignoring absorption, calculating energy changes due to displacements of the dielectrics, and only then admitting absorption by allowing permittivities to be complex. As a first step towards a better understanding of this situation we consider in this paper the model of a dielectric as a collection of oscillators, each of which is coupled to a reservoir giving rise to damping and Langevin forces on the oscillators and a noise polarization acting as a source of a fluctuating electromagnetic (EM) field in the dielectric. The model leads naturally to expressions for the quantized EM fields that are consistent with those obtained by different approaches, and also results in a fluctuation-dissipation relation between the noise polarization and the imaginary part of the permittivity; comparison with the Rytov fluctuation-dissipation relation employed in the well-known Lifshitz theory for the van der Waals (or Casimir) force shows that the Lifshitz theory is actually a classical stochastic electrodynamical theory. The approximate classical expression for the energy density in a band of frequencies at which absorption in a dielectric is negligible is shown to be exact as a spectral thermal equilibrium expectation value in the quantum-electrodynamical theory. Our main result is the derivation of an expression for the QED energy density of a uniform dispersive, absorbing media in thermal equilibrium. The spectral density of the energy is found to have the same form with or without absorption. We also show how the fluctuation-dissipation theorem ensures a detailed balance of energy exchange between the (absorbing) medium, the reservoir and the EM field in thermal equilibrium.

Far-infrared dielectric functions and phonon spectra of [formula omitted] alloys determined by spectroscopic ellipsometry

We have used spectroscopic ellipsometry to determine the complex dielectric function of a series of ternary Be x Zn 1− x Te thin films grown by molecular beam epitaxy. The II–VI semiconductor alloys were grown on InP substrates that had an InGaAs buffer layer. After the growth, X-ray diffraction experiments were performed in order to determine the alloy concentration. A standard inversion technique was used to obtain the dielectric functions from the measured ellipsometric spectra, obtained between 2000 nm (5000 cm −1) and 40,000 nm (250 cm −1). By modelling the dielectric function as a collection of oscillators, representing longitudinal and transverse optical phonons of the Be x Zn 1− x Te lattice, we were able to recover the phonon spectra for this alloy system. It is argued that the additional phonon modes that are obtained from ellipsometry are best understood from the recently-proposed percolation model.

The History and Philosophy of Quantum Field Theory

In November of 1925 Born, Heisenberg and Jordan wrote an article together in which they demonstrated that Einstein's energy fluctuation formula could be derived from quantum mechanics. They remark that the equations are subject to reinterpretation. Specifically, the states of radiation oscillators can be reinterpreted as numbers of quanta of radiation. They also connected this latter idea up with Bose-Einstein statistics. Heisenberg wrote to Pauli that it was Jordan who contributed the idea of reinterpreting the terms. This was the first step toward quantum field theory. In August of the following year Dirac derived Einstein's A and B coefficients for induced transitions between states but on the assumption that the electromagnetic field could be treated classically (Dirac 1927). In 1927 Dirac lay the mathematical foundations for quantum electrodynamics. Early that year he combined quantum mechanics, special relativity, and radiation theory in treating the electromagnetic field as if it were an infinite collection of oscillators.

Nonequilibrium entropy in classical and quantum field theory

This paper proposes a definition of nonequilibrium entropy appropriate for a bosonic classical or quantum field, viewed as a collection of oscillators with equations of motion which satisfy a Liouville theorem (as is guaranteed for a Hamiltonian system). This entropy S is constructed explicitly to provide a measure of correlations and, as such, is conserved absolutely in the absence of couplings between degrees of freedom. This means, e.g., that there can be no entropy generation for a source-free linear field in flat space, but that S need no longer be conserved in the presence of couplings induced by nonlinearities, material sources, or a nontrivial dynamical background space-time. Moreover, through the introduction of a ‘‘subdynamics,’’ it is proved that, in the presence of such couplings, the entropy will satisfy an H-theorem inequality, at least in one particular limit. Specifically, if at some initial time t0 the field is free of any correlations, it then follows rigorously that, at time t0+Δt, the entropy will be increasing: dS/dt>0. Similar arguments demonstrate that this S is the only measure of ‘‘entropy’’ consistent mathematically with the subdynamics. It is argued that this entropy possesses an intrinsic physical meaning, this meaning being especially clear in the context of a quantum theory, where a direct connection exists between entropy generation and particle creation. Reasonable conjectures regarding the more general time dependence of the entropy, which parallel closely the conventional wisdom of particle mechanics, lead to an interpretation of S which corroborates one’s naive intuition as to the behavior of an ‘‘entropy.’’

Collective electron effects in molecular liquids

A knowledge of the interactions of radiation with molecular liquids such as glycerol, water and benzene has direct biological application in terms of understanding radiation damage to living material. Not only the amount of energy but the modes of energy deposition can be extracted from the dielectric functions if these are known over a sufficiently wide energy range. The experimental techniques and methods of data analysis which yield the dielectric functions are reviewed. The conditions necessary for the existence of collective electron effects in molecular liquids are considered and the collective behavior associated with a single oscillator and with a collection of oscillators is compared with the behavior of a free-electron gas. Experimental spectra for some molecular liquids in the energy region from 0 to 26 eV are analyzed for the degree of collective behavior exhibited.