Cosine and Sine Operators Related with Orthogonal Polynomial Sets on the Intervall [-1,1]

The quantization of phase is still an open problem. In the approach of Susskind and Glogower so called cosine and sine operators play a fundamental role. Their eigenstates in the Fock representation are related with the Chebyshev polynomials of the second kind. Here we introduce more general cosine and sine operators whose eigenfunctions in the Fock basis are related in a similar way with arbitrary orthogonal polynomial sets on the intervall [-1,1]. To each polynomial set defined in terms of a weight function there corresponds a pair of cosine and sine operators. Depending on the symmetry of the weight function we distinguish generalized or extended operators. Their eigenstates are used to define cosine and sine representations and probability distributions. We consider also the inverse arccosine and arcsine operators and use their eigenstates to define cosine-phase and sine-phase distributions, respectively. Specific, numerical and graphical results are given for the classical orthogonal polynomials and for particular Fock and coherent states.Comment: 1 tex-file (24 pages), 11 figure

Toward a microscopic description of flow near the jamming threshold

We study the relationship between microscopic structure and viscosity in non-Brownian suspensions. We argue that the formation and opening of contacts between particles in flow effectively leads to a negative selection of the contacts carrying weak forces. We show that an analytically tractable model capturing this negative selection correctly reproduces scaling properties of flows near the jamming transition. In particular, we predict that (i) the viscosity {\eta} diverges with the coordination z as {\eta} ~ (z_c-z)^{-(3+{\theta})/(1+{\theta})}, (ii) the operator that governs flow displays a low-frequency mode that controls the divergence of viscosity, at a frequency {\omega}_min\sim(z_c-z)^{(3+{\theta})/(2+2{\theta})}, and (iii) the distribution of forces displays a scale f* that vanishes near jamming as f*/\sim(z_c-z)^{1/(1+{\theta})} where {\theta} characterizes the distribution of contact forces P(f)\simf^{\theta} at jamming, and where z_c is the Maxwell threshold for rigidity.Comment: 6 pages, 4 figure

Determination of biomembrane bending moduli in fully atomistic simulations.

The bilayer bending modulus (Kc) is one of the most important physical constants characterizing lipid membranes, but precisely measuring it is a challenge, both experimentally and computationally. Experimental measurements on chemically identical bilayers often differ depending upon the techniques employed, and robust simulation results have previously been limited to coarse-grained models (at varying levels of resolution). This Communication demonstrates the extraction of Kc from fully atomistic molecular dynamics simulations for three different single-component lipid bilayers (DPPC, DOPC, and DOPE). The results agree quantitatively with experiments that measure thermal shape fluctuations in giant unilamellar vesicles. Lipid tilt, twist, and compression moduli are also reported

Ejection Energy of Photoelectrons in Strong Field Ionization

We show that zero ejection energy of the photoelectrons is classically impossible for hydrogen-like ions, even when field ionization occurs adiabatically. To prove this we transform the basic equations to those describing two 2D anharmonic oscillators. The same method yields an alternative way to derive the anomalous critical field of hydrogen-like ions. The analytical results are confirmed and illustrated by numerical simulations. PACS Number: 32.80.RmComment: 7 pages, REVTeX, postscript file including the figures is available at http://www.physik.th-darmstadt.de/tqe/dieter/publist.html or via anonymous ftp from ftp://tqe.iap.physik.th-darmstadt.de/pub/dieter/publ_I_pra_pre.ps, accepted for publication in Phys. Rev.

Transmission of a Symmetric Light Pulse through a Wide QW

The reflection, transmission and absorption of a symmetric electromagnetic pulse, which carrying frequency is close to the frequency of an interband transition in a QW (QW), are obtained. The energy levels of a QW are assumed discrete, one exited level is taken into account. The case of a wide QW is considered when a length of the pulse wave, appropriate to the carrying frequency, is comparable to the QW's width. In figures the time dependencies of the dimensionless reflection, absorption are transmission are represented. It is shown, that the spatial dispersion and a distinction in refraction indexes influence stronger reflection.Comment: 8 pages,8 figures with caption

The personal belief in a just world and domain-specific beliefs about justice at school and in the family: A longitudinal study with adolescents

This article investigates the relationship between the personal belief in a just world (BJW) and domain-specific beliefs about justice and examines how justice cognitions impact on adolescents' development, particularly on their achievement at school and their subjective well-being. A longitudinal questionnaire study with German adolescents aged 14-19 years was conducted over a period of five to eight months. The pattern of results revealed that evaluations of the school climate and of the family climate as being just were two distinct phenomena, both of which impacted on the personal BJW, which in turn affected the domain-specific beliefs about justice. However, the domain-specific beliefs about justice did not impact on each other directly. Moreover, an evaluation of the family climate (but not of the school climate) as being just reduced depressive symptoms, whereas depressive symptoms did not weaken the evaluation of one's family as being just. The evaluation of the school climate as being just improved the grades received in the next school report, whereas the grades received did not affect the justice evaluation of the school climate. Finally, all relationships persisted when controlling for age and gender. In sum, the pattern of findings supports the notion that justice cognitions impact on development during adolescence

Effect of the Spatial Dispersion on the Shape of a Light Pulse in a Quantum Well

Reflectance, transmittance and absorbance of a symmetric light pulse, the carrying frequency of which is close to the frequency of interband transitions in a quantum well, are calculated. Energy levels of the quantum well are assumed discrete, and two closely located excited levels are taken into account. A wide quantum well (the width of which is comparable to the length of the light wave, corresponding to the pulse carrying frequency) is considered, and the dependance of the interband matrix element of the momentum operator on the light wave vector is taken into account. Refractive indices of barriers and quantum well are assumed equal each other. The problem is solved for an arbitrary ratio of radiative and nonradiative lifetimes of electronic excitations. It is shown that the spatial dispersion essentially affects the shapes of reflected and transmitted pulses. The largest changes occur when the radiative broadening is close to the difference of frequencies of interband transitions taken into account.Comment: 7 pages, 5 figure

Complementary Patents and Market Structure

Many high technology goods are based on standards that require several essential patents owned by different IP holders. This gives rise to a complements and a double mark-up problem. We compare the welfare effects of two different business strategies dealing with these problems. Vertical integration of an IP holder and a downstream producer solves the double mark-up problem between these firms. Nevertheless, it may raise royalty rates and reduce output as compared to non-integration. Horizontal integration of IP holders solves the complements problem but not the double mark-up problem. Vertical integration discourages entry and reduces innovation incentives, while horizontal integration always benefits from entry and innovatio

A two-dimensional, two-electron model atom in a laser pulse: exact treatment, single active electron-analysis, time-dependent density functional theory, classical calculations, and non-sequential ionization

Owing to its numerical simplicity, a two-dimensional two-electron model atom, with each electron moving in one direction, is an ideal system to study non-perturbatively a fully correlated atom exposed to a laser field. Frequently made assumptions, such as the ``single active electron''- approach and calculational approximations, e.g. time dependent density functional theory or (semi-) classical techniques, can be tested. In this paper we examine the multiphoton short pulse-regime. We observe ``non-sequential'' ionization, i.e.\ double ionization at lower field strengths as expected from a sequential, single active electron-point of view. Since we find non-sequential ionization also in purely classical simulations, we are able to clarify the mechanism behind this effect in terms of single particle trajectories. PACS Number(s): 32.80.RmComment: 10 pages, 16 figures (gzipped postscript), see also http://www.physik.tu-darmstadt.de/tqe

Higher order eigenpair perturbations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76914/1/AIAA-11149-583.pd