Thermal energies of classical and quantum damped oscillators coupled to reservoirs

We consider the global thermal state of classical and quantum harmonic oscillators that interact with a reservoir. Ohmic damping of the oscillator can be exactly treated with a 1D scalar field reservoir, whereas general non-Ohmic damping is conveniently treated with a continuum reservoir of harmonic oscillators. Using the diagonalized Hamiltonian of the total system, we calculate a number of thermodynamic quantities for the damped oscillator: the mean force internal energy, mean force free energy, and another internal energy based on the free-oscillator Hamiltonian. The classical mean force energy is equal to that of a free oscillator, for both Ohmic and non-Ohmic damping and no matter how strong the coupling to the reservoir. In contrast, the quantum mean force energy depends on the details of the damping and diverges for strictly Ohmic damping. These results give additional insight into the steady-state thermodynamics of open systems with arbitrarily strong coupling to a reservoir, complementing results for energies derived within dynamical approaches (e.g. master equations) in the weak-coupling regime.Comment: 13 page

An Enhanced Perturbational Study on Spectral Properties of the Anderson Model

The infinite-$U$ single impurity Anderson model for rare earth alloys is examined with a new set of self-consistent coupled integral equations, which can be embedded in the large $N$ expansion scheme ($N$ is the local spin degeneracy). The finite temperature impurity density of states (DOS) and the spin-fluctuation spectra are calculated exactly up to the order $O(1/N^2)$. The presented conserving approximation goes well beyond the $1/N$-approximation ({\em NCA}) and maintains local Fermi-liquid properties down to very low temperatures. The position of the low lying Abrikosov-Suhl resonance (ASR) in the impurity DOS is in accordance with Friedel's sum rule. For $N=2$ its shift toward the chemical potential, compared to the {\em NCA}, can be traced back to the influence of the vertex corrections. The width and height of the ASR is governed by the universal low temperature energy scale $T_K$. Temperature and degeneracy $N$-dependence of the static magnetic susceptibility is found in excellent agreement with the Bethe-Ansatz results. Threshold exponents of the local propagators are discussed. Resonant level regime ($N=1$) and intermediate valence regime ($|\epsilon_f| <\Delta$) of the model are thoroughly investigated as a critical test of the quality of the approximation. Some applications to the Anderson lattice model are pointed out.Comment: 19 pages, ReVTeX, no figures. 17 Postscript figures available on the WWW at http://spy.fkp.physik.th-darmstadt.de/~frithjof

Tunable superlattice p-i-n photodetectors: characteristics, theory, and application

Extended measurements and theory on the recently developed monolithic wavelength demultiplexer consisting of voltage-tunable superlattice p-i-n photodetectors in a waveguide confirmation are discussed. It is shown that the device is able to demultiplex and detect two optical signals with a wavelength separation of 20 nm directly into different electrical channels at a data rate of 1 Gb/s and with a crosstalk attenuation varying between 20 and 28 dB, depending on the polarization. The minimum acceptable crosstalk attenuation at a data rate of 100 Mb/s is determined to be 10 dB. The feasibility of using the device as a polarization angle sensor for linearly polarized light is also demonstrated. A theory for the emission of photogenerated carriers out of the quantum wells is included, since this is potentially a speed limiting mechanism in these detectors. It is shown that a theory of thermally assisted tunneling by polar optical phonon interaction is able to predict emission times consistent with the observed temporal response

The Separation Principle in Stochastic Control, Redux

Over the last 50 years a steady stream of accounts have been written on the separation principle of stochastic control. Even in the context of the linear-quadratic regulator in continuous time with Gaussian white noise, subtle difficulties arise, unexpected by many, that are often overlooked. In this paper we propose a new framework for establishing the separation principle. This approach takes the viewpoint that stochastic systems are well-defined maps between sample paths rather than stochastic processes per se and allows us to extend the separation principle to systems driven by martingales with possible jumps. While the approach is more in line with "real-life" engineering thinking where signals travel around the feedback loop, it is unconventional from a probabilistic point of view in that control laws for which the feedback equations are satisfied almost surely, and not deterministically for every sample path, are excluded.Comment: 23 pages, 6 figures, 2nd revision: added references, correction

On time-reversibility of linear stochastic models

Reversal of the time direction in stochastic systems driven by white noise has been central throughout the development of stochastic realization theory, filtering and smoothing. Similar ideas were developed in connection with certain problems in the theory of moments, where a duality induced by time reversal was introduced to parametrize solutions. In this latter work it was shown that stochastic systems driven by arbitrary second-order stationary processes can be similarly time-reversed. By combining these two sets of ideas we present herein a generalization of time-reversal in stochastic realization theory.Comment: 10 pages, 4 figure

Likelihood Analysis of Power Spectra and Generalized Moment Problems

We develop an approach to spectral estimation that has been advocated by Ferrante, Masiero and Pavon and, in the context of the scalar-valued covariance extension problem, by Enqvist and Karlsson. The aim is to determine the power spectrum that is consistent with given moments and minimizes the relative entropy between the probability law of the underlying Gaussian stochastic process to that of a prior. The approach is analogous to the framework of earlier work by Byrnes, Georgiou and Lindquist and can also be viewed as a generalization of the classical work by Burg and Jaynes on the maximum entropy method. In the present paper we present a new fast algorithm in the general case (i.e., for general Gaussian priors) and show that for priors with a specific structure the solution can be given in closed form.Comment: 17 pages, 4 figure

Unexpected Accumulation of ncm\u3csup\u3e5\u3c/sup\u3eU and ncm\u3csup\u3e5\u3c/sup\u3es\u3csup\u3e2\u3c/sup\u3eU in a \u3cem\u3etrm9\u3c/em\u3e Mutant Suggests an Additional Step in the Synthesis of mcm\u3csup\u3e5\u3c/sup\u3eU and mcm\u3csup\u3e5\u3c/sup\u3es\u3csup\u3e2\u3c/sup\u3eU

Background Transfer RNAs are synthesized as a primary transcript that is processed to produce a mature tRNA. As part of the maturation process, a subset of the nucleosides are modified. Modifications in the anticodon region often modulate the decoding ability of the tRNA. At position 34, the majority of yeast cytosolic tRNA species that have a uridine are modified to 5-carbamoylmethyluridine (ncm5U), 5-carbamoylmethyl-2′-O-methyluridine (ncm5Um), 5-methoxycarbonylmethyl-uridine (mcm5U) or 5-methoxycarbonylmethyl-2-thiouridine (mcm5s2U). The formation of mcm5 and ncm5 side chains involves a complex pathway, where the last step in formation of mcm5 is a methyl esterification of cm5 dependent on the Trm9 and Trm112 proteins. Methodology and Principal Findings Both Trm9 and Trm112 are required for the last step in formation of mcm5 side chains at wobble uridines. By co-expressing a histidine-tagged Trm9p together with a native Trm112p in E. coli, these two proteins purified as a complex. The presence of Trm112p dramatically improves the methyltransferase activity of Trm9p in vitro. Single tRNA species that normally contain mcm5U or mcm5s2U nucleosides were isolated from trm9Δ or trm112Δ mutants and the presence of modified nucleosides was analyzed by HPLC. In both mutants, mcm5U and mcm5s2U nucleosides are absent in tRNAs and the major intermediates accumulating were ncm5U and ncm5s2U, not the expected cm5U and cm5s2U. Conclusions Trm9p and Trm112p function together at the final step in formation of mcm5U in tRNA by using the intermediate cm5U as a substrate. In tRNA isolated from trm9Δ and trm112Δ strains, ncm5U and ncm5s2U nucleosides accumulate, questioning the order of nucleoside intermediate formation of the mcm5 side chain. We propose two alternative explanations for this observation. One is that the intermediate cm5U is generated from ncm5U by a yet unknown mechanism and the other is that cm5U is formed before ncm5U and mcm5U

Anyons on Higher Genus Surfaces - a Constructive Approach

We reconsider the problem of anyons on higher genus surfaces by embedding them in three dimensional space. From a concrete realization based on three dimensional flux tubes bound to charges moving on the surface, we explicitly derive all the representations of the spinning braid group. The component structure of the wave functions arises from winding the flux tubes around the handles. We also argue that the anyons in our construction must fulfil the generalized spin-statistics relation.Comment: 8 pages, LaTex, 2 figures available on request ([email protected]), USITP-93-1