20,844 research outputs found
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
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
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
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
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
Teaching computers to fold proteins
A new general algorithm for optimization of potential functions for protein
folding is introduced. It is based upon gradient optimization of the
thermodynamic stability of native folds of a training set of proteins with
known structure. The iterative update rule contains two thermodynamic averages
which are estimated by (generalized ensemble) Monte Carlo. We test the learning
algorithm on a Lennard-Jones (LJ) force field with a torsional angle
degrees-of-freedom and a single-atom side-chain. In a test with 24 peptides of
known structure, none folded correctly with the initial potential functions,
but two-thirds came within 3{\AA} to their native fold after optimizing the
potential functions.Comment: 4 pages, 3 figure
An Enhanced Perturbational Study on Spectral Properties of the Anderson Model
The infinite- 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 expansion scheme ( 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 . The
presented conserving approximation goes well beyond the -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 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 . Temperature and
degeneracy -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 () and intermediate
valence regime () 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
A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models
We present a novel technique for the calculation of dynamical correlation
functions of quantum impurity systems in equilibrium with Wilson's numerical
renormalization group. Our formulation is based on a complete basis set of the
Wilson chain. In contrast to all previous methods, it does not suffer from
overcounting of excitation. By construction, it always fulfills sum rules for
spectral functions. Furthermore, it accurately reproduces local thermodynamic
expectation values, such as occupancy and magnetization, obtained directly from
the numerical renormalization group calculations.Comment: 13 pages, 7 figur
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