11,034 research outputs found
Path integrals and symmetry breaking for optimal control theory
This paper considers linear-quadratic control of a non-linear dynamical
system subject to arbitrary cost. I show that for this class of stochastic
control problems the non-linear Hamilton-Jacobi-Bellman equation can be
transformed into a linear equation. The transformation is similar to the
transformation used to relate the classical Hamilton-Jacobi equation to the
Schr\"odinger equation. As a result of the linearity, the usual backward
computation can be replaced by a forward diffusion process, that can be
computed by stochastic integration or by the evaluation of a path integral. It
is shown, how in the deterministic limit the PMP formalism is recovered. The
significance of the path integral approach is that it forms the basis for a
number of efficient computational methods, such as MC sampling, the Laplace
approximation and the variational approximation. We show the effectiveness of
the first two methods in number of examples. Examples are given that show the
qualitative difference between stochastic and deterministic control and the
occurrence of symmetry breaking as a function of the noise.Comment: 21 pages, 6 figures, submitted to JSTA
Scaling for Interfacial Tensions near Critical Endpoints
Parametric scaling representations are obtained and studied for the
asymptotic behavior of interfacial tensions in the \textit{full} neighborhood
of a fluid (or Ising-type) critical endpoint, i.e., as a function \textit{both}
of temperature \textit{and} of density/order parameter \textit{or} chemical
potential/ordering field. Accurate \textit{nonclassical critical exponents} and
reliable estimates for the \textit{universal amplitude ratios} are included
naturally on the basis of the ``extended de Gennes-Fisher'' local-functional
theory. Serious defects in previous scaling treatments are rectified and
complete wetting behavior is represented; however, quantitatively small, but
unphysical residual nonanalyticities on the wetting side of the critical
isotherm are smoothed out ``manually.'' Comparisons with the limited available
observations are presented elsewhere but the theory invites new, searching
experiments and simulations, e.g., for the vapor-liquid interfacial tension on
the two sides of the critical endpoint isotherm for which an amplitude ratio
is predicted.Comment: 42 pages, 6 figures, to appear in Physical Review
The possible explanation of electric-field-doped C60 phenomenology in the framework of Eliashberg theory
In a recent paper (J.H. Schon, Ch. Kloc, R.C. Haddon and B. Batlogg, Nature
408 (2000) 549) a large increase in the superconducting critical temperature
was observed in C60 doped with holes by application of a high electric field.
We demonstrate that the measured Tc versus doping curves can be explained by
solving the (four) s-wave Eliashberg equations in the case of a finite,
non-half-filled energy band. In order to reproduce the experimental data, we
assume a Coulomb pseudopotential depending on the filling in a very simple and
plausible way. Reasonable values of the physical parameters involved are
obtained. The application of the same approach to new experimental data (J.H.
Schon, Ch. Kloc and B. Batlogg, Science 293 (2001) 2432) on electric
field-doped, lattice-expanded C60 single crystals (Tc=117 K in the hole-doped
case) gives equally good results and sets a theoretical limit to the linear
increase of Tc at the increase of the lattice spacing.Comment: latex2e, 6 pages, 7 figures, 1 table, revised versio
Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins
Without invoking the Markov approximation, we derive formulas for vibrational
energy relaxation (VER) and dephasing for an anharmonic system oscillator using
a time-dependent perturbation theory. The system-bath Hamiltonian contains more
than the third order coupling terms since we take a normal mode picture as a
zeroth order approximation. When we invoke the Markov approximation, our theory
reduces to the Maradudin-Fein formula which is used to describe VER properties
of glass and proteins. When the system anharmonicity and the renormalization
effect due to the environment vanishes, our formulas reduce to those derived by
Mikami and Okazaki invoking the path-integral influence functional method [J.
Chem. Phys. 121 (2004) 10052]. We apply our formulas to VER of the amide I mode
of a small amino-acide like molecule, N-methylacetamide, in heavy water.Comment: 16 pages, 5 figures, 5 tables, submitted to J. Chem. Phy
Competitive market for multiple firms and economic crisis
The origin of economic crises is a key problem for economics. We present a
model of long-run competitive markets to show that the multiplicity of
behaviors in an economic system, over a long time scale, emerge as statistical
regularities (perfectly competitive markets obey Bose-Einstein statistics and
purely monopolistic-competitive markets obey Boltzmann statistics) and that how
interaction among firms influences the evolutionary of competitive markets. It
has been widely accepted that perfect competition is most efficient. Our study
shows that the perfectly competitive system, as an extreme case of competitive
markets, is most efficient but not stable, and gives rise to economic crises as
society reaches full employment. In the economic crisis revealed by our model,
many firms condense (collapse) into the lowest supply level (zero supply,
namely bankruptcy status), in analogy to Bose-Einstein condensation. This
curious phenomenon arises because perfect competition (homogeneous
competitions) equals symmetric (indistinguishable) investment direction, a fact
abhorred by nature. Therefore, we urge the promotion of monopolistic
competition (heterogeneous competitions) rather than perfect competition. To
provide early warning of economic crises, we introduce a resolving index of
investment, which approaches zero in the run-up to an economic crisis. On the
other hand, our model discloses, as a profound conclusion, that the
technological level for a long-run social or economic system is proportional to
the freedom (disorder) of this system; in other words, technology equals the
entropy of system. As an application of this new concept, we give a possible
answer to the Needham question: "Why was it that despite the immense
achievements of traditional China it had been in Europe and not in China that
the scientific and industrial revolutions occurred?"Comment: 17 pages; 3 figure
Bayesian credible interval construction for Poisson statistics
The construction of the Bayesian credible (confidence) interval for a Poisson
observable including both the signal and background with and without systematic
uncertainties is presented. Introducing the conditional probability satisfying
the requirement of the background not larger than the observed events to
construct the Bayesian credible interval is also discussed. A Fortran routine,
BPOCI, has been developed to implement the calculation.Comment: 7 pages, 1 figur
Coexistence of hexatic and isotropic phases in two-dimensional Yukawa systems
We have performed Brownian dynamics simulations on melting of two-dimensional
colloidal crystal in which particles interact with Yukawa potential. The pair
correlation function and bond-orientational correlation function was calculated
in the Yukawa system. An algebraic decay of the bond orientational correlation
function was observed. By ruling out the coexistence region, only a unstable
hexatic phase was found in the Yukawa systems. But our work shows that the
melting of the Yukawa systems is a two-stage melting not consist with the KTHNY
theory and the isotropic liquid and the hexatic phase coexistence region was
found. Also we have studied point defects in two-dimensional Yukawa systems.Comment: 9 pages, 8 figures. any comments are welcom
Theoretical evidence for the superluminality of evanescent modes
Though both theoretical and experimental investigations have revealed the
superluminal behavior of evanescent electromagnetic waves, there are many
disputes about the physical meaning and validity of such superluminal
phenomenon, which is due to the fact that the traditional investigations are
based on the theory of tunneling time, and concerned with the problem of what
the group velocity of evanescent waves means. In this paper, by studying the
quantum probability amplitude for photons to propagate over a spacelike
interval along an undersized waveguide, we present theoretical evidence for
such superluminality
A New Method of Probing the Phonon Mechanism in Superconductors including MgB
Weak localization has a strong influence on both the normal and
superconducting properties of metals. In particular, since weak localization
leads to the decoupling of electrons and phonons, the temperature dependence of
resistance (i.e., ) is decreasing with increasing disorder, as
manifested by Mooij's empirical rule. In addition, Testardi's universal
correlation of (i.e., ) and the resistance ratio (i.e.,
) follows. This understanding provides a new means to probe the
phonon mechanism in superconductors including MgB. The merits of this
method are its applicability to any superconductors and its reliability because
the McMillan's electron-phonon coupling constant and
change in a broad range, from finite values to zero, due to weak localization.
Karkin et al's preliminary data of irradiated MgB show the Testardi
correlation, indicating that the dominant pairing mechanism in MgB is the
phonon-mediated interaction.Comment: 9 pages, latex, 3 figure
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