31,177 research outputs found
The Structure of Langevin's Memory Kernel From Lagrangian Dynamics
We obtain the memory kernel of the generalized Langevin equation, describing
a particle interacting with longitudinal phonons in a liquid. The kernel is
obtained analytically at T=0 Kelvin and numerically at T>0 Kelvin. We find that
it shows some non-trivial structural features like negative correlations for
some range of time separations. The system is shown to have three
characteristic time scales, that control the shape of the kernel, and the
transition between quadratic and linear behavior of the mean squared distance
(MSD). Although the derivation of the structure in the memory kernel is
obtained within a specific dynamical model, the phenomenon is shown to be quite
generic.Comment: 8 pages, 5 figures, latex, include europhys.sty and euromacr.te
Energy conditions for a generally coupled scalar field outside a reflecting sphere
We calculate the stress-energy tensor for a scalar field with general
curvature coupling, outside a perfectly reflecting sphere with Dirichlet
boundary conditions. For conformal coupling we find that the null energy
condition is always obeyed, and therefore the averaged null energy condition
(ANEC) is also obeyed. Since the ANEC is independent of curvature coupling, we
conclude that the ANEC is obeyed for scalar fields with any curvature coupling
in this situation. We also show how the spherical case goes over to that of a
flat plate as one approaches the sphere.Comment: Accepted for publication in Phys. Rev.
Electron Self Energy for Higher Excited S Levels
A nonperturbative numerical evaluation of the one-photon electron self energy
for the 3S and 4S states with charge numbers Z=1 to 5 is described. The
numerical results are in agreement with known terms in the expansion of the
self energy in powers of Zalpha.Comment: 3 pages, RevTeX, to appear in Phys. Rev.
Lexicographic choice functions without archimedeanicity
We investigate the connection between choice functions and lexicographic probabilities, by means of the convexity axiom considered by Seidenfeld, Schervisch and Kadane (2010) but without imposing any Archimedean condition. We show that lexicographic probabilities are related to a particular type of sets of desirable gambles, and investigate the properties of the coherent choice function this induces via maximality. Finally, we show that the convexity axiom is necessary but not sufficient for a coherent choice function to be the infimum of a class of lexicographic ones
Generalized Supersymmetric Perturbation Theory
Using the basic ingredient of supersymmetry, we develop a simple alternative
approach to perturbation theory in one-dimensional non-relativistic quantum
mechanics. The formulae for the energy shifts and wave functions do not involve
tedious calculations which appear in the available perturbation theories. The
model applicable in the same form to both the ground state and excited bound
states, unlike the recently introduced supersymmetric perturbation technique
which, together with other approaches based on logarithmic perturbation theory,
are involved within the more general framework of the present formalism.Comment: 13 pages article in LaTEX (uses standard article.sty). No Figures.
Sent to Ann. Physics (2004
Virial Masses of Black Holes from Single Epoch Spectra of AGN
We describe the general problem of estimating black hole masses of AGN by
calculating the conditional probability distribution of M_BH given some set of
observables. Special attention is given to the case where one uses the AGN
continuum luminosity and emission line widths to estimate M_BH, and we outline
how to set up the conditional probability distribution of M_BH given the
observed luminosity, line width, and redshift. We show how to combine the broad
line estimates of M_BH with information from an intrinsic correlation between
M_BH and L, and from the intrinsic distribution of M_BH, in a manner that
improves the estimates of M_BH. Simulation was used to assess how the
distribution of M_BH inferred from the broad line mass estimates differs from
the intrinsic distribution, and we find that this can lead to an inferred
distribution that is too broad. We use these results and a sample of 25 sources
that have recent reverberation mapping estimates of AGN black hole masses to
investigate the effectiveness of using the C IV emission line to estimate M_BH
and to indirectly probe the C IV region size--luminosity (R--L) relationship.
We estimated M_BH from both C IV and H-Beta for a sample of 100 sources,
including new spectra of 29 quasars. We find that the two emission lines give
consistent estimates if one assumes R \propto L^{1/2}_{UV} for both lines.Comment: 38 pages, 6 figures, accepted by Ap
The oscillating wing with aerodynamically balanced elevator
The two-dimensional problem of the oscillating wing with aerodynamically balanced elevator is treated in the manner that the wing is replaced by a plate with bends and stages and the airfoil section by a mean line consisting of one or more straights. The computed formulas and tables permit, on these premises, the prediction of the pressure distribution and of the aerodynamic reactions of oscillating elevators and tabs with any position of elevator hinge in respect to elevator leading edge
The nature of the long time decay at a second order transition point
We show that at a second order phase transition, of \phi^4 like system, a
necessary condition for streched exponential decay of the time structure factor
is obeyed. Using the ideas presented in this proof a crude estimate of the
decay of the structure factor is obtained and shown to yield stretched
exponential decay under very reasonable conditions.Comment: 7 page
Hybrid simulations of lateral diffusion in fluctuating membranes
In this paper we introduce a novel method to simulate lateral diffusion of
inclusions in a fluctuating membrane. The regarded systems are governed by two
dynamic processes: the height fluctuations of the membrane and the diffusion of
the inclusion along the membrane. While membrane fluctuations can be expressed
in terms of a dynamic equation which follows from the Helfrich Hamiltonian, the
dynamics of the diffusing particle is described by a Langevin or Smoluchowski
equation. In the latter equations, the curvature of the surface needs to be
accounted for, which makes particle diffusion a function of membrane
fluctuations. In our scheme these coupled dynamic equations, the membrane
equation and the Langevin equation for the particle, are numerically integrated
to simulate diffusion in a membrane. The simulations are used to study the
ratio of the diffusion coefficient projected on a flat plane and the
intramembrane diffusion coefficient for the case of free diffusion. We compare
our results with recent analytical results that employ a preaveraging
approximation and analyze the validity of this approximation. A detailed
simulation study of the relevant correlation functions reveals a surprisingly
large range where the approximation is applicable.Comment: 12 pages, 9 figures, accepted for publication in Phys. Rev.
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