Hyperbolic Motion in the Finite-size Model of the Radiating Electron

1975 ◽  
Vol 30 (12) ◽  
pp. 1535-1542
Author(s):  
M. Sorg
Keyword(s):  
Exact Solution ◽  
Field Strength ◽  
External Field ◽  
Critical Phenomena ◽  
Finite Size ◽  
Momentum Balance ◽  
Hyperbolic Motion ◽  
Size Model

Abstract Within the framework of the finite-size model of the electron recently dovelopped the case of hyperbolic motion is studied rigorously by means of an exact solution. The energy-momentum balance is discussed as well as the critical phenomena arising if the external field strength comes into the range of order of the maximal self-field strength of the particle. It is found that the commonly accepted Lorentz-Dirac-Rohrlich theory is only a good approximation for small values of the external field strength.

The Problem of Runaway Solutions in the Lorentz-Dirac Theory

1976 ◽  
Vol 31 (7) ◽  
pp. 683-689
Author(s):  
M. Sorg
Keyword(s):  
Dirac Equation ◽  
General Theory ◽  
Finite Size ◽  
Finite Extension ◽  
Point Of View ◽  
Existence Proof ◽  
Dirac Theory ◽  
Hyperbolic Motion ◽  
Size Model

Abstract A rigorous non-existence proof for runaway solutions in the finite-size model of the electron is given. Since a consistent point limit, such as the Lorentz-Dirac equation claims to be, should not exhibit features which are completely missing in the more general theory of finite extension, it is proposed that the point-like approximation of the finite-size theory be the integrodifferential formulation of the Lorentz-Dirac theory. This point of view is supported by a new discussion of the hyperbolic motion in the latter theory.

Classical, Covariant Finite-size Model of the Radiating Electron

1974 ◽  
Vol 29 (11) ◽  
pp. 1671-1684 ◽  
Author(s):  
M. Sorg
Keyword(s):  
Dirac Equation ◽  
Finite Size ◽  
Finite Extension ◽  
Equation Of Motion ◽  
Mass Renormalization ◽  
Classical Electron ◽  
Size Model

The finite extension of the classical electron is defined in a new, covariant manner. This new definition enables one to calculate exactly the bound and emitted four-momentum and to find an equation of motion different from the Lorentz-Dirac equation and from other equations proposed in the literature. Neither mass renormalization nor use of advanced quantities nor asymptotic conditions are necessary. Runaway solutions and pre-acceleration do not occur in the framework of the model presented here.

Exact Dynamics in a Model of the Bimolecular Reaction A+B→ 0

1992 ◽  
Vol 290 ◽  
Author(s):  
Eric Clément ◽  
Patrick Leroux-Hugon ◽  
Leonard M. Sander
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Initial Conditions ◽  
Finite Size ◽  
Bimolecular Reaction ◽  
Reaction Model

AbstractWe have previously given an exact solution [1] for the steady state of a model of the bimolecular reaction model A+B→ 0 due to Fichthorn et al. [2]. The dimensionality of the substrate plays a central role, and below d=2 segregation on macroscopic scales becomes important: above d=2 saturation sets in for finite size systems. Here we extend our treatment to give an exact account of the dynamics and show how various initial conditions develop into the segregated and saturated regimes. In certain conditions we find logarithmic relaxation which is related to the dimensionality.

scholarly journals Derivative expansion for the one-loop effective Lagrangian in QED

1996 ◽  
Vol 74 (5-6) ◽  
pp. 282-289 ◽  
Author(s):  
V. P. Gusynin ◽  
I. A. Shovkovy
Keyword(s):  
Electromagnetic Field ◽  
Field Strength ◽  
External Field ◽  
Explicit Expression ◽  
Derivative Expansion ◽  
Effective Lagrangian ◽  
Constant Electromagnetic Field ◽  
The One ◽  
Derivatives Of

The derivative expansion of the one-loop effective Lagrangian in QED4 is considered. The first term in such an expansion is the famous Schwinger result for a constant electromagnetic field. In this paper we give an explicit expression for the next term containing two derivatives of the field strength Fμν. The results are presented for both fermion and scalar electrodynamics. Some possible applications of an inhomogeneous external field are pointed out.

The Curie–Weiss–Néel model of a ferrimagnet

1981 ◽  
Vol 59 (7) ◽  
pp. 883-887 ◽  
Author(s):  
R. G. Bowers ◽  
S. L. Schofield
Keyword(s):  
Exact Solution ◽  
Critical Phenomena ◽  
Critical Exponents ◽  
Mean Field ◽  
The Other ◽  
New Model ◽  
Total Magnetization ◽  
Present Context ◽  
Elementary Methods ◽  
Parallel Fashion

An analogue, for ferrimagnetism, of the Curie–Weiss model ferromagnet is introduced. The resulting structure, the Curie–Weiss–Néel model, is based on a two sublattice description in which spins of one magnitude occupy one sublattice and spins of another magnitude occupy the other. Attention is concentrated on the case in which spins on the different sublattices tend to align in an anti-parallel fashion. Many properties of the new model are similar to those of the Curie–Weiss ferromagnet. Artificially long-ranged interactions connect spins on the different sublattices. The complete thermodynamics can be obtained exactly by relatively elementary methods. The exact solution of the model is essentially identical with the appropriate mean field results (of Néel). Attention is given to the Néel point and associated critical phenomena. Many standard critical exponents are calculated and, of course, classical exponent values result. Novel features of critical phenomena in ferrimagnets are considered. These are associated with the fact that, theoretically, the staggered magnetization and staggered fields are important while, experimentally, the total magnetization and uniform fields are usually employed. It is shown that, within the present context, corresponding staggered and uniform properties have identical exponent values.

Exact solution of the thermodynamics and size parameters of a polymer confined to a lattice of finite size: Large chain limit

2014 ◽  
Vol 140 (3) ◽  
pp. 034905 ◽  
Author(s):  
Chad R. Snyder ◽  
Charles M. Guttman ◽  
Edmund A. Di Marzio
Keyword(s):  
Exact Solution ◽  
Finite Size

Elektrochromie von Chlorophyll-a und Chlorophyll-b in monomolekularen Filmen / Electrochromie Effects of a Chlorophyll a and a Chlorophyll b Monolayer

1969 ◽  
Vol 24 (11) ◽  
pp. 1371-1374 ◽  
Author(s):  
D. Kleuser ◽  
H. Bücher
Keyword(s):  
Fatty Acid ◽  
Optical Absorption ◽  
Field Strength ◽  
External Field ◽  
Electric Field ◽  
Chlorophyll A ◽  
Chlorophyll B ◽  
Chlorophyll A And B ◽  
Electrochromic Effect

A electric field induced linear and quadratic change in the optical absorption of a chlorophyll a and chlorophyll b monolayer is reported. The chlorophylls are incorporated in a fatty acid monolayer condenser which allows the application of external field strength up to 4 · 106 V/cm. The spectrum of the quadratic electrochromic effect shows evidence of different species of aggregates of chlorophyll a and of different behaviour of aggregation of chlorophyll a and b.

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