摘要:

In 1946 Cameron and Martin concluded a paper [‘‘The orthogonal development of non‐linear functionals in series of Fourier–Hermite functionals,’’ Ann. Math.48, 385–392 (1947)] by saying: ‘‘This paper opens up the whole set of techniques of Orthogonal Developments...for use...in the study of non‐linear functionals... .’’ Here, the Cameron–Martin–Wiener expansion is developed with mathematics familiar to physicists, and its use is illustrated and applied to a quantum theory of electron transport.

ISSN:0002-9505    

DOI:10.1119/1.16194

出版商:American Association of Physics Teachers    

年代:1990

数据来源: AIP

摘要:

While no simple image method exists that yields an exact solution for the potential around the parallel conducting cylinders of a quadrupole electrostatic lens, we have found that using two line image charges in each cylinder makes an excellent approximation. Graphs are presented of the equipotentials and contours of electric field squared for different rod spacing.

ISSN:0002-9505    

DOI:10.1119/1.16195

出版商:American Association of Physics Teachers    

年代:1990

数据来源: AIP

摘要:

Lise Meitner (1878–1968) achieved prominence as a nuclear physicist in Germany; although of Jewish origin, her Austrian citizenship exempted her from Nazi racial laws until the annexation of Austria in 1938 precipitated her dismissal. Forbidden to emigrate, she narrowly escaped to the Netherlands with the help of concerned friends in the international physics community.

ISSN:0002-9505    

DOI:10.1119/1.16196

出版商:American Association of Physics Teachers    

年代:1990

数据来源: AIP

摘要:

An elementary discussion of the statistical properties of theproductofNindependent random variables is given. The motivation is to emphasize the essential differences between the asymptoticN→∞ behavior of a random product and the asymptotic behavior of asumof random variables—a random additive process. For this latter process, it is widely appreciated that the asymptotic behavior of the sum and its distribution is provided by the central limit theorem. However, no such universal principle exists for a random multiplicative process. In this case, the ratio between the average value of the product 〈P〉 and the most probable valuePmpdiverges exponentially inNasN→∞. Within a continuum approximation, the classical log‐normal form is often invoked to describe the distribution of the product. It is shown, however, that the log‐normal provides a poor approximation for the asymptotic behavior of the average value and, also, for the higher moments of the product. A procedure for computing the correct leading asymptotic behavior of the moments is outlined. The implications of these results for simulations of random multiplicative processes are also discussed. For such a simulation, the numerically observed ‘‘average’’ value of the product is of the order ofPmp, and it is only when the simulation is large enough to sample a finite fraction of all the states in the system that a monotonic crossover to the true average value 〈P〉 occurs. An idealized, but quantitative account for this crossover is provided.

ISSN:0002-9505    

DOI:10.1119/1.16497

出版商:American Association of Physics Teachers    

年代:1990

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.16197

出版商:American Association of Physics Teachers    

年代:1990

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.16198

出版商:American Association of Physics Teachers    

年代:1990

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.16199

出版商:American Association of Physics Teachers    

年代:1990

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.16200

出版商:American Association of Physics Teachers    

年代:1990

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.16201

出版商:American Association of Physics Teachers    

年代:1990

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.16202

出版商:American Association of Physics Teachers    

年代:1990

数据来源: AIP