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101.
Erik G. F. Thomas 《Acta Appl Math》1996,43(2):191-232
We construct an analogue of the Feynman path integral for the case of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% aaaeaacaaIXaaabaGaamyAaaaadaWcaaqaaiabgkGi2cqaaiabgkGi% 2kaadshaaaqeduuDJXwAKbYu51MyVXgaiuaacqWFvpGAcaWG0bGaey% ypa0JaamisamaaBaaaleaacaGGOaaabeaakmaaBaaaleaacaGGPaaa% beaakiab-v9aQjaadshaaaa!4A8D!\[ - \frac{1}{i}\frac{\partial }{{\partial t}}\varphi t = H_( _) \varphi t\] in which H
() is a self-adjoint operator in the space L
2(M)= % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeSOaHmkaaa!3744!\[\mathbb{C}\], where
M
is a finite set, the paths being functions of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeSyhHekaaa!375D!\[\mathbb{R}\] with values in M. The path integral is a family of measures F
t,t with values in the operators on L
2(M), or equivalently, a family of complex measures corresponding to matrix coefficients.It is shown that these measures on path space are in some sense dominated by the measure of a Markov process. This implies that F
t,t is concentrated on the set of step functions S[t,t].This allows one to make sense of, and prove, the analogue of Feynman's formula for the propagator of the Hamiltonian H=H
0+V, where V is a potential, namely the formula: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyzamaaCa% aaleqabaGaeyOeI0IaamyAaiaacIcacaWG0bGaai4jaiabgkHiTiaa% dshacaGGPaGaamisaaaakiabg2da9maapebabaGaaeyzamaaCaaale% qabaGaeyOeI0IaamyAamaapedabaGaamOvaiaacIcatCvAUfKttLea% ryqr1ngBPrgaiuGacqWF4baEcaGGOaGaam4CaiaacMcacaGGPaGaae% izaiaabohaaWqaaiaadshaaeaacaWG0bGaai4jaaGdcqGHRiI8aaaa% kiaadAeadaWgaaWcbaGaamiDaiaacEcacaGGSaGaamiDaaqabaGcca% GGOaGaaeizaiab-Hha4jaacMcaaSqaaiaadofacaGGBbGaamiDaiaa% cYcacaWG0bGaai4jaiaac2faaeqaniabgUIiYdaaaa!6410!\[{\text{e}}^{ - i(t' - t)H} = \int_{S[t,t']} {{\text{e}}^{ - i\int_t^{t'} {V(x(s)){\text{ds}}} } F_{t',t} ({\text{d}}x)} \]and the corresponding formulas for the matrix coefficients, in which the integral extends over the paths beginning and ending in the appropriate points. We show that the measures F
t,t are completely determined by these equations and by a certain multiplicative property.The path integral corresponding to a two-particle system without interaction is the direct product of the corresponding path integrals. The propagator for a two-particle system with interaction can be obtained by repeated integration.Finally, we show that the above integral formula can be generalized to the case where the potential is time dependent. 相似文献
102.
103.
Gerhard Hasslinger Erik S. Rieger 《The Journal of the Operational Research Society》1996,47(5):640-653
This paper deals with approximate analysis methods for open queueing networks. External and internal flows from and to the nodes are characterized by renewal processes with discrete time distributions of their interarrival times. Stationary distributions of the waiting time, the queue size and the interdeparture times are obtained using efficient discrete time algorithms for single server (GI/G/1) and multi-server (GI/D/c) nodes with deterministic service. The network analysis is extended to semi-Markovian representations of each flow among the nodes, which include parameters of the autocorrelation function. 相似文献
104.
105.
106.
A beam of relativistic antihydrogen atoms — the bound state (
e+) — can be created by circulating the beam of an antiproton storage ring through an internal gas target. An antiproton which
passes through the Coulomb field of a nucleus will create e+e− pairs, and antihydrogen will form when a positron is created in a bound instead of continuum state about the antiproton.
The cross section for this process is roughly 3Z
2 pb for antiproton momenta about 6 GeV/c. A sample of 600 antihydrogen atoms in a low-emittance, neutral beam will be made in 1995 as an accidental byproduct of Fermilab
experiment E760. We describe a simple experiment, Fermilab Proposal P862, which can detect this beam, and outline how a sample
of a few-104 atoms can be used to measure the antihydrogen Lamb shift to 1 %.
Work supported in part by Department of Energy contract DE-AC03-76SF00515 (SLAC).
Work supported by Fondo Nacional de Investigación Científica y Tecnológica, Chile. 相似文献
107.
Summary We prove that every mixing
d
by automorphisms of a compact, connected, abelian group is mixing of all orders.Oblatum 5-II-1992The second author gratefully acknowledges support from NSF grant DMS-91-03056 at the Ohio State University 相似文献
108.
109.
Bean A Gronberg J Kutschke R Menary S Morrison RJ Nelson H Richman J Tajima H Schmidt D Sperka D Witherell M Procario M Yang S Daoudi M Ford WT Johnson DR Lingel K Lohner M Rankin P Smith JG Alexander JP Bebek C Berkelman K Besson D Browder TE Cassel DG Coffman DM Drell PS Ehrlich R Galik RS Garcia-Sciveres M Geiser B Gittelman B Gray SW Hartill DL Heltsley BK Honscheid K Jones C Kandaswamy J Katayama N Kim PC Kreinick DL Ludwig GS Masui J Mevissen J Mistry NB Ng CR Nordberg E O'Grady C 《Physical review letters》1993,70(2):138-142
110.
Schmidt R Blaich T Elze TW Emling H Freiesleben H Grimm K Henning W Holzmann R Keller JG Klingler H Kulessa R Kratz JV Lambrecht D Lange JS Leifels Y Lubkiewicz E Moore EF Wajda E Prokopowicz W Schütter C Spies H Stelzer K Stroth J Walus W Wollersheim HJ Zinser M Zude E 《Physical review letters》1993,70(12):1767-1770