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ÍÅÑÒÀÁÈËÜÍÛÅ ÊÂÀÍÒÎÂÛÅ ÑÈÑÒÅÌÛ È ÈÍÒÅÃÐÀËÛ ÔÅÉÍÌÀÍÀ

Ï. Ýêñíåð

Îáúåäèíåííûé èíñòèòóò ÿäåðíûõ èññëåäîâàíèé, Äóáíà

Ðàññìàòðèâàþòñÿ îáùèå ñâîéñòâà íåñòàáèëüíûõ ñèñòåì (÷àñòèö, ÿäåð è ò. ä.) Ñôîðìóëèðîâàí îñíîâíîé êðèòåðèé äëÿ ñóùåñòâîâàíèÿ ðåøåíèÿ îáðàòíîé çàäà÷è ðàñïàäà. Ðàññìîòðåíî âëèÿíèå ïîâòîðíûõ èçìåðåíèé íà ýêñïîíåíöèàëüíîñòü çàêîíîâ ðàñïàäà è èçìåðÿåìîå âðåìÿ æèçíè. Îöåíêà ïîðÿäêà ýòèõ ýôôåêòîâ ïðîâåäåíà â ðàìêàõ ìîäåëè ðàñïàäà çàðÿæåííûõ êàîíîâ â ïóçûðüêîâîé êàìåðå. Ýòè ñîîáðàæåíèÿ äàþò ôèçè÷åñêîå îñíîâàíèå äëÿ ïîëóãðóïïîâîãî ïðèáëèæåíèÿ ïðè îïèñàíèè äèíàìèêè íåñòàáèëüíûõ ñèñòåì. Ïîêàçàíî, ÷òî âñÿêóþ òàêóþ ïîëóãðóïïó ìîæíî õàðàêòåðèçîâàòü òàê íàçûâàåìûì ïñåâäîãàìèëüòîíèàíîì. Óêàçàíà ñâÿçü ýòîãî ïñåâäîãàìèëüòîíèàíà ñ ïîëíûì ãàìèëüòîíèàíîì ñèñòåìû. Äàåòñÿ îáçîð ñòðîãèõ ïîäõîäîâ ê îïðåäåëåíèþ èíòåãðàëîâ Ôåéíìàíà. Ïîêàçàíî, êàê â ðàìêàõ íåêîòîðûõ èç ýòèõ ïîäõîäîâ ìîæíî âûðàçèòü ýâîëþöèîííûé îïåðàòîð, ñîîòâåòñòâóþùèé ïñåâäîãàìèëüòîíèàíó øðåäèíãåðîâñêîãî òèïà ñ ëîêàëüíûì êîìïëåêñíûì ïîòåíöèàëîì.  êà÷åñòâå ïðèìåðà ðàññìîòðåí ìíîãîìåðíûé çàòóõàþùèé ãàðìîíè÷åñêèé îñöèëëÿòîð.

General properties of unstable quantum systems (as elementary particles, nuclei etc.) are discussed. The basic criterion is formulated for existence of a solution to the inverse decay problem. Further we discuss influence of repeated measurements on the decay law exponentiality and the measured lifetime; an order of magnitude of this effect is estimated within a model describing the decay of charged kaons in a bubble chamber. These considerations can be used to justify physically the semigroup approximation for describing dynamics of unstable systems. Each such semigroup can be characterized by a so-called pseudo-Hamiltonian; relations of the latter to the total Hamiltonian of the system are given. Further we review rigorous approaches to the Feynman path integrals, and we show how the evolution operator corresponding to Schrdinger pseudo-Hamiltonian with a local complex potential can be expressed within some of these approaches. As an example, the multidimensional damped harmonic oscillator is discussed.

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