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ФИЗИКА ЭЛЕМЕНТАРНЫХ ЧАСТИЦ И АТОМНОГО ЯДРА

Вероятность квантовых переходов в стохастическом процессе в пространстве совместных событий: Аннотации

A. A. Biryukov, A. A. Бирюков

Published May 31, 2024• 0 citations
OpenAlex

Abstract

The evolution of the system is described as a stochastic process in the space of random joint events. A symmetric difference and a symmetric sum of random joint events are introduced in the space. The probability of quantum transitions of the system between certain random events is represented by the sum of the probabilities of joint events (two, three...). It is noteworthy that the obtained expression for the transition probabilities coincides with that for the transition probability in quantum theory, if only pairwise joint random events are taken into account in the model.

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The evolution of the system is described as a stochastic process in the space of random joint events. A symmetric difference and a symmetric sum of random joint events are introduced in the space. The probability of quantum transitions of the system between certain random events is represented by the sum of the probabilities of joint events (two, three...). It is noteworthy that the obtained expression for the transition probabilities coincides with that for the transition probability in quantum theory, if only pairwise joint random events are taken into account in the model.
Abstract The evolution of the system is described as a stochastic process in the space of random joint events. A symmetric difference and a symmetric sum of random joint events are introduced in space. The probability of quantum transitions of the system between certain random events is represented by the sum of the probabilities of joint events (two, three, … ). It is noteworthy that the obtained expression for the transition probabilities coincides with the transition probability in quantum theory, if only pairwise joint random events are taken into account in the model.
Abstract The evolution of the system is described as a stochastic process in the space of random joint events, in which both a symmetric difference and a symmetric sum of events are introduced. The probability of a system transition between states is represented by a series of double, triple, etc., integrals of real functionals of joint event trajectories. The expression coincides with the transition probability in quantum theory if only pairwise joint random trajectories are taken into account in the model.
A model of the space of random joint events is constructed. In the space, along with the existence of a symmetric difference of joint events, a new postulate about the existence of a symmetric sum of random joint events is introduced. In the generated space, a stochastic equation of the system motion and an equation for the probabilities of the system transition between two events are constructed. The probability of transition depends on the probabilities of compatibility of two, three, etc. events. The equation is equivalent to the equation of quantum theory if the events are compatible only in pairs. The proposed equation for incompatible events passes into the equation of the Markov chain.
The dynamics of the system in the space of random joint events is considered. The symmetric difference of events is introduced in space based on the Kolmogorov axioms. To describe quantum effects in the dynamics of the system, an additional axiom is introduced for random joint events: “the symmetric sum of random events.” In the generated space of random joint events, an equation is constructed for the probability of a system transition between two events. It is shown that for pairwise joint events it is equivalent to the equation of quantum mechanics.
Для унитарных расширений квантовой динамической полугруппы в квантовой теории вероятностей мы изучаем их аналог в классической теории вероятностей.Для заданной (не обязательно однородной) марковской цепи с дискретным временем и конечным пространством состояний E мы вводим еще одну систему -среду и детерминированную, обратимую, однородную во времени эволюцию системы E в этой среде такую, что начальная марковская эволюция пространства E реализуется правильным выбором начального случайного состояния среды.Мы также сравниваем это расширение с унитарными расширениями квантовой динамической полугруппы в квантовой теории вероятностей: мы