Path integrals for particles under the influence of gravity and electromagnetism

Alexander Alexandrovich Biryukov, Марк Александрович Шлеенков

We study the dynamics of multi-level quantum systems under the influence of electromagnetic field.Basing on the path integral approach to the quantum density matrix and transitions probability we represent functional averaging electromagnetic field influence.We demonstrate that the transition probability can be written as a path integral of real functional (the product of exponent and cosine).The numerical integration algorithm of the transitions probability in energy representation was developed.The numerical simulations of the quantum system dynamics under electromagnetic field action describe the well-known Rabi oscillations, their fluctuations and multi-photon quantum transitions.

Mekki Aouachria

The movement of a two-level atom interacting with an electromagnetic wave while subject to gravity is studied using path-integral formalism. The propagator is first written in a standard form, ∫[Formula: see text](path) exp(i/ℏ)S(path), by replacing the spin with a unit vector aligned along the polar and azimuthal directions to determine the propagator exactly. Thus, the exact wave functions of the system are deduced.

成介 大高, Sigeyuki Otaka

Mark S. Swanson

Michael B. Mensky

This chapter applies the path-integral approach to the quantum theory of continuous measurements to investigate the quantum Universe, taking into account its self-measurement. It describes the way to apply the path-integral theory of continuous measurements in quantum cosmology in a general form and develops a minisuperspace model. The path-integral approach can be applied to describe the measurement of a quantum field. The measurement of curvature in the framework of quantum gravity has been considered in such a way by Mensky using a functional integral over configurations of the gravitational field. The chapter considers the possible influence of self-measurement on the dynamics of the quantum Universe. The influence could be caused by reduction of the wavefunction of the Universe in the process of continuous measurement. Therefore the time evolution of the quantum Universe makes sense in quantum cosmology provided its self-measurement is correctly taken into account.