Semiclassical regime of a three-dimensional wave collapse

Alexander Rudol'fovich Its, Victor Yu. Novokshenov

Vladimir Evgen'evich Zakharov, Evgeniy A. Kuznetsov

Sergei N Vlasov, L. V. Piskunova, V. I. Talanov

Sergei N Vlasov, L. V. Piskunova, V. I. Talanov

John Adam

This chapter discusses the connection between the classical and semiclassical domains of scattering. Scattering phenomena may be described via three regimes: the scattering of waves by objects with small, large, or comparable sizes with the wavelength of the incident (plane wave) radiation. All three regions can be related to three domains: the classical domain (geometrical optics, particle and particle/ray-like trajectories); the wave domain (physical optics, acoustic and electromagnetic waves, quantum mechanics); and the semiclassical domain (the vast intermediate region between the first and second domain). The chapter first provides an overview of classical and semiclassical scattering domains before beginning with an analysis of the semiclassical formulation. It also considers the radial equation, scattering by a one-dimensional potential barrier, and the radially symmetric problem. Solutions for phase shifts and the potential well are presented.

Maaneli Derakhshani

Using as a testbed the recently proposed "gravcat" experimental scheme in [1], we compare the properties of gravitational cat states in three descriptions: (1) canonical quantum theory (CQT) combined with the Newtonian limit of GR, (2) objective collapse theories (OCTs) extended to the regime of semiclassical Newtonian gravity, and (3) OCTs extended to incorporate quantized Newtonian gravity. For the CQT approach, we follow the treatment of Hu and Anastopoulos in [2]. For the OCTs, we consider the GRW, CSL, DP, and Karolyhazy theories, based on the semiclassical approaches of Derakhshani [3] and Tilloy-Diosi [4], respectively, and we consider the most straightforward extension of the aforementioned OCTs to the regime of quantized Newtonian gravity. We show that the gravitational cat scheme can, in principle, experimentally discriminate the quantum jumps in gravitational cat states predicted by the CQT approach and the quantized-gravity OCTs (which we show make effectively the same predictions as each other), from the predictions of the semiclassical-gravitational OCTs. We also show that the GRW and Karolyhazy versions of semiclassical gravity (based on Derakhshani's approach) make distinctly different predictions from the CSL and DP versions of semiclassical gravity (based either on Derakhshani's approach or the Tilloy-Diosi approach).