Phenomenology of Quantum Systems and Wave Mechanics: An Overview

Valter Moretti

Joaquin Trujillo

The articles provides a phenomenological reading of the Many-Worlds Interpretation (MWI) of quantum mechanics and its answer to the measurement problem, or the question of “why only one of a wave function’s probable values is observed when the system is measured.” Transcendental-phenomenological and hermeneutic-phenomenological approaches are employed. The project comprises four parts. Parts one and two review MWI and the standard (Copenhagen) interpretation of quantum mechanics. Part three reviews the phenomenologies. Part four deconstructs the hermeneutics of MWI. It agrees with the confidence the theory derives from its (1) unforgiving appropriation of the Schrödinger equation and (2) association of branching universes with the evolution of the wave function insofar as that understanding comes from the formalism itself. Part four also reveals the hermeneutical shortcomings of the standard interpretation.

Akira Shudo

In generic Hamiltonian systems that are neither completely integrable nor fully chaotic, phase space consists of a mixture of regular and chaotic components. In classical dynamics, transitions between different invariant sets in phase space are strictly forbidden, and these sets act as dynamical barriers to one another. In quantum mechanics, in contrast, wave effects allow transitions through such dynamical barriers. This process, known as dynamical tunneling, refers to penetration through dynamical barriers in phase space and was first recognized in the early 1980s. Since then, various aspects of dynamical tunneling have been elucidated, significantly advancing our understanding of such a novel quantum phenomenon. In this article, we provide an overview of several phenomenological perspectives of dynamical tunneling, including chaos-assisted and resonance-assisted tunneling, and also introduce approaches based on classical mechanics extended into the complex domain. In particular, we seek to clarify what is meant by the common claim that "chaos leads to an enhancement of the tunneling probability", which is often made when dynamical tunneling is dressed. We discuss what regime this refers to and, if such an enhancement occurs, what its likely origin is.

Robert P Crease, Delicia Antoinette Kamins, Paul Rubery

Thomas B. Andrews