Duality and Scaling in Quantum Mechanics

TL;DR

This paper explores how the nonadiabatic geometric phase in quantum mechanics introduces an intrinsic concept of time with dual properties, revealing a fractal-like temporal structure and scaling laws that extend traditional quantum theory.

Contribution

It presents a novel extension of quantum mechanics by linking geometric phases to an intrinsic, dual notion of time and uncovering fractal temporal structures.

Findings

Identification of dual properties of intrinsic time

Discovery of fractal-like structure in quantum time

Derivation of new scaling laws in quantum evolution

Abstract

The nonadiabatic geometric phase in a time dependent quantum evolution is shown to provide an intrinsic concept of time having dual properties relative to the external time. A nontrivial extension of the ordinary quantum mechanics is thus obtained with interesting scaling laws. A fractal like structure in time is thus revealed.