Lifshitz Quantum Mechanics and Anisotropic Josephson Junction

TL;DR

This paper explores Lifshitz quantum mechanics with anisotropic time derivatives, demonstrating probability conservation and showing how anisotropy enhances Josephson Junction performance by altering tunneling rates.

Contribution

It introduces Lifshitz quantum mechanics with fractional derivatives and applies it to Josephson Junctions, revealing effects of anisotropy on tunneling and device efficiency.

Findings

Probability conservation is maintained with proper current identification.

Anisotropy modifies tunneling rates in Josephson Junctions.

Enhanced performance of Josephson Junctions due to Lifshitz anisotropy.

Abstract

We consider quantum mechanics in spacetime with anisotropy in time. Such Lifshitz quantum mechanics is characterized by a kinetic term with fractional derivatives. We show that, contrary to a common claim in the literature, local conservation of probability is respected when the probability current is properly identified. As an application we consider a Josephson Junction with an insulating layer exhibiting Lifshitz anisotropy. We show that anisotropy modifies the tunneling rate and can significantly enhance the performance of the Josephson Junction.