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arXiv · 2507.14996

Lifshitz Quantum Mechanics and Anisotropic Josephson Junction

Chong-Sun Chu·Alfian Gunawan
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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.

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Chong-Sun Chu, Alfian Gunawan. 2025-07-20. Lifshitz Quantum Mechanics and Anisotropic Josephson Junction. https://arxiv.org/abs/2507.14996

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