Continuous-Time Quantum Walk on Locally Infinite Graph

Ce Wang

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arXiv · 2602.23970

Continuous-Time Quantum Walk on Locally Infinite Graph

Ce Wang

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Abstract

Time-reversal symmetry is of fundamental importance to physics. In the classical theory of time-reversal symmetry, the time-reversal symmetry of a quantum system is described by an anti-unitary operator, which is known as the time-reversal operator of the system. In this paper, we introduce and study a model of continuous-time quantum walk on a special locally infinite graph. After examining its spectral property, we investigate the time-reversal symmetry of the model. To our surprise, we find that its time-reversal symmetry can be described directly by a unitary operator, which contrasts sharply with that in the classical theory of time-reversal symmetry. Some other related results are also proven.

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Ce Wang. 2026-02-27. Continuous-Time Quantum Walk on Locally Infinite Graph. https://arxiv.org/abs/2602.23970

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