Continuous-Time Quantum Walk on Locally Infinite Graph

• URL: http://arxiv.org/abs/2602.23970v1
• Date: Fri, 27 Feb 2026 12:26:50 GMT
• Title: Continuous-Time Quantum Walk on Locally Infinite Graph
• Authors: Ce Wang,
• Abstract summary: We study a model of continuous-time quantum walk on a special locally infinite graph.<n>We find that its time-reversal symmetry can be described directly by a unitary operator.
• Score: 5.246888191460796
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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