Quantum Walk on Orbit Spaces
| Autor: | Satoshi Ohya |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | INSPIRE-HEP |
| DOI: | 10.48550/arxiv.2301.03193 |
| Popis: | Inspired by the covering-space method in path integral on multiply connected spaces, we here present a universal formula of time-evolution kernels for continuous- and discrete-time quantum walks on orbit spaces. In this note, we focus on the case in which walkers' configuration space is the orbit space $\Lambda/\Gamma$, where $\Lambda$ is an arbitrary lattice and $\Gamma$ is a discrete group whose action on $\Lambda$ has no fixed points. We show that the time-evolution kernel on $\Lambda/\Gamma$ can be written as a weighted sum of time-evolution kernels on $\Lambda$, where the summation is over the orbit of initial point in $\Lambda$ and weight factors are given by a one-dimensional unitary representation of $\Gamma$. Focusing on one dimension, we present a number of examples of the formula. We also present universal formulas of resolvent kernels, canonical density matrices, and unitary representations of arbitrary groups in quantum walks on $\Lambda/\Gamma$, all of which are constructed in exactly the same way as for the time-evolution kernel. Comment: 23 pages, 5 eepic figures; typos corrected, discussions improved |
| Databáze: | OpenAIRE |
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