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Cayley graphs that have a quantum ergodic eigenbasis

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Abstract

We investigate which finite Cayley graphs admit a quantum ergodic eigenbasis, proving that this holds for any Cayley graph on a group of size n for which the sum of the dimensions of its irreducible representations is o(n), yet there exist Cayley graphs that do not have any quantum ergodic eigenbasis.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Princeton University, Princeton, NJ, 08544-1000, USA

    Assaf Naor

  2. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Ashwin Sah, Mehtaab Sawhney & Yufei Zhao

Authors
  1. Assaf Naor
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  2. Ashwin Sah
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  3. Mehtaab Sawhney
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  4. Yufei Zhao
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Corresponding author

Correspondence to Assaf Naor.

Additional information

In celebration of the 70’th birthday of Nati Linial

Naor was supported by NSF grant DMS-2054875 and a Simons Investigator award.

Sah and Sawhney were supported by NSF Graduate Research Fellowship Program DGE-1745302.

Sah was supported by the PD Soros Fellowship.

Zhao was supported by NSF CAREER Award DMS-2044606, a Sloan Research Fellowship, and the MIT Solomon Buchsbaum Fund.

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Naor, A., Sah, A., Sawhney, M. et al. Cayley graphs that have a quantum ergodic eigenbasis. Isr. J. Math. 256, 599–617 (2023). https://doi.org/10.1007/s11856-023-2516-6

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  • DOI: https://doi.org/10.1007/s11856-023-2516-6

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