Time Operators and Time Crystals
- Published: 28 Nov 2017
- Los Alamos National Laboratory United States
- Asahikawa Medical University Japan
- Hokkaido University Japan
[1] More precisely, if the eigenvalues of a Hamiltonian are continuous and bounded below, then there is no selfadjoint time operators which satisfy the canonical commutation relation (1).
[2] M. Reed and B. Simon, Fourier Analysis, Self-Adjointness (Methods of Modern Mathematical Physics, Vol. 2) (Academic Press, 1975).
[3] J. Muga and C. Leavens, Phys. Rep. 338, 353 (2000).
[4] Y. Aharonov and D. Bohm, Phys. Rev. 122, 1649 (1961).
[5] F. Wilczek, Phys. Rev. Lett. 109, 160401 (2012).
[6] T. Li, Z.-X. Gong, Z.-Q. Yin, H. T. Quan, X. Yin, P. Zhang, L.-M. Duan, and X. Zhang, Phys. Rev. Lett. 109, 163001 (2012).
[7] F. Wilczek, Phys. Rev. Lett. 111, 250402 (2013).
[8] C. W. von Keyserlingk and S. L. Sondhi, Phys. Rev. B 93, 245146 (2016).
[9] N. Y. Yao, A. C. Potter, I.-D. Potirniche, and A. Vishwanath, Phys. Rev. Lett. 118, 030401 (2017). [OpenAIRE]
[10] D. V. Else, B. Bauer, and C. Nayak, Phys. Rev. X 7, 011026 (2017).
[11] S. Choi and others., Nature 543, 9 (2017).
[12] J. Zhang et al., Nature 543, 217 (2017).
[13] K. Nakatsugawa, T. Fujii, and S. Tanda, Phys. Rev. B 96, 094308 (2017).
[14] A. Arai, Rev. Math. Phys. 17, 1071 (2005).
[15] E. Galapon, Proc. Royal Soc. Lond. A: Math. Phys. Eng. Sci. 458, 451 (2002).