Markov constant and quantum instabilities

作者：Pelantova Edita; Starosta Stepan^*; Znojil Miloslav

来源：Journal of Physics A-Mathematical and Theoretical, 2016, 49(15): 155201.

DOI：10.1088/1751-8113/49/15/155201

• renormalizable quantum theories with ghosts
• Pais-Uhlenbeck model
• singular spectra
• square-well model
• number theory analysis
• physical applications
• metamaterials

For a qualitative analysis of spectra of certain two-dimensional rectangular-well quantum systems several rigorous methods of number theory are shown productive and useful. These methods (and, in particular, a generalization of the concept of Markov constant known in Diophantine approximation theory) are shown to provide a new mathematical insight in the phenomenologically relevant occurrence of anomalies in the spectra. Our results may inspire methodical innovations ranging from the description of the stability properties of metamaterials and of certain hiddenly unitary quantum evolution models up to the clarification of the mechanisms of occurrence of ghosts in quantum cosmology.

• 出版日期2016-4-15