Non-Hermitian β-ensemble with real eigenvalues
Source abstract
Abstract
By removing the Hermitian condition of the so-called β-ensemble of tridiagonal matrices, an ensemble of non-Hermitian random matrices is constructed whose eigenvalues are all real. It is shown that they belong to the class of pseudo-Hermitian operators. Its statistical properties are investigated.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Quantum Mechanics and Non-Hermitian Physics · Random Matrices and Applications · Spectral Theory in Mathematical Physics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Université Paris-Sud 1 CNRS, , UMR8626, LPTMS, Orsay Cedex, F-91405, France
Universidade de São Paulo 2 Instítuto de Física, , Caixa Postal 66318, 05314-970 São Paulo, S.P., Brazil
References (22)
Show source-provided references
1. Phys. Rev. Lett. · 1998 · 80 · 524310.1103/PhysRevLett.80.5243 ↗
2. J. Math. Phys. · 1999 · 40 · 220110.1063/1.532860 ↗
3. Phys. Rev. Lett. · 2002 · 89 · 27040110.1103/PhysRevLett.89.270401 ↗
4. Rep. Prog. Phys. · 2007 · 70 · 94710.1088/0034-4885/70/6/R03 ↗
5. J. Math. Phys. · 2002 · 43 · 20510.1063/1.1418246 ↗
6. J. Math. Phys. · 2002 · 43 · 281410.1063/1.1461427 ↗
7. J. Math. Phys. · 2002 · 43 · 394410.1063/1.1489072 ↗
8. Czech J. Phys. · 2006 · 56 · 102110.1007/s10582-006-0397-7 ↗
9. Fortschr. Phys. · 2012 · 61 · 00107
10. J. Math. Phys. · 1965 · 6 · 44010.1063/1.1704292 ↗
11. Ann. Math. · 1958 · 68 · 32510.2307/1970008 ↗
12. J. Math. Phys. · 1962 · 3 · 119910.1063/1.1703863 ↗
13. Commun. Math. Phys. · 1997 · 188 · 17510.1007/s002200050161 ↗
14. J. Math. Phys. · 2002 · 43 · 583010.1063/1.1507823 ↗
15. 2004
16. J. Phys. A: Math. Gen. · 2003 · 36 · 330310.1088/0305-4470/36/12/326 ↗
17. Phys. Rev. E · 2012 · 61 · 1899
18. J. Amer. Math. Soc. · 2011 · 24 · 91910.1090/S0894-0347-2011-00703-0 ↗
19. Annals of Probability · 2010 · 38 · 126310.1214/09-AOP508 ↗
20. 1939
21. Phys. Rev. E · 2003 · 67 · 04510610.1103/PhysRevE.67.045106 ↗
22. J. Phys. A · 2003 · 36 · 334910.1088/0305-4470/36/12/327 ↗