PT -symmetric brachistochrone problem, Lorentz boosts, and nonunitary operator equivalence classes

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 78, Issue 4, 2008, Pages

  Günther, Uwe ^a   Samsonov, Boris F ^b  

^a INSTITUTE OF ION BEAM PHYSICS AND MATERIALS RESEARCH   (Germany)

^b TOMSK STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL THEORY; PHOTOTRANSISTORS; QUANTUM ELECTRONICS; QUANTUM OPTICS; SET THEORY;

BRACHISTOCHRONE PROBLEMS; CONJUGACY CLASSES; GEOMETRIC ANALYSES; HERMITIAN; LORENTZ; LOWER BOUNDS; NATURAL INGREDIENTS; NONUNITARY; PASSAGE TIMES; QUANTUM SYSTEMS; SET-UPS; SUB SYSTEMS;

EQUIVALENCE CLASSES;

EID: 55749115448     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.78.042115     Document Type: Article

References (40)

1. C. M. Bender and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998). 10.1103/PhysRevLett.80.5243
2. C. M. Bender, Rep. Prog. Phys. 70, 947 (2007). 10.1088/0034-4885/70/6/R03
3. A. Mostafazadeh, J. Math. Phys. 43, 2814 (2002). 10.1063/1.1461427
4. C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. D 70, 025001 (2004); 10.1103/PhysRevD.70.025001
5. C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. D 71, 049901 (E) (2005). 10.1103/PhysRevD.71.049901
6. A. Mostafazadeh, J. Phys. A 36, 7081 (2003); 10.1088/0305-4470/36/25/312
7. A. Mostafazadeh, J. Phys. A 38, 6557 (2005); 10.1088/0305-4470/38/29/010
8. A. Mostafazadeh, J. Phys. A 38, 8185 (E) (2005). 10.1088/0305-4470/38/37/ C01
9. C. M. Bender, D. C. Brody, H. F. Jones, and B. K. Meister, Phys. Rev. Lett. 98, 040403 (2007). 10.1103/PhysRevLett.98.040403
10. A. Mostafazadeh, Phys. Rev. Lett. 99, 130502 (2007). 10.1103/PhysRevLett. 99.130502
11. U. Günther, I. Rotter and B. Samsonov, J. Phys. A 40, 8815 (2007). 10.1088/1751-8113/40/30/014
12. A. S. Holevo, Statistical Structure of Quantum Theory (Springer, Berlin, 2001);
13. A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (Nauka, Moscow, 1980).
14. A. Peres, Quantum Theory: Concepts and Methods (Kluwer, Dordrecht, 1993).
15. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
16. C. W. Helstrom, Quantum Detection and Estimation Theory (Academic, New York, 1976), pp. 74-83;
17. D. B. Osteyee and I. J. Good, Information, Weight of Evidence, the Singularity Between Probability Measures, and Signal Detection, Lecture Notes in Mathematics No. 376 (Springer, New York, 1974);
18. A. Peres, Found. Phys. 20, 1441 (1990); 10.1007/BF01883517
19. J. Bergou, U. Herzog, and M. Hillery, in Discrimination of Quantum States, Lecture Notes in Physics No. 649 (Springer, Berlin, 2004), p. 417;
20. J. A. Bergou, J. Phys.: Conf. Ser. 84, 012001 (2007). 10.1088/1742-6596/84/1/012001
21. L. Diósi, A Short Course in Quantum Information Theory, Lecture Notes in Physics No. 713 (Springer, Berlin, 2007).
22. H. Langer and C. Tretter, Czech. J. Phys. 54, 1113 (2004); 10.1023/B:CJOP.0000044012.95629.b2
23. S. Albeverio and S. Kuzhel, Lett. Math. Phys. 67, 223 (2004); 10.1023/B:MATH.0000035041.51625.ce
24. U. Günther, F. Stefani, and M. Znojil, J. Math. Phys. 46, 063504 (2005). 10.1063/1.1915293
25. F. G. Scholtz, H. B. Geyer, and F. J. W. Hahne, Ann. Phys. (N.Y.) 213, 74 (1992). 10.1016/0003-4916(92)90284-S
26. A. Mostafazadeh, J. Math. Phys. 43, 205 (2002). 10.1063/1.1418246
27. A. Mostafazadeh, J. Math. Phys. 44, 974 (2003). 10.1063/1.1539304
28. L. H. Ryder, Quantum Field Theory (Cambridge University Press, Cambridge, England, 1985).
29. B. F. Samsonov and U. Günther (unpublished).
30. J. Anandan and Y. Aharonov, Phys. Rev. Lett. 65, 1697 (1990). 10.1103/PhysRevLett.65.1697
31. P. R. Giri, Int. J. Theor. Phys. 47, 2095 (2008). 10.1007/s10773-008- 9650-0
32. D. J. Brody, J. Phys. A 36, 5587 (2003); 10.1088/0305-4470/36/20/314
33. D. J. Brody and D. W. Hook, J. Phys. A 39, L167 (2006). 10.1088/0305-4470/39/11/L02
34. U. Hertrich-Jeromin, Introduction to Möbius Differential Geometry (Cambridge University Press, Cambridge, England, 2003).
35. K. Ito, Encyclopedic Dictionary of Mathematics (MIT Press, Cambridge, MA, 1993).
36. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, New York, 1983).
37. M. Nakahara, Geometry, Topology and Physics (IOP Publishing, Bristol, 1990).
38. W. Rindler, Relativity: Special, General, and Cosmological (Oxford University Press, Oxford, 2007).
39. T. Ya. Azizov and I. S. Iokhvidov, Linear Operators in Spaces With an Indefinite Metric (Wiley-Interscience, New York, 1989).
40. A. Dijksma and H. Langer, in Lectures on Operator Theory and Its Applications, edited by, P. Lancaster, Fields Institute Monographs No. 3 (Am. Math. Soc., Providence, RI, 1996), p. 75.