Characterization of classical and quantum poisson systems by thinnings and splittings

Mathematische Nachrichten

Volumn 218, Issue , 2000, Pages 25-47

  Fichtner, Karl Heinz ^a   Freudenberg, Wolfgang ^b   Liebscher, Volkmar ^a,c  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^b BRANDENBURG UNIVERSITY OF TECHNOLOGY   (Germany)

^c INSTITUTE OF EPIDEMIOLOGY   (Germany)

Author keywords

Beam splitting; Coherent state; Cox process; Poisson process; Quasilocal algebra; Thinning

Indexed keywords

EID: 0039550217     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/1522-2616(200010)218:1<25::aid-mana25>3.0.co;2-y     Document Type: Article

References (44)

1. ACCARDI, L., and OHYA, M.: Compound Channels, Transition Expectations and Liftings, Appl. Math. Optim. 39 (1999), 33-59
2. AHARONOV, Y., FALKOFF, D., LERNER, E., and PENDLETON, H.: A Quantum Characterization of Classical Radiation, Ann. Phys. 39 (1966), 498-512
3. ARAKI, H., and WOODS, E. J.: Representations of the Canonical Commutation Relations Describing a Nonrelativistic Infinite Free Bose Gas, J. Math. Phys. 4 (5) (1963), 637-662
4. BAUER, H.: Wahrscheinlichkeitstheorie, fourth edition, de Gruyter, Berlin-New York, 1991
5. BRATTELI, O., and ROBINSON, D.W.: Operator Algebras and Quantum Statistical Mechanics I, 2nd edition, Springer-Verlag, Berlin-Heidelberg-New York, 1987
6. BRATTELI, O., and ROBINSON, D. W.: Operator Algebras and Quantum Statistical Mechanics II, 2nd edition, Springer-Verlag, Berlin-Heidelberg-New York, 1997
7. CAMPOS, R. A., SALEH, B. E. A., and TEICH, M. C.: Quantum-Mechanical Lossless Beam Splitter: SU(2) Symmetry and Photon Statistics, Phys. Rev. A 40 (3) (1989), 1371-1384
8. DAMASCHKE, T.: States of Infinite Boson Systems on a Lattice, Forschungsergebnisse der FSU Jena N/90/13, 1990
9. DAMASCHKE, T., and FREUDENBERG, W.: On the Position Distribution of Infinite Boson Systems on the Lattice, Forschungsergebnisse der FSU Jena N/88/27, 1988
10. DAVIES, E. B.: Quantum Theory of Open Systems, Academic Press, New York, 1976
11. FICHTNER, K.-H.: Charakterisierung Poissonscher zufälliger Punktfolgen und infinitesimale Verdünnungsschemata, Math. Nachr. 68 (1975), 93-104
12. FICHTNER, K.-H., and FREUDENBERG, W.: Point Processes and the Position Distribution of Infinite Boson Systems, J. Stat. Phys. 47 (1987), 959-978
13. FICHTNER, K. -H., and FREUDENBERG, W.: Characterization of States of Infinite Boson Systems I. On the Construction of States of Boson Systems, Commun. Math. Phys. 137 (1991), 315-357
14. FICHTNER, K.-H., FREUDENBERG, W., and LIEBSCHER, V.: Time Evolution and Invariance of Boson Systems Given by Beam Splittings, Infinite Dimensional Analysis, Quantum Probability and Related Topics 1 (4) (1998), 511-531
15. FICHTNER, K.-H., and SCHREITER, U.: Locally Independent Boson Systems. In: L. ACCARDI and W. VON WALDENFELS (editors), Quantum Probability and Applications V, Lecture Notes in Mathematics Volume 1442, pp. 145-161, Springer-Verlag, Berlin-Heidelberg-New York, 1990
16. FREUDENBERG, W.: Characterization of States of Infinite Boson Systems II. On the Existence of the Conditional Reduced Density Matrix, Commun. Math. Phys. 137 (1991), 461-472
17. FREUDENBERG, W.: On a Class of Quantum Markov Chains on the Fock Space. In: L. ACCARDI (editor), Quantum Probability & Related Topics XI, pp. 215-237, World Scientific Publishing Co., Singapore, 1994
18. GLAUBER, R. J.: Phys. Rev. 130 (1963), 2529
19. GUICHARDET, A.: Symmetric Hilbert Spaces and Related Topics, Lecture Notes in Mathematics Volume 231, Springer-Verlag, Berlin-Heidelberg-New York, 1972
20. JEFFERS, J. R., IMOTO, N., and LOUDON, R.: Quantum Optics of Travelling - Wave Attenuators and Amplifiers, Phys. Rev. A 47(4) (1993), 3346-3359
21. JORDAN, T. F.: Characterizing Coherent States of the Radiation Field, J. Math. Phys. 7 (11) (1966), 2006-2008
22. KRENGEL, U.: Ergodic Theorems, 1st edition, de Gruyter Studies in Mathematics Volume 6, W. de Gruyter, Berlin-New York, 1985
23. LEWIS, J. T., and PULÉ, J. V.: The Equilibrium States of the Free Boson Gas, Commun. Math. Phys. 36 (1974), 1-18
24. LIEBSCHER, V.: Bedingte lokale Zustände und Charakterisierung lokalnormaler Zustände un-endlicher Bosonensysteme, Ph. D. Thesis, FSU Jena, 1993
25. LINDSAY, J. M.: Quantum and Noncausal Stochastic Calculus, Prob. Th. Rel. Fields 97 (1993), 65-80
26. LINDSAY, J. M., and PARTHASARATHY, K. R.: Cohomology of Power Sets with Applications in Quantum Probability, Commun. Math. Phys. 124 (1989), 337-364
27. LINDSAY, M., and MAASSEN, H.: An Integral Kernel Approach to Noise. In: L. ACCARDI and W. VON WALDENFELS (editors) Quantum Probability and Applications III, Lecture Notes in Mathematics Volume 1303, pp. 192-208, Springer-Verlag, Heidelberg, 1988
28. MAASSEN, H.: Quantum Markov Processes on Fock Space Described by Integral Kernels. In: L. ACCARDI and W. VON WALDENFELS (editors), Quantum Probability and Applications II, Lecture Notes in Mathematics Volume 1136, pp. 361-374, Springer-Verlag, Berlin-Heidelberg-New York, 1985
29. MATTHES, K., KERSTAN, J., and MECKE, J.: Infinitely Divisible Point Processes, Wiley, Chichester, 1978
30. MECKE, J.: Eine charakteristische Eigenschaft der doppelt stochastischen Poissonschen Punktprozesse, Z. Wahrscheinlichkeitstheorie verw. Gebiete 11 (1968), 74-81
31. OHYA, M., and SUYARI, H.: An Application of Lifting Theory to Optical Communication Processes, Rep. Math. Phys. 36 (2) (1995), 403-420
32. PARTHASARATHY, K. R.: Probability Measures on Metric Spaces, Academic Press, Boston, 1967
33. PARTHASARATHY, K. R.: An Introduction to Quantum Stochastic Calculus, Birkhäuser, Basel-Boston-Berlin, 1992
34. PETZ, D.: An Invitation to the Algebra of Canonical Commutation Relations, Leuven Notes in Mathematical and Theoretical Physics Volume 2, Leuven University Press, Leuven, 1990
35. REED, M., and SIMON, B.: Methods of Modern Mathematical Physics Volume 1, Academic Press, New York-London, 1972
36. SAKAI, SH.: C* and W* Algebras, Ergebnisses der Mathematik und ihrer Grenzgebiete Springer-Veralg, Berlin-Heidelberg-New York, 1971
37. SCHÜRMANN, M.: White Noise on Bialgebras, Lecture Notes in Mathematics Volume 1544, Springer-Veralg, Berlin-Heidelberg-New York, 1993
38. SHIRJAEV, A. N.: Wahrscheinlichkeit, Deutscher Verlag der Wissenschaften, Berlin, 1987
39. TITULAER, U. M.: Factorization Properties of Coherent Fields. In: R. J. GLAUBER (editor), Proceedings of the International School of Physics "Enrico Fermi", Course XLII, pp. 153-159, Academic Press, 1969
40. TITULAER, U. M., and GLAUBER, R. J.: Phys. Rev. 140 (1963), 745
41. TITULAER, U. M., and GLAUBER, R. J.: Density Operators for Coherent Fields, Phys. Rev. 145 (4) (1966), 1041-1050
42. VARADARAJAN, V. S.: Geometry of Quantum Theory, 2nd edition, Springer-Verlag, Berlin-Heidelberg-New York, 1985
43. YAMASAKI, Y.: Lecture Note on Measures on Infinite Dimensional Spaces, RIMS, Kyoto, 1984
44. YOSIDA, K.: Functional Analysis, 7th edition, Classics in Mathematics, Springer-Verlag, Berlin-Heidelberg-New York, 1995