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Volumn 41, Issue 6, 2000, Pages 3556-3603

Classical and quantum probability

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EID: 0034382449     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533322     Document Type: Article
Times cited : (65)

References (159)
  • 5
    • 0002261964 scopus 로고
    • Characteristic exponents for a viscous fluid
    • D. Ruelle, "Characteristic exponents for a viscous fluid," Commun. Math. Phys. 93, 285-300 (1984); Thermodynamic Formalism, Encyclopedia of Mathematics (Addison-Wesley, Reading, MA, 1978), Vol. 5.
    • (1984) Commun. Math. Phys. , vol.93 , pp. 285-300
    • Ruelle, D.1
  • 6
    • 0002261964 scopus 로고
    • Thermodynamic formalism
    • Addison-Wesley, Reading, MA
    • D. Ruelle, "Characteristic exponents for a viscous fluid," Commun. Math. Phys. 93, 285-300 (1984); Thermodynamic Formalism, Encyclopedia of Mathematics (Addison-Wesley, Reading, MA, 1978), Vol. 5.
    • (1978) Encyclopedia of Mathematics , vol.5
  • 10
    • 0000562779 scopus 로고
    • Information theory and variational principles in statistical physics
    • R. S. Ingarden, "Information theory and variational principles in statistical physics," Bull. Acad. Pol. Sci., Ser. Sci. Tech. 11, 541-547 (1963).
    • (1963) Bull. Acad. Pol. Sci., Ser. Sci. Tech. , vol.11 , pp. 541-547
    • Ingarden, R.S.1
  • 11
    • 11944266539 scopus 로고
    • Information theory and statistical mechanics
    • E. T. Jaynes, "Information theory and statistical mechanics," Phys. Rev. 106, 620 (1957); 108, 171-190 (1957).
    • (1957) Phys. Rev. , vol.106 , pp. 620
    • Jaynes, E.T.1
  • 12
    • 11944275853 scopus 로고
    • E. T. Jaynes, "Information theory and statistical mechanics," Phys. Rev. 106, 620 (1957); 108, 171-190 (1957).
    • (1957) Phys. Rev. , vol.108 , pp. 171-190
  • 13
    • 0001915002 scopus 로고
    • Information and accuracy attainable in the estimation of statistical parameters
    • C. R. Rao, "Information and accuracy attainable in the estimation of statistical parameters," Bull. Calcutta Math. Soc. 37, 81-91 (1945).
    • (1945) Bull. Calcutta Math. Soc. , vol.37 , pp. 81-91
    • Rao, C.R.1
  • 14
    • 84939431353 scopus 로고
    • Theory of statistical estimation
    • R. A. Fisher, "Theory of statistical estimation," Proc. Cambridge Philos Soc. 22, 700-725 (1925).
    • (1925) Proc. Cambridge Philos Soc. , vol.22 , pp. 700-725
    • Fisher, R.A.1
  • 15
    • 0019654394 scopus 로고
    • Information geometry in functional spaces
    • R. S. Ingarden, "Information geometry in functional spaces," Int. J. Eng. Sci. 19, 1609-1633 (1981).
    • (1981) Int. J. Eng. Sci. , vol.19 , pp. 1609-1633
    • Ingarden, R.S.1
  • 16
    • 0003658081 scopus 로고
    • Differential-geometric methods in statistics
    • Springer, Berlin, 2nd ed.
    • S.-I. Amari, "Differential-Geometric Methods in Statistics," Lecture Notes in Statistics (Springer, Berlin, 1985), 2nd ed.
    • (1985) Lecture Notes in Statistics
    • Amari, S.-I.1
  • 19
    • 0040106226 scopus 로고
    • N. N. Chentsov, Statistical Decision and Optimal Inference (Nauka, Moscow, 1972); Trans. Am. Math. Soc. 53, (1982).
    • (1982) Trans. Am. Math. Soc. , vol.53
  • 20
    • 0012458021 scopus 로고    scopus 로고
    • Non-commutative extension of information geometry. II
    • edited by Hirota et al. Plenum, New York
    • H. Hasagawa and D. Petz, "Non-commutative extension of information geometry. II," in Quantum Communication, Computing and Measurement, edited by Hirota et al. (Plenum, New York, 1997), pp. 109-118.
    • (1997) Quantum Communication, Computing and Measurement , pp. 109-118
    • Hasagawa, H.1    Petz, D.2
  • 21
    • 0003029969 scopus 로고
    • Théorie de la speculation
    • reprint edited by J. Gabay Gauthier-Villars, Paris
    • L. Bachelier, "Théorie de la speculation," Ann. Sci. Ecole Norm. Sup. 17, 21 (1900); reprint edited by J. Gabay (Gauthier-Villars, Paris, 1995).
    • (1900) Ann. Sci. Ecole Norm. Sup. , vol.17 , pp. 21
    • Bachelier, L.1
  • 24
    • 0039923878 scopus 로고    scopus 로고
    • R. F. Streater, J. Stat. Phys. 88, 447 (1997); Rep. Math. Phys. 40, 557 (1997).
    • (1997) J. Stat. Phys. , vol.88 , pp. 447
    • Streater, R.F.1
  • 25
    • 0031539306 scopus 로고    scopus 로고
    • R. F. Streater, J. Stat. Phys. 88, 447 (1997); Rep. Math. Phys. 40, 557 (1997).
    • (1997) Rep. Math. Phys. , vol.40 , pp. 557
  • 28
    • 0007172445 scopus 로고
    • de Gruyter, Leipzig, 1914; reprint, Chelsea, New York
    • F. Hausdorff, Grundzüge der Mengenlehre (de Gruyter, Leipzig, 1914); reprint, Chelsea, New York, 1949, 1965.
    • (1949) Grundzüge der Mengenlehre
    • Hausdorff, F.1
  • 31
    • 84967773775 scopus 로고
    • Tensor algebras over Hilbert space I
    • I. E. Segal, "Tensor algebras over Hilbert space I," Trans. Am. Math. Soc. 81, 106-143 (1956).
    • (1956) Trans. Am. Math. Soc. , vol.81 , pp. 106-143
    • Segal, I.E.1
  • 32
    • 0000786435 scopus 로고
    • The homogeneous chaos
    • N. Wiener, "The homogeneous chaos," Am. J. Math. 55, 897-936 (1938).
    • (1938) Am. J. Math. , vol.55 , pp. 897-936
    • Wiener, N.1
  • 33
    • 33845232342 scopus 로고
    • Evaluation of the collision matrix
    • G. C. Wick, "Evaluation of the collision matrix," Phys. Rev. 80, 268 (1950).
    • (1950) Phys. Rev. , vol.80 , pp. 268
    • Wick, G.C.1
  • 36
    • 0002033550 scopus 로고
    • On the violation of Bell's inequality in quantum theory
    • L. J. Landau, "On the Violation of Bell's inequality in quantum theory," Phys. Lett. A 120, 54-56 (1987).
    • (1987) Phys. Lett. A , vol.120 , pp. 54-56
    • Landau, L.J.1
  • 39
    • 0000194417 scopus 로고
    • Logic of quantum mechanics
    • G. D. Birkhoff and J. von Neumann, "Logic of quantum mechanics," Ann. Math. 37, 823-843 (1936).
    • (1936) Ann. Math. , vol.37 , pp. 823-843
    • Birkhoff, G.D.1    Von Neumann, J.2
  • 54
  • 58
    • 85037771695 scopus 로고
    • edited by D. Williams, LNM 851 Springer, Berlin
    • D. Williams, in Stochastic Integrals, edited by D. Williams, LNM 851 (Springer, Berlin, 1981).
    • (1981) Stochastic Integrals
    • Williams, D.1
  • 60
    • 38249035718 scopus 로고
    • Quantum stochastic integrals understanding hypotheses
    • C. Barnett, R. F. Streater, and I. F. Wilde, "Quantum stochastic integrals understanding hypotheses," J. Math. Anal. Appl. 127, 181-192 (1987).
    • (1987) J. Math. Anal. Appl. , vol.127 , pp. 181-192
    • Barnett, C.1    Streater, R.F.2    Wilde, I.F.3
  • 61
    • 0003021436 scopus 로고
    • Some connections between probability theory and differential and integral equations
    • edited by J. Neyman University of California Press, Berkeley
    • M. Kac, "Some connections between probability theory and differential and integral equations," Proceedings of the Second Berkeley Symposium, edited by J. Neyman (University of California Press, Berkeley, 1951).
    • (1951) Proceedings of the Second Berkeley Symposium
    • Kac, M.1
  • 63
    • 0000431067 scopus 로고
    • Feynman integrals and the Schrödinger equation
    • E. Nelson, "Feynman Integrals and the Schrödinger Equation," J. Math. Phys. 5, 332-343 (1964).
    • (1964) J. Math. Phys. , vol.5 , pp. 332-343
    • Nelson, E.1
  • 68
    • 0038968112 scopus 로고
    • Schwinger functions and their generating functionals. I
    • J. Fröhlich, "Schwinger functions and their generating functionals. I," Helv. Phys. Acta 47, 265-306 (1974); "II, Markovian and generalized path space measures on S," Adv. Math. 23, 119-180 (1977).
    • (1974) Helv. Phys. Acta , vol.47 , pp. 265-306
    • Fröhlich, J.1
  • 69
    • 0002149728 scopus 로고
    • II, Markovian and generalized path space measures on S
    • J. Fröhlich, "Schwinger functions and their generating functionals. I," Helv. Phys. Acta 47, 265-306 (1974); "II, Markovian and generalized path space measures on S," Adv. Math. 23, 119-180 (1977).
    • (1977) Adv. Math. , vol.23 , pp. 119-180
  • 70
    • 0001620162 scopus 로고
    • 2 Euclidean quantum field theory as classical statistical mechanics
    • 2 Euclidean quantum field theory as classical statistical mechanics," Ann. Math. 101, 111-259 (1975).
    • (1975) Ann. Math. , vol.101 , pp. 111-259
    • Guerra, F.1    Rosen, L.2    Simon, B.3
  • 71
    • 36149021943 scopus 로고
    • The S-matrix in quantum electrodynamics
    • F. J. Dyson, "The S-matrix in quantum electrodynamics," Phys. Rev. 75, 1736-1755 (1949).
    • (1949) Phys. Rev. , vol.75 , pp. 1736-1755
    • Dyson, F.J.1
  • 75
    • 0003210311 scopus 로고
    • Euclidean quantum field theory
    • edited by R. Jost Academic, New York
    • K. Symanzik, "Euclidean quantum field theory," in Local Quantum Theory, edited by R. Jost (Academic, New York, 1969), pp. 152-226.
    • (1969) Local Quantum Theory , pp. 152-226
    • Symanzik, K.1
  • 78
    • 49549166117 scopus 로고
    • The free Markov field
    • E. Nelson, "The free Markov field," J. Funct. Anal. 12, 211-227 (1973).
    • (1973) J. Funct. Anal. , vol.12 , pp. 211-227
    • Nelson, E.1
  • 80
    • 0010677791 scopus 로고
    • The free euclidean proca and electromagnetic fields
    • edited by A. M. Arthurs Oxford University Press, New York
    • L. Gross, "The free Euclidean Proca and electromagnetic fields," in Functional Integration and its Applications, edited by A. M. Arthurs (Oxford University Press, New York, 1975), pp. 69-82.
    • (1975) Functional Integration and Its Applications , pp. 69-82
    • Gross, L.1
  • 81
    • 36149006827 scopus 로고
    • Dissipation in quantum mechanics: The harmonic oscillator I, II
    • I. R. Senitzsky, "Dissipation in Quantum Mechanics: The harmonic oscillator I, II," Phys. Rev. 119, 670-679 (1960); 124, 642-648 (1961).
    • (1960) Phys. Rev. , vol.119 , pp. 670-679
    • Senitzsky, I.R.1
  • 82
    • 0040106223 scopus 로고
    • I. R. Senitzsky, "Dissipation in Quantum Mechanics: The harmonic oscillator I, II," Phys. Rev. 119, 670-679 (1960); 124, 642-648 (1961).
    • (1961) Phys. Rev. , vol.124 , pp. 642-648
  • 83
    • 0038954072 scopus 로고
    • Damped oscillator with quantum noise
    • R. F. Streater, "Damped oscillator with quantum noise," J. Phys. A 15, 1477-1486 (1982).
    • (1982) J. Phys. A , vol.15 , pp. 1477-1486
    • Streater, R.F.1
  • 84
    • 0038922023 scopus 로고
    • M. Lax, Phys. Rev. 145, 111 (1965).
    • (1965) Phys. Rev. , vol.145 , pp. 111
    • Lax, M.1
  • 85
    • 0001214859 scopus 로고
    • Quantum Ito's formula and stochastic evolutions
    • R. L. Hudson and K. R. Parthasarathy, "Quantum Ito's formula and stochastic evolutions," Commun. Math. Phys. 93, 301-303 (1984).
    • (1984) Commun. Math. Phys. , vol.93 , pp. 301-303
    • Hudson, R.L.1    Parthasarathy, K.R.2
  • 88
  • 91
    • 85037784365 scopus 로고
    • Temperature-dependent lamb shift of a quantum oscillator
    • LNM 1136, edited by L. Accardi and W. von Waldenfels Springer, Berlin
    • G. W. Ford, "Temperature-dependent Lamb shift of a quantum oscillator," in Quantum Probability and Applications II, LNM 1136, edited by L. Accardi and W. von Waldenfels (Springer, Berlin, 1985), pp. 202-206.
    • (1985) Quantum Probability and Applications II , pp. 202-206
    • Ford, G.W.1
  • 96
    • 0010987624 scopus 로고
    • Current commutation relations, continuous tensor products, and infinitely divisible group representations
    • edited by R. Jost Academic, New York
    • R. F. Streater, "Current commutation relations, continuous tensor products, and infinitely divisible group representations," in Local Quantum Theory, edited by R. Jost (Academic, New York, 1969), pp. 247-263.
    • (1969) Local Quantum Theory , pp. 247-263
    • Streater, R.F.1
  • 97
    • 84996013419 scopus 로고
    • Factorizable representations of current algebras
    • H. Araki, "Factorizable representations of current algebras," Proc. R. I. M. S. Kyoto 5, 361-422 (1970/71).
    • (1970) Proc. R. I. M. S. Kyoto , vol.5 , pp. 361-422
    • Araki, H.1
  • 98
    • 0003199972 scopus 로고
    • Positive definite kernels, continuous tensor products, and central limit theorems of probability theory
    • Springer-Verlag, Berlin
    • K. Parthasarathy and K. Schmidt, "Positive definite kernels, continuous tensor products, and central limit theorems of probability theory," Lect. Notes Math. 272 (Springer-Verlag, Berlin, 1972).
    • (1972) Lect. Notes Math. , vol.272
    • Parthasarathy, K.1    Schmidt, K.2
  • 100
    • 0002045160 scopus 로고
    • Representations of the group SL(2,R), where R is a ring of functions
    • I. M. Gelfand, M. I. Graev, and A. M. Vershik, "Representations of the group SL(2,R), where R is a ring of functions." Usp. Mat. Nauk 28, 83-128 (1973).
    • (1973) Usp. Mat. Nauk , vol.28 , pp. 83-128
    • Gelfand, I.M.1    Graev, M.I.2    Vershik, A.M.3
  • 102
    • 33748777013 scopus 로고
    • Low order cohomology and applications
    • Springer-Verlag, Berlin
    • J. Erven, and B.-J. Falkowski, Low Order Cohomology and Applications [Lect. Notes Math. 877, (Springer-Verlag, Berlin, 1981)].
    • (1981) Lect. Notes Math. , vol.877
    • Erven, J.1    Falkowski, B.-J.2
  • 104
    • 84971814902 scopus 로고
    • Infinitely divisible projective representations of the lie algebras
    • D. Mathon, "Infinitely divisible projective representations of the Lie algebras," Proc. Cambridge Philos. Soc. 72, 357-368 (1972).
    • (1972) Proc. Cambridge Philos. Soc. , vol.72 , pp. 357-368
    • Mathon, D.1
  • 106
    • 0001072713 scopus 로고
    • A quantum mechanical central limit theorem
    • C. D. Cushen and R. L. Hudson, "A quantum mechanical central limit theorem," J. Appl. Probab. 8, 454-469 (1971).
    • (1971) J. Appl. Probab. , vol.8 , pp. 454-469
    • Cushen, C.D.1    Hudson, R.L.2
  • 107
    • 0000938937 scopus 로고
    • A quantum-mechanical central limit theorem for anticommuting variables
    • R. L. Hudson, "A quantum-mechanical central limit theorem for anticommuting variables," J. Appl. Probab. 10, 502-509 (1973).
    • (1973) J. Appl. Probab. , vol.10 , pp. 502-509
    • Hudson, R.L.1
  • 108
    • 0009300260 scopus 로고
    • Prime field-decompositions and infinitely divisible states on Borchers' tensor algebra
    • G. C. Hegerfeldt, "Prime field-decompositions and infinitely divisible states on Borchers' tensor algebra," Commun. Math. Phys. 45, 137-151 (1975).
    • (1975) Commun. Math. Phys. , vol.45 , pp. 137-151
    • Hegerfeldt, G.C.1
  • 109
    • 4243829610 scopus 로고
    • Positive and conditionally positive linear functionals on coalgebras
    • edited by L. Accardi and W. von Waldenfels, LNM Springer-Verlag, Berlin
    • M. Schürmann, "Positive and conditionally positive linear functionals on coalgebras," in Quantum Probability II, edited by L. Accardi and W. von Waldenfels, LNM 136 (Springer-Verlag, Berlin, 1985), pp. 475-492: Proceedings on the Probability Measures on Groups IX, Oberwohlfach (unpublished), 1988; White Noise on Bialgebras [Lect. Notes Math. 1544 (Springer-Verlag, Berlin, 1993)].
    • (1985) Quantum Probability II , vol.136 , pp. 475-492
    • Schürmann, M.1
  • 110
    • 0039514441 scopus 로고
    • Oberwohlfach (unpublished)
    • M. Schürmann, "Positive and conditionally positive linear functionals on coalgebras," in Quantum Probability II, edited by L. Accardi and W. von Waldenfels, LNM 136 (Springer-Verlag, Berlin, 1985), pp. 475-492: Proceedings on the Probability Measures on Groups IX, Oberwohlfach (unpublished), 1988; White Noise on Bialgebras [Lect. Notes Math. 1544 (Springer-Verlag, Berlin, 1993)].
    • (1988) Proceedings on the Probability Measures on Groups IX
  • 111
    • 0003342920 scopus 로고
    • White noise on bialgebras
    • Springer-Verlag, Berlin
    • M. Schürmann, "Positive and conditionally positive linear functionals on coalgebras," in Quantum Probability II, edited by L. Accardi and W. von Waldenfels, LNM 136 (Springer-Verlag, Berlin, 1985), pp. 475-492: Proceedings on the Probability Measures on Groups IX, Oberwohlfach (unpublished), 1988; White Noise on Bialgebras [Lect. Notes Math. 1544 (Springer-Verlag, Berlin, 1993)].
    • (1993) Lect. Notes Math. , vol.1544
  • 112
    • 85037762182 scopus 로고
    • Ph.D. thesis, Princeton
    • H. Araki, Ph.D. thesis, Princeton, 1960.
    • (1960)
    • Araki, H.1
  • 113
    • 0000410986 scopus 로고
    • Fock space revisited
    • J. R. Klauder, "Fock space revisited," J. Math. Phys. 11, 609-630 (1970); "Ultralocal scalar field models," Commun. Math. Phys. 18, 307-318 (1970).
    • (1970) J. Math. Phys. , vol.11 , pp. 609-630
    • Klauder, J.R.1
  • 114
    • 0009299425 scopus 로고
    • Ultralocal scalar field models
    • J. R. Klauder, "Fock space revisited," J. Math. Phys. 11, 609-630 (1970); "Ultralocal scalar field models," Commun. Math. Phys. 18, 307-318 (1970).
    • (1970) Commun. Math. Phys. , vol.18 , pp. 307-318
  • 116
    • 0003359771 scopus 로고
    • Quantum probability for probabilists
    • Springer-Verlag, Berlin
    • P.-A. Meyer, Quantum Probability for Probabilists [Lect. Notes Math. 1538, (Springer-Verlag, Berlin, 1991)].
    • (1991) Lect. Notes Math. , vol.1538
    • Meyer, P.-A.1
  • 117
    • 0000404789 scopus 로고
    • Addition of certain non-commuting random variables
    • D. Voiculescu, "Addition of certain non-commuting random variables," J. Funct. Anal. 66, 323-346 (1986).
    • (1986) J. Funct. Anal. , vol.66 , pp. 323-346
    • Voiculescu, D.1
  • 118
    • 84859082234 scopus 로고
    • Some Markov processes and Markov fields
    • edited by D. Williams, LNM Springer, Berlin
    • S. Albeverio and R. Hoegh-Krohn, "Some Markov processes and Markov fields," in Stochastic Integrals, edited by D. Williams, LNM 851 (Springer, Berlin, 1981), pp. 497-540.
    • (1981) Stochastic Integrals , vol.851 , pp. 497-540
    • Albeverio, S.1    Hoegh-Krohn, R.2
  • 120
    • 0003007332 scopus 로고
    • General state changes in quantum theory
    • K. Kraus, "General state changes in quantum theory," Ann. of Phys. 64, 311-335 (1971).
    • (1971) Ann. of Phys. , vol.64 , pp. 311-335
    • Kraus, K.1
  • 121
    • 36749106315 scopus 로고
    • Completely positive dynamical semigroups of n-level systems
    • V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, "Completely positive dynamical semigroups of n-level systems," J. Math. Phys. 17, 821-825 (1976).
    • (1976) J. Math. Phys. , vol.17 , pp. 821-825
    • Gorini, V.1    Kossakowski, A.2    Sudarshan, E.C.G.3
  • 124
    • 33748791941 scopus 로고
    • Infinite divisibility and central limit theorems for completely positive mappings
    • LNM 1136, edited by L. Accardi and W. von Waldenfels Springer, Berlin
    • M. Fannes and J. Quaegebure, "Infinite divisibility and central limit theorems for completely positive mappings," Quantum Probability and Applications, LNM 1136, edited by L. Accardi and W. von Waldenfels (Springer, Berlin, 1985).
    • (1985) Quantum Probability and Applications
    • Fannes, M.1    Quaegebure, J.2
  • 125
    • 84968466834 scopus 로고
    • Positive functions on C*-algebras
    • W. F. Stinespring, "Positive functions on C*-algebras," Proc. Am. Math. Soc. 6, 242-247 (1955).
    • (1955) Proc. Am. Math. Soc. , vol.6 , pp. 242-247
    • Stinespring, W.F.1
  • 126
    • 84972487716 scopus 로고
    • Conditional expectation in an operator algebra
    • H. Umegaki, "Conditional expectation in an operator algebra," Tohoku Math. J. 8, 86-100 (1956).
    • (1956) Tohoku Math. J. , vol.8 , pp. 86-100
    • Umegaki, H.1
  • 127
    • 0039514443 scopus 로고
    • Supermartingales on semi-finite von Neumann algebras
    • C. Barnett, "Supermartingales on semi-finite von Neumann algebras," J. Lond. Math. Soc. 24, 175-181 (1981).
    • (1981) J. Lond. Math. Soc. , vol.24 , pp. 175-181
    • Barnett, C.1
  • 128
    • 0010861233 scopus 로고
    • Martingales on von Neumann algebras
    • I. Cuculescu, "Martingales on von Neumann algebras," J. Multivariate Anal. 1, 17-27 (1971).
    • (1971) J. Multivariate Anal. , vol.1 , pp. 17-27
    • Cuculescu, I.1
  • 129
    • 4243806354 scopus 로고
    • Examples of quantum martingales
    • R. L. Hudson and R. F. Streater, "Examples of quantum martingales," Phys. Lett. 85A, 64-67 (1981).
    • (1981) Phys. Lett. , vol.85 A , pp. 64-67
    • Hudson, R.L.1    Streater, R.F.2
  • 130
    • 51249188624 scopus 로고
    • Ontinuous tensor products of Hilbert spaces and generalized random fields
    • R. F. Streater and A. Wulfsohn, "Continuous tensor products of Hilbert spaces and generalized random fields," Nuovo Cimento Series X 57, 330-339 (1968).
    • (1968) Nuovo Cimento Series X , vol.57 , pp. 330-339
    • Streater, R.F.1    Wulfsohn, A.2
  • 131
    • 0039514437 scopus 로고
    • Noncommutative martingales and stochastic integrals in Fock space
    • Stochastic Processes in Quantum Theory and Statistical Physics, edited by S. Albeverio, Ph. Combe, and M. Sirugue-Collin, Springer-Verlag, Berlin
    • R. L. Hudson and R. F. Streater, "Noncommutative martingales and stochastic integrals in Fock space," in Stochastic Processes in Quantum Theory and Statistical Physics, edited by S. Albeverio, Ph. Combe, and M. Sirugue-Collin, [Lect. Notes Phys. 173, 216-222 (Springer-Verlag, Berlin, 1981)].
    • (1981) Lect. Notes Phys. , vol.173 , pp. 216-222
    • Hudson, R.L.1    Streater, R.F.2
  • 133
    • 0000114353 scopus 로고
    • A non-commutative extension of abstract integration
    • I. E. Segal, "A non-commutative extension of abstract integration," Ann. Math. 57, 401-457 (1953); 57, 595 (1953).
    • (1953) Ann. Math. , vol.57 , pp. 401-457
    • Segal, I.E.1
  • 134
    • 0040699634 scopus 로고
    • I. E. Segal, "A non-commutative extension of abstract integration," Ann. Math. 57, 401-457 (1953); 57, 595 (1953).
    • (1953) Ann. Math. , vol.57 , pp. 595
  • 135
    • 0000906048 scopus 로고
    • Tensor algebras over Hilbert space II
    • I. E. Segal, "Tensor algebras over Hilbert space II," Ann. Math. 63, 160-175 (1956).
    • (1956) Ann. Math. , vol.63 , pp. 160-175
    • Segal, I.E.1
  • 139
    • 0031549892 scopus 로고    scopus 로고
    • Non-commutative martingale inequalities
    • G. Pisier and Q. Xu, "Non-commutative martingale inequalities," Commun. Math. Phys. 189, 667-698 (1997).
    • (1997) Commun. Math. Phys. , vol.189 , pp. 667-698
    • Pisier, G.1    Xu, Q.2
  • 140
    • 0002541370 scopus 로고
    • Quasi-free quantum stochastic integrals for the CAR and CCR
    • C. Barnett, R. F. Streater, and I. F. Wilde, "Quasi-free quantum stochastic integrals for the CAR and CCR," J. Funct. Anal. 52, 19-47 (1983).
    • (1983) J. Funct. Anal. , vol.52 , pp. 19-47
    • Barnett, C.1    Streater, R.F.2    Wilde, I.F.3
  • 141
    • 0011509262 scopus 로고
    • On non-fock boson stochastic integrals
    • M. Lindsay and I. F. Wilde, "On non-Fock boson stochastic integrals," J. Funct. Anal. 65, 76-82 (1986).
    • (1986) J. Funct. Anal. , vol.65 , pp. 76-82
    • Lindsay, M.1    Wilde, I.F.2
  • 142
    • 85037762068 scopus 로고    scopus 로고
    • private communication
    • P.-A. Meyer (private communication).
    • Meyer, P.-A.1
  • 144
    • 0003329419 scopus 로고
    • Unitary quantum stochastic evolutions
    • G. F. Vincent-Smith, "Unitary quantum stochastic evolutions," Proc. London Math. Soc. 63, 401-425 (1991).
    • (1991) Proc. London Math. Soc. , vol.63 , pp. 401-425
    • Vincent-Smith, G.F.1
  • 145
    • 0031516785 scopus 로고    scopus 로고
    • Quantum stochastic positive evolutions
    • V. P. Belavkin, "Quantum stochastic positive evolutions," Commun. Math. Phys. 184, 533-566 (1997); "On stochastic generators of completely positive co-cycles," Russ. J. Math. Phys. 3, 523 (1995).
    • (1997) Commun. Math. Phys. , vol.184 , pp. 533-566
    • Belavkin, V.P.1
  • 146
    • 0031516785 scopus 로고    scopus 로고
    • On stochastic generators of completely positive co-cycles
    • V. P. Belavkin, "Quantum stochastic positive evolutions," Commun. Math. Phys. 184, 533-566 (1997); "On stochastic generators of completely positive co-cycles," Russ. J. Math. Phys. 3, 523 (1995).
    • (1995) Russ. J. Math. Phys. , vol.3 , pp. 523
  • 147
    • 0007081274 scopus 로고
    • Construction of stationary quantum Markov processes
    • LNM 1136, edited by L. Accardi and W. von Waldenfels Springer, Berlin
    • A. Frigerio, "Construction of stationary quantum Markov processes," in Quantum Probability and Applications II, LNM 1136, edited by L. Accardi and W. von Waldenfels (Springer, Berlin, 1985), pp. 207-222.
    • (1985) Quantum Probability and Applications II , pp. 207-222
    • Frigerio, A.1
  • 148
    • 0009151604 scopus 로고
    • Ito's formula is the chain rule with Wick ordering
    • R. L. Hudson and R. F. Streater, "Ito's formula is the chain rule with Wick ordering," Phys. Lett. 86A, 277-279 (1981).
    • (1981) Phys. Lett. , vol.86 A , pp. 277-279
    • Hudson, R.L.1    Streater, R.F.2
  • 149
    • 0002488398 scopus 로고
    • Fermion Ito's formula and stochastic evolutions
    • D. Applebaum and R. L. Hudson, "Fermion Ito's formula and stochastic evolutions," Commun. Math. Phys. 96, 473-496 (1984).
    • (1984) Commun. Math. Phys. , vol.96 , pp. 473-496
    • Applebaum, D.1    Hudson, R.L.2
  • 150
    • 0007142385 scopus 로고
    • Quantum Markov processes on Fock space described by integral kernels
    • Quantum Probability II, edited by L. Accardi and W. von Waldenfels
    • H. Maassen, "Quantum Markov processes on Fock space described by integral kernels," in Quantum Probability II, edited by L. Accardi and W. von Waldenfels [Lect. Notes Math. 1136, 361 (1985)].
    • (1985) Lect. Notes Math. , vol.1136 , pp. 361
    • Maassen, H.1
  • 151
    • 0000115557 scopus 로고    scopus 로고
    • Wick product of white noise operators and quantum stochastic differential equations
    • N. Obata, "Wick product of white noise operators and quantum stochastic differential equations," J. Math. Soc. J. 51, 613-641 (1999).
    • (1999) J. Math. Soc. J. , vol.51 , pp. 613-641
    • Obata, N.1
  • 152
    • 3042792044 scopus 로고
    • Failure of the quantum regression theorem
    • P. Talkner, "Failure of the quantum regression theorem," Ann. Phys. 167, 390-436 (1986).
    • (1986) Ann. Phys. , vol.167 , pp. 390-436
    • Talkner, P.1
  • 153
    • 0032376880 scopus 로고    scopus 로고
    • Brownian motion of quantum harmonic oscillators
    • G. Lindblad, "Brownian motion of quantum harmonic oscillators," J. Math. Phys. 39, 2763-2780 (1998).
    • (1998) J. Math. Phys. , vol.39 , pp. 2763-2780
    • Lindblad, G.1
  • 154
    • 0003062639 scopus 로고
    • Quantum dynamical semigroups and applications
    • Springer-Verlag, Berlin
    • R. Alicki and K. Lendl, Quantum Dynamical Semigroups and Applications [Lect. Notes Phys. 286, (Springer-Verlag, Berlin, 1987)].
    • (1987) Lect. Notes Phys. , vol.286
    • Alicki, R.1    Lendl, K.2
  • 155
    • 0011045955 scopus 로고
    • Nonlinear quantum dynamical semigroups for many-body open systems
    • R. Alicki and J. Messer, "Nonlinear quantum dynamical semigroups for many-body open systems," J. Stat. Phys. 32, 299-312 (1983).
    • (1983) J. Stat. Phys. , vol.32 , pp. 299-312
    • Alicki, R.1    Messer, J.2
  • 156
    • 0001945248 scopus 로고
    • Dissipation in many-body systems: A geometric approach based on information theory
    • R. Balian, Y. Alhassid, and R. Reinhardt, "Dissipation in many-body systems: a geometric approach based on information theory," Phys. Rep. 131, 1-146 (1986).
    • (1986) Phys. Rep. , vol.131 , pp. 1-146
    • Balian, R.1    Alhassid, Y.2    Reinhardt, R.3
  • 158
    • 0039514435 scopus 로고    scopus 로고
    • Onsager symmetry in statistical dynamics
    • R. F. Streater, "Onsager symmetry in statistical dynamics," Open Systems and Information Dynamics 6, 87-100 (1999); "The Soret and Dufour effects in statistical dynamics," Proc. R. Soc. London, Ser. A 456, 205-221 (2000).
    • (1999) Open Systems and Information Dynamics , vol.6 , pp. 87-100
    • Streater, R.F.1
  • 159
    • 33746467015 scopus 로고    scopus 로고
    • The Soret and Dufour effects in statistical dynamics
    • R. F. Streater, "Onsager symmetry in statistical dynamics," Open Systems and Information Dynamics 6, 87-100 (1999); "The Soret and Dufour effects in statistical dynamics," Proc. R. Soc. London, Ser. A 456, 205-221 (2000).
    • (2000) Proc. R. Soc. London, Ser. A , vol.456 , pp. 205-221


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