메뉴 건너뛰기




Volumn 120, Issue 9, 2010, Pages 1722-1747

Existence, uniqueness and approximation of the jump-type stochastic Schrdinger equation for two-level systems

Author keywords

Euler scheme; Poisson random measure; Quantum trajectories; stochastic differential equation with jump; Stochastic intensity; Stochastic Schrdinger equations

Indexed keywords

EULER SCHEME; POISSON RANDOM MEASURE; QUANTUM TRAJECTORIES; SCHRDINGER EQUATIONS; STOCHASTIC DIFFERENTIAL EQUATIONS; STOCHASTIC INTENSITY;

EID: 77955419781     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2010.03.010     Document Type: Article
Times cited : (44)

References (34)
  • 1
    • 33644882745 scopus 로고    scopus 로고
    • From repeated to continuous quantum interactions
    • S. Attal, and Y. Pautrat From repeated to continuous quantum interactions Ann. Henri Poincar 7 1 2006 59 104
    • (2006) Ann. Henri Poincar , vol.7 , Issue.1 , pp. 59-104
    • Attal, S.1    Pautrat, Y.2
  • 2
    • 0000015586 scopus 로고
    • Measurements continuous in time and a posteriori states in quantum mechanics
    • A. Barchielli, and V.P. Belavkin Measurements continuous in time and a posteriori states in quantum mechanics J. Phys. A 24 7 1991 1495 1514
    • (1991) J. Phys. A , vol.24 , Issue.7 , pp. 1495-1514
    • Barchielli, A.1    Belavkin, V.P.2
  • 3
    • 0000765698 scopus 로고
    • Constructing quantum measurement processes via classical stochastic calculus
    • A. Barchielli, and A.S. Holevo Constructing quantum measurement processes via classical stochastic calculus Stochastic Processes Appl. 58 1995 293 317
    • (1995) Stochastic Processes Appl. , vol.58 , pp. 293-317
    • Barchielli, A.1    Holevo, A.S.2
  • 4
    • 14844322888 scopus 로고    scopus 로고
    • Instrumental processes, entropies, information in quantum continual measurements
    • A. Barchielli, and G. Lupieri Instrumental processes, entropies, information in quantum continual measurements Quantum Inf. Comput. 4 67 2004 437 449
    • (2004) Quantum Inf. Comput. , vol.4 , Issue.67 , pp. 437-449
    • Barchielli, A.1    Lupieri, G.2
  • 5
    • 52449141083 scopus 로고    scopus 로고
    • On a class of stochastic differential equations used in quantum optics
    • A. Barchielli, and F. Zucca On a class of stochastic differential equations used in quantum optics Rend. Sem. Mat. Fis. Milano 66 1998 355 376
    • (1998) Rend. Sem. Mat. Fis. Milano , vol.66 , pp. 355-376
    • Barchielli, A.1    Zucca, F.2
  • 6
    • 0000017251 scopus 로고
    • Quantum stochastic calculus and quantum nonlinear filtering
    • V.P. Belavkin Quantum stochastic calculus and quantum nonlinear filtering J. Multivariate Anal. 42 1992 171
    • (1992) J. Multivariate Anal. , vol.42 , pp. 171
    • Belavkin, V.P.1
  • 7
  • 8
    • 0742334132 scopus 로고    scopus 로고
    • A stochastic hamiltonian approach for quantum jumps, spontaneous localizations, and continuous trajectories
    • V.P. Belavkin, and O. Melsheimer A stochastic hamiltonian approach for quantum jumps, spontaneous localizations, and continuous trajectories Quantum Semiclass. Opt. 8 1996 167
    • (1996) Quantum Semiclass. Opt. , vol.8 , pp. 167
    • Belavkin, V.P.1    Melsheimer, O.2
  • 9
    • 0034345636 scopus 로고    scopus 로고
    • Quantum stochastic differential equation
    • V.P. Belavkin, and P. Staszewski Quantum stochastic differential equation J. Math. Phys. 41 2000 7220
    • (2000) J. Math. Phys. , vol.41 , pp. 7220
    • Belavkin, V.P.1    Staszewski, P.2
  • 10
    • 1642393418 scopus 로고    scopus 로고
    • Stochastic Schrdinger equations
    • L. Bouten, M. Gu, and H. Maassen Stochastic Schrdinger equations J. Phys. A 37 9 2004 3189 3209
    • (2004) J. Phys. A , vol.37 , Issue.9 , pp. 3189-3209
    • Bouten, L.1    Gu, M.2    Maassen, H.3
  • 12
    • 0039300547 scopus 로고    scopus 로고
    • Quantum measurement and the transformation from quantum to classical probabilities
    • H.P. Breuer, and F. Petruccione Quantum measurement and the transformation from quantum to classical probabilities Phys. Rev. A 54 1996 1146 1153
    • (1996) Phys. Rev. A , vol.54 , pp. 1146-1153
    • Breuer, H.P.1    Petruccione, F.2
  • 13
    • 4243440751 scopus 로고
    • Reduced system dynamics as a stochastic process in Hilbert space
    • H.P. Breuer, and F. Petruccione Reduced system dynamics as a stochastic process in Hilbert space Phys. Rev. lett 74 1995 3778 3791
    • (1995) Phys. Rev. Lett , vol.74 , pp. 3778-3791
    • Breuer, H.P.1    Petruccione, F.2
  • 14
    • 26144439344 scopus 로고
    • Stochastic dynamics of quantum jumps
    • H.P. Breuer, and F. Petruccione Stochastic dynamics of quantum jumps Phys. Rev. E 52 1995 428 441
    • (1995) Phys. Rev. e , vol.52 , pp. 428-441
    • Breuer, H.P.1    Petruccione, F.2
  • 15
    • 0001038758 scopus 로고
    • Some Poisson approximations using compensators
    • T.C. Brown Some Poisson approximations using compensators Ann. Probab. 11 3 1983 726 744
    • (1983) Ann. Probab. , vol.11 , Issue.3 , pp. 726-744
    • Brown, T.C.1
  • 16
    • 34247193446 scopus 로고    scopus 로고
    • Research Paper Series 157, Quantitative Finance Research Centre, University of Technology, Sydney, April
    • N. Bruti-Liberati, E. Platen, On the strong approximation of jump-diffusion processes. Research Paper Series 157, Quantitative Finance Research Centre, University of Technology, Sydney, April 2005. Available at http://ideas.repec.org/p/uts/rpaper/157.html.
    • (2005) On the Strong Approximation of Jump-diffusion Processes
    • Bruti-Liberati, N.1    Platen, E.2
  • 17
    • 0001771043 scopus 로고
    • An open systems approach to quantum optics
    • Springer Verlag Berlin
    • H.J. Carmichael An open systems approach to quantum optics Lectures Notes in Physics 1993 Springer Verlag Berlin
    • (1993) Lectures Notes in Physics
    • Carmichael, H.J.1
  • 18
    • 0037527083 scopus 로고    scopus 로고
    • Quantum Noise. A Handbook of Markovian and non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics
    • third ed. Springer-Verlag Berlin
    • C.W. Gardiner, and P. Zoller Quantum Noise. A Handbook of Markovian and non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics third ed. Springer Series in Synergetics 2004 Springer-Verlag Berlin
    • (2004) Springer Series in Synergetics
    • Gardiner, C.W.1    Zoller, P.2
  • 19
    • 0001137441 scopus 로고
    • Quantum measurements and stochastic processes
    • N. Gisin Quantum measurements and stochastic processes Phys. Rev. Lett. 52 1984 1657 1660
    • (1984) Phys. Rev. Lett. , vol.52 , pp. 1657-1660
    • Gisin, N.1
  • 21
    • 8644231753 scopus 로고    scopus 로고
    • Stochastic Schrdinger equations as limit of discrete filtering
    • J. Gough, and A. Sobolev Stochastic Schrdinger equations as limit of discrete filtering Open Syst. Inf. Dyn. 11 3 2004 235 255
    • (2004) Open Syst. Inf. Dyn. , vol.11 , Issue.3 , pp. 235-255
    • Gough, J.1    Sobolev, A.2
  • 22
    • 33947200770 scopus 로고    scopus 로고
    • Exploring the Quantum
    • Oxford University Press Oxford
    • S. Haroche, and J.M. Raimond Exploring the Quantum Oxford Graduate Texts 2006 Oxford University Press Oxford Atoms, cavities and photons.
    • (2006) Oxford Graduate Texts
    • Haroche, S.1    Raimond, J.M.2
  • 23
    • 0003516778 scopus 로고
    • Calcul stochastique et problmes de martingales
    • Springer Berlin
    • J. Jacod Calcul stochastique et problmes de martingales Lecture Notes in Mathematics vol. 714 1979 Springer Berlin
    • (1979) Lecture Notes in Mathematics , vol.714
    • Jacod, J.1
  • 24
    • 4544330746 scopus 로고    scopus 로고
    • The Euler scheme for Lévy driven stochastic differential equations: Limit theorems
    • J. Jacod The Euler scheme for Lévy driven stochastic differential equations: limit theorems Ann. Probab. 32 3A 2004 1830 1872
    • (2004) Ann. Probab. , vol.32 , Issue.3 A , pp. 1830-1872
    • Jacod, J.1
  • 25
    • 17444362986 scopus 로고    scopus 로고
    • The approximate Euler method for Lévy driven stochastic differential equations
    • J. Jacod, T.G. Kurtz, S. Mlard, and P. Protter The approximate Euler method for Lévy driven stochastic differential equations Ann. Inst. H. Poincar Probab. Statist. 41 3 2005 523 558
    • (2005) Ann. Inst. H. Poincar Probab. Statist. , vol.41 , Issue.3 , pp. 523-558
    • Jacod, J.1    Kurtz, T.G.2    Mlard, S.3    Protter, P.4
  • 26
    • 21244458477 scopus 로고
    • Quelques remarques sur un nouveau type d'quations diffrentielles stochastiques
    • Springer Berlin
    • J. Jacod, and P. Protter Quelques remarques sur un nouveau type d'quations diffrentielles stochastiques Seminar on Probability, XVI Lecture Notes in Math. vol. 920 1982 Springer Berlin 447 458
    • (1982) Lecture Notes in Math. , vol.920 , pp. 447-458
    • Jacod, J.1    Protter, P.2
  • 27
    • 0141547655 scopus 로고    scopus 로고
    • Fundamental Principles of Mathematical Science
    • second edition Springer-Verlag Berlin
    • J. Jacod, and A.N. Shiryaev Limit theorems for stochastic processes second edition Grundlehren der Mathematischen Wissenschaften Fundamental Principles of Mathematical Science vol. 288 2003 Springer-Verlag Berlin
    • (2003) Grundlehren der Mathematischen Wissenschaften , vol.288
    • Jacod, J.1    Shiryaev, A.N.2
  • 28
    • 0000367265 scopus 로고
    • Weak limit theorems for stochastic integrals and stochastic differential equations
    • T.G. Kurtz, and P. Protter Weak limit theorems for stochastic integrals and stochastic differential equations Ann. Probab. 19 3 1991 1035 1070
    • (1991) Ann. Probab. , vol.19 , Issue.3 , pp. 1035-1070
    • Kurtz, T.G.1    Protter, P.2
  • 29
    • 0009220140 scopus 로고
    • Wong-Zakai corrections, random evolutions, and simulation schemes for SDEs
    • Academic Press Boston, MA
    • T.G. Kurtz, and P. Protter Wong-Zakai corrections, random evolutions, and simulation schemes for SDEs Stochastic Analysis 1991 Academic Press Boston, MA 331 346
    • (1991) Stochastic Analysis , pp. 331-346
    • Kurtz, T.G.1    Protter, P.2
  • 30
    • 0027552687 scopus 로고
    • Monte Carlo wave-function method in quantum optics
    • K. Mølmer, Y. Castin, and J. Dalibard Monte Carlo wave-function method in quantum optics J. Opt. Soc. Am. B 10 1993 524 538
    • (1993) J. Opt. Soc. Am. B , vol.10 , pp. 524-538
    • Mølmer, K.1    Castin, Y.2    Dalibard, J.3
  • 31
    • 52949083967 scopus 로고    scopus 로고
    • Basic properties of non-linear stochastic Schrdinger equations driven by Brownian motions
    • C.M. Mora, and R. Rebolledo Basic properties of non-linear stochastic Schrdinger equations driven by Brownian motions Ann. Appl. Probab. 18 2 2008 591 619
    • (2008) Ann. Appl. Probab. , vol.18 , Issue.2 , pp. 591-619
    • Mora, C.M.1    Rebolledo, R.2
  • 32
    • 61849156803 scopus 로고    scopus 로고
    • Existence, uniqueness and approximation of a stochastic Schrdinger equation: The Diffusive case
    • C. Pellegrini Existence, uniqueness and approximation of a stochastic Schrdinger equation: the Diffusive case Ann. Probab. 36 6 2008 2332 2353
    • (2008) Ann. Probab. , vol.36 , Issue.6 , pp. 2332-2353
    • Pellegrini, C.1
  • 33
    • 0000867143 scopus 로고
    • Stochastic quantum dynamics of a continuously monitored laser
    • H.M. Wiseman Stochastic quantum dynamics of a continuously monitored laser Phys. Rev. A 47 1993 5180 5192
    • (1993) Phys. Rev. A , vol.47 , pp. 5180-5192
    • Wiseman, H.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.