Stochastic collapse and decoherence of a non-dissipative forced harmonic oscillator

Journal of Physics A: Mathematical and General

Volumn 38, Issue 12, 2005, Pages 2729-2745

  Adler, Stephen L ^a  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17044378954     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/38/12/014     Document Type: Article

References (42)

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3. Bialynicki-Birula I and Mycielski J 1976 Nonlinear wave mechanics Ann. Phys. 100 62-93 Weinberg S 1989 Particle states as realizations (linear or nonlinear) of spacetime symmetries Nucl. Phys. B Proc. Suppl. Spacetime Symmetries ed Y S Kim and W W Zachary (Amsterdam: North Holland) pp 67-75 Weinberg S 1989 Precision tests of quantum mechanics Phys. Rev. Lett. 62 485-8 Weinberg S 1989 Testing quantum mechanics Ann. Phys. 194 336-86
4. Bialynicki-Birula I and Mycielski J 1976 Nonlinear wave mechanics Ann. Phys. 100 62-93 Weinberg S 1989 Particle states as realizations (linear or nonlinear) of spacetime symmetries Nucl. Phys. B Proc. Suppl. Spacetime Symmetries ed Y S Kim and W W Zachary (Amsterdam: North Holland) pp 67-75 Weinberg S 1989 Precision tests of quantum mechanics Phys. Rev. Lett. 62 485-8 Weinberg S 1989 Testing quantum mechanics Ann. Phys. 194 336-86
5. Bialynicki-Birula I and Mycielski J 1976 Nonlinear wave mechanics Ann. Phys. 100 62-93 Weinberg S 1989 Particle states as realizations (linear or nonlinear) of spacetime symmetries Nucl. Phys. B Proc. Suppl. Spacetime Symmetries ed Y S Kim and W W Zachary (Amsterdam: North Holland) pp 67-75 Weinberg S 1989 Precision tests of quantum mechanics Phys. Rev. Lett. 62 485-8 Weinberg S 1989 Testing quantum mechanics Ann. Phys. 194 336-86
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8. Gisin N 1989 Stochastic quantum dynamics and relativity Helv. Phys. Acta 62 363-71 Gisin N 1990 Weinberg's nonlinear quantum mechanics and supraluminal communications Phys. Lett. A 143 1-2 Polchinski J 1991 Weinberg's nonlinear quantum mechanics and the Einstein-Podolsky-Rosen paradox Phys. Rev. Lett. 66 397-400 Gisin N and Rigo M 1995 Relevant and irrelevant nonlinear Schrödinger equations J. Phys. A: Math. Gen. 28 7375-90
9. Gisin N 1989 Stochastic quantum dynamics and relativity Helv. Phys. Acta 62 363-71 Gisin N 1990 Weinberg's nonlinear quantum mechanics and supraluminal communications Phys. Lett. A 143 1-2 Polchinski J 1991 Weinberg's nonlinear quantum mechanics and the Einstein-Podolsky-Rosen paradox Phys. Rev. Lett. 66 397-400 Gisin N and Rigo M 1995 Relevant and irrelevant nonlinear Schrödinger equations J. Phys. A: Math. Gen. 28 7375-90
10. For reviews, see Bassi A and Ghirardi G C 2003 Dynamical reduction models Phys. Rep. 379 257-426 Pearle P 1999 Collapse models Open Systems and Measurements in Relativistic Quantum Field Theory (Lecture Notes in Physics vol 526) ed H-P Breuer and F Pettrucione (Berlin: Springer) See also Adler S L 2004 Quantum Theory as an Emergent Phenomenon (Cambridge: Cambridge University Press) chapter 6
11. For reviews, see Bassi A and Ghirardi G C 2003 Dynamical reduction models Phys. Rep. 379 257-426 Pearle P 1999 Collapse models Open Systems and Measurements in Relativistic Quantum Field Theory (Lecture Notes in Physics vol 526) ed H-P Breuer and F Pettrucione (Berlin: Springer) See also Adler S L 2004 Quantum Theory as an Emergent Phenomenon (Cambridge: Cambridge University Press) chapter 6
12. For reviews, see Bassi A and Ghirardi G C 2003 Dynamical reduction models Phys. Rep. 379 257-426 Pearle P 1999 Collapse models Open Systems and Measurements in Relativistic Quantum Field Theory (Lecture Notes in Physics vol 526) ed H-P Breuer and F Pettrucione (Berlin: Springer) See also Adler S L 2004 Quantum Theory as an Emergent Phenomenon (Cambridge: Cambridge University Press) chapter 6
13. For a brief catalog of the different forms of localization models, and references, see reference [6] of Bassi A, Ippoliti E and Adler S L 2005 Towards quantum superpositions of a mirror: stochastic collapse analysis Phys. Rev. Lett. 94 030401 See also [11]
14. Adler S L 2004 Quantum Theory as an Emergent Phenomenon (Cambridge: Cambridge University Press) p 188
15. 60 molecules Nature 401 680-2 Nairz O, Arndt M and Zeilinger A 2000 Experimental challenges in fullerene interferometry J. Mod. Opt. 47 2811-21 Nairz O, Brezger B, Arndt M and Zeilinger A 2001 Diffraction of complex molecules by structures made of light Phys. Rev. Lett. 87 160401
16. 60 molecules Nature 401 680-2 Nairz O, Arndt M and Zeilinger A 2000 Experimental challenges in fullerene interferometry J. Mod. Opt. 47 2811-21 Nairz O, Brezger B, Arndt M and Zeilinger A 2001 Diffraction of complex molecules by structures made of light Phys. Rev. Lett. 87 160401
17. 60 molecules Nature 401 680-2 Nairz O, Arndt M and Zeilinger A 2000 Experimental challenges in fullerene interferometry J. Mod. Opt. 47 2811-21 Nairz O, Brezger B, Arndt M and Zeilinger A 2001 Diffraction of complex molecules by structures made of light Phys. Rev. Lett. 87 160401
18. 60 molecules Nature 401 680-2 Nairz O, Arndt M and Zeilinger A 2000 Experimental challenges in fullerene interferometry J. Mod. Opt. 47 2811-21 Nairz O, Brezger B, Arndt M and Zeilinger A 2001 Diffraction of complex molecules by structures made of light Phys. Rev. Lett. 87 160401
19. Bassi A, Ippoliti E and Adler S L 2005 Towards quantum superpositions of a mirror: stochastic collapse analysis Phys. Rev. Lett. 94 030401 Adler S L, Bassi A and Ippoliti E 2005 Towards quantum superpositions of a mirror: stochastic collapse analysis - calculational details J. Phys. A: Math. Gen. 38 2715-27
20. Bassi A, Ippoliti E and Adler S L 2005 Towards quantum superpositions of a mirror: stochastic collapse analysis Phys. Rev. Lett. 94 030401 Adler S L, Bassi A and Ippoliti E 2005 Towards quantum superpositions of a mirror: stochastic collapse analysis - calculational details J. Phys. A: Math. Gen. 38 2715-27
21. Marshall W, Simon C, Penrose R and Bouwmeester D 2003 Towards quantum superpositions of a mirror Phys. Rev. Lett. 91 130401
22. Braginsky V B and Ya Khalili F 1991 Quantum Measurements (Cambridge: Cambridge University Press) Caves C M, Thorne K S, Drever R W P, Sandberg V D and Zimmerman M 1980 On the measurement of a weak classical force coupled to a quantum-mechanical oscillator: I. Issues of principle Rev. Mod. Phys. 52 341-92 Bocko M F and Onofrio R 1996 On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress Rev. Mod. Phys. 68 755-99
23. Braginsky V B and Ya Khalili F 1991 Quantum Measurements (Cambridge: Cambridge University Press) Caves C M, Thorne K S, Drever R W P, Sandberg V D and Zimmerman M 1980 On the measurement of a weak classical force coupled to a quantum-mechanical oscillator: I. Issues of principle Rev. Mod. Phys. 52 341-92 Bocko M F and Onofrio R 1996 On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress Rev. Mod. Phys. 68 755-99
24. Braginsky V B and Ya Khalili F 1991 Quantum Measurements (Cambridge: Cambridge University Press) Caves C M, Thorne K S, Drever R W P, Sandberg V D and Zimmerman M 1980 On the measurement of a weak classical force coupled to a quantum-mechanical oscillator: I. Issues of principle Rev. Mod. Phys. 52 341-92 Bocko M F and Onofrio R 1996 On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress Rev. Mod. Phys. 68 755-99
25. The models for localization that are considered here are: Ghirardi G C, Rimini A and Weber T 1986 Unified dynamics for microscopic and macroscopic systems Phys. Rev. D 34 470-91, known as GRW or as QMSL (quantum mechanics with spontaneous localizations) Pearle P 1989 Combining stochastic dynamical state-vector reduction with spontaneous localization Phys. Rev. A 39 2277-89, and Ghirardi G C, Pearle P and Rimini A 1990 Markov processes in Hubert space and continuous spontaneous localization of systems of identical particles Phys. Rev. A 42 78-89, known as CSL (continuous spontaneous localization) Diósi L 1989 Models for universal reduction of macroscopic quantum fluctuations Phys. Rev. A 40 1165-74, known as QMUPL (quantum mechanics with universal position localization)
26. The models for localization that are considered here are: Ghirardi G C, Rimini A and Weber T 1986 Unified dynamics for microscopic and macroscopic systems Phys. Rev. D 34 470-91, known as GRW or as QMSL (quantum mechanics with spontaneous localizations) Pearle P 1989 Combining stochastic dynamical state-vector reduction with spontaneous localization Phys. Rev. A 39 2277-89, and Ghirardi G C, Pearle P and Rimini A 1990 Markov processes in Hubert space and continuous spontaneous localization of systems of identical particles Phys. Rev. A 42 78-89, known as CSL (continuous spontaneous localization) Diósi L 1989 Models for universal reduction of macroscopic quantum fluctuations Phys. Rev. A 40 1165-74, known as QMUPL (quantum mechanics with universal position localization)
27. The models for localization that are considered here are: Ghirardi G C, Rimini A and Weber T 1986 Unified dynamics for microscopic and macroscopic systems Phys. Rev. D 34 470-91, known as GRW or as QMSL (quantum mechanics with spontaneous localizations) Pearle P 1989 Combining stochastic dynamical state-vector reduction with spontaneous localization Phys. Rev. A 39 2277-89, and Ghirardi G C, Pearle P and Rimini A 1990 Markov processes in Hubert space and continuous spontaneous localization of systems of identical particles Phys. Rev. A 42 78-89, known as CSL (continuous spontaneous localization) Diósi L 1989 Models for universal reduction of macroscopic quantum fluctuations Phys. Rev. A 40 1165-74, known as QMUPL (quantum mechanics with universal position localization)
28. The models for localization that are considered here are: Ghirardi G C, Rimini A and Weber T 1986 Unified dynamics for microscopic and macroscopic systems Phys. Rev. D 34 470-91, known as GRW or as QMSL (quantum mechanics with spontaneous localizations) Pearle P 1989 Combining stochastic dynamical state-vector reduction with spontaneous localization Phys. Rev. A 39 2277-89, and Ghirardi G C, Pearle P and Rimini A 1990 Markov processes in Hubert space and continuous spontaneous localization of systems of identical particles Phys. Rev. A 42 78-89, known as CSL (continuous spontaneous localization) Diósi L 1989 Models for universal reduction of macroscopic quantum fluctuations Phys. Rev. A 40 1165-74, known as QMUPL (quantum mechanics with universal position localization)
29. See, e.g., Joos E and Zeh H D 1985 The emergence of classical properties through interaction with the environment Z. Phys. B 59 223-43
30. Ghirardi G C, Pearle P and Rimini A 1990 Markov processes in Hubert space and continuous spontaneous localization of systems of identical particles Phys. Rev. A 42 78-89 (equations (3.38a-c) and (3.41a-c))
31. Agarwal G S 1969 Master equations in phase-space formulation of quantum optics Phys. Rev. 178 2025-35 Agarwal G S 1971 Brownian motion of a quantum oscillator Phys. Rev. A 4 739-47 Extensive further references can be found in: Karrlein R and Grabert H 1997 Exact time evolution and master equations for the damped harmonic oscillator Phys. Rev. E 55 153-64 Isar A, Sandulescu A and Scheid W 1999 Purity and decoherence in the theory of a damped harmonic oscillator Phys. Rev. E 60 6371-81
32. Agarwal G S 1969 Master equations in phase-space formulation of quantum optics Phys. Rev. 178 2025-35 Agarwal G S 1971 Brownian motion of a quantum oscillator Phys. Rev. A 4 739-47 Extensive further references can be found in: Karrlein R and Grabert H 1997 Exact time evolution and master equations for the damped harmonic oscillator Phys. Rev. E 55 153-64 Isar A, Sandulescu A and Scheid W 1999 Purity and decoherence in the theory of a damped harmonic oscillator Phys. Rev. E 60 6371-81
33. Agarwal G S 1969 Master equations in phase-space formulation of quantum optics Phys. Rev. 178 2025-35 Agarwal G S 1971 Brownian motion of a quantum oscillator Phys. Rev. A 4 739-47 Extensive further references can be found in: Karrlein R and Grabert H 1997 Exact time evolution and master equations for the damped harmonic oscillator Phys. Rev. E 55 153-64 Isar A, Sandulescu A and Scheid W 1999 Purity and decoherence in the theory of a damped harmonic oscillator Phys. Rev. E 60 6371-81
34. Agarwal G S 1969 Master equations in phase-space formulation of quantum optics Phys. Rev. 178 2025-35 Agarwal G S 1971 Brownian motion of a quantum oscillator Phys. Rev. A 4 739-47 Extensive further references can be found in: Karrlein R and Grabert H 1997 Exact time evolution and master equations for the damped harmonic oscillator Phys. Rev. E 55 153-64 Isar A, Sandulescu A and Scheid W 1999 Purity and decoherence in the theory of a damped harmonic oscillator Phys. Rev. E 60 6371-81
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