闵氏时空中与标量场导数相耦合的加速原子的辐射性质
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摘要
真空涨落，辐射反作用，或者二者的联合被提出来解释自发发射的原因，在Heisenberg图象方法中，物理解释的不确定性源于原子和场不同对易算符次序的选择。Dalibard，Dupont-Roc，Cohen Tannoudji(DDC)解决了这个问题，他们认为存在一个对称算符次序，可以使真空涨落和辐射反作用对原子变量变化率的贡献分别厄米，且每一种贡献都拥有独立的物理意义，并把这种程序推广到子系统和热库的相互作用中去，热库的真空涨落极化子系统(热库的涨落效应)，子系统极化热库(自反作用效应)，这就是著名的DDC方法。
Jǖrgen Audretsch和Rainer Mǖller利用DDC方法研究了无边界闵氏时空中原子与无质量量子标量场的相互作用，讨论了量子真空中任意稳态运动原子能量的变化率，并计算了原子向平衡态的演化。他们的主要意图是定量区分和分析真空涨落和辐射反作用各自对匀加速基态原子自发激发的贡献，这有助于理解构成Unruh效应的物理基础。
陆世专和余洪伟运用Jǖrgen Audretsch和Rainer Mǖller的方法研究了边界存在时两能级加速原子与无质量量子标量场的相互作用，边界的出现修正了标量场的量子涨落，也改变了原子的辐射性质。通过计算惯性和匀加速运动原子的平均能量变化率，发现边界诱导的修正使激发态惯性原子的自发辐射率在边界附近振荡，这种振荡方式提供了一种用实验检验几何边界效应的可能性。边界的出现和原子加速导致真空涨落的改变，即使在真空，基态加速原子跃迁到激发态也有可能，这可以被认为是构成Unruh效应的真实物理过程。
Jǖgen Audretsch和Rainer Mǖller考虑了在Minkowski空间加速度对原子辐射能级移动的影响。他们研究了两能级原子和量子标量场的耦合，使用了Heisenberg图象方法，分别求出了真空涨落和辐射反作用对两能级原子Lamb移动的贡献，并对匀加速原子的能级移动和静止时的情况进行比较。
本文用Jǖrgen Audretsch和Rainer Mǖller的方法来研究与无质量量子标量场导数耦合的多能级加速原子的自发激发，并分别计算真空涨落和辐射反作用对平均原子能量变化率的贡献。我们发现，与原子和场之间的单极子类型的相互作用相比较，除了Unruh温度热库下的修正外，这里出现了与加速度的平方成正比的额外修正，加速度诱导的修正项显示出各向异性，对于各向同性的极化加速原子而言，纵向极化的贡献四倍于横向极化的贡献。边界的出现修正了量子场，也修正了与这些场相互作用的加速原子的自发激发率。在偶极子-导数耦合中我们研究了边界对匀加速多能级原子自发激发的影响，分别计算了修正的真空涨落和辐射反作用对原子自发激发率的贡献，结果显示边界修正了激发率，使得它成为原子与边界距离的函数。当原子越来越靠近边界时，边界效应越来越明显，平行于边界的原子极化对自发激发率的贡献被压制而垂直方向的贡献被增强。我们还研究了加速多能级原子的能级移动，分别计算了真空涨落和辐射反作用对能级移动的贡献。与单极子类型的相互作用相比，加速度改变了真空涨落和辐射反作用的贡献。我们的结果显示即使是考虑同样的量子标量场，平均原子能量变化率和能级移动的加速效应不仅依赖于与原子耦合的量子场，还依赖于相互作用的种类。
本文组织如下：第一章介绍DDC方法，第二章介绍已有的利用DDC方法研究与标量场相耦合的两能级原子的自发激发和能级移动，第三、四、五章介绍我们自己的工作——运用DDC方法讨论与标量场导数相耦合的多能级加速原子的自发激发和能级移动。在第六章是对我们自己工作的回顾与对未来研究的展望。
Mechanisms such as vacuum fluctuations, radiation reaction, or a combina-tion of them have been put forward to explain why spontaneous emission occurs.The ambiguity in physical interpretation arises from different choices of orderingof commuting operators of atom and field in a Heisenberg picture approach to theproblem. Significant progress has been made by Dalibard, Dupont-Roc, CohenTannoudji that there exists a symmetric operator ordering that the distinct con-tributions of vacuum fluctuations and radiation reaction to the rate of change ofan atomic observable are separately Hermitian. if one demands such an ordering,each contribution can possess an independent physical meaning. Such a procedureis generalized to the case of a small system S interacting with a large reservoir R,which is known as the formalism of DDC, and allows the separation of the twotypes of physical processes, those where R fluctuates and polarizes S (effects ofreservior fluctuations), those where S polarizes R (effects of self reaction).
Jǖrgen Audretsch and Rainer Mǖller have considered an atom in interactionwith a massless scalar quantum field. They have discussed the structure of therate of variation of the atomic energy for an arbitrary stationary motion of theatom through the quantum vacuum. Their main intention is to identify and toanalyze quantitatively the distinct contributions of vacuum fluctuations and radi-ation reaction to the spontaneous excitation of a uniformly accelerated atom inits ground state. This gives an understanding of the role of the different physicalprocesses underlying the Unruh effect. The atom's evolution into equilibrium forspontaneous excitation and spontaneous emission are calculated.
Shizhuan Lu and Hongwei Yu have studied a two-level atom in interactionwith a real massless scalar quantum field in a spacetime with a reflecting boundary.The presence of the boundary modifies the quantum fluctuations of the scalar field,which in turn modifies the radiative properties of atoms. They have calculatedthe rate of change of the mean atomic energy for both inertial motion and uniformacceleration. It is found that the modifications induced by the presence of aboundary make the spontaneous radiation rate of an excited inertial atom oscillatenear the boundary and this oscillatory behavior may offer a possible opportunityfor experimental tests for geometrical (boundary) effects in flat spacetime. Whilefor accelerated atoms, the transitions from ground states to excited states arefound to be possible even in a vacuum due to changes in the vacuum fluctuationsinduced by both the presence of the boundary and acceleration of atoms, and thiscan be regarded as an actual physical process underlying the Unruh effect.
Jǖrgen Audretsch and Rainer Mǖller have also considered the influence of ac-celeration on the radiative energy shifts of atoms in Minkowski space. They havestudied a two-level atom coupled to a scalar quantum field. Using a Heisenberg pic-ture approach, they are able to separate the contributions of vacuum fluctuationsand radiation reaction to Lamb shift of the two-level atom. The resulting energyshifts for the special case of a uniformly accelerated atom are then compared withthose of an atom at rest.
In this dissertation, we study the spontaneous excitation of an acceleratedmultilevel atom in dipole coupling to the derivative of a massless quantum scalarfield and separately calculate the contributions of the vacuum fluctuations andradiation reaction to the rate of change of the mean atomic energy of the atom. Itis found that, in contrast to the case where a monopole like interaction betweenthe atom and the field is assumed, there appear extra corrections proportional to the acceleration squared, in addition to corrections which can be viewed as aresult of an ambient thermal bath at the Unruh temperature, as compared withthe inertial case, and the acceleration induced correction terms show anisotropywith the contribution from longitudinal polarization being four times that from thetransverse polarization for isotropically polarized accelerated atoms. Our resultssuggest that the effect of acceleration on the rate of change of the mean atomicenergy is dependent not only on the quantum field to which the atom is coupled,but also on the type of the interaction even if the same scalar quantum field isconsidered.
The presence of boundaries modifies the modes of quantum fields, which mayin turn modifies the spontaneous excitation rate of accelerated atoms in interactionwith these fields. We study the effect of the presence of a reflecting boundary onthe spontaneous excitation of a uniformly accelerated polarized multilevel atominteracting with quantum scalar fields in a dipole-derivative coupling scheme. Weseparately calculate the contributions of modified vacuum fluctuations and theradiation reaction to the spontaneous excitation rate of the atom. Our results showthat the presence of the boundary modulates the excitation rate and makes it afunction of the atom's distance from the boundary. When the atom is placed closerand closer to the boundary, the influence of the boundary becomes more and moredrastic, with the contribution of the atom's polarization in the direction parallelto the boundary to the spontaneous excitation rate dramatically suppressed whilethat in the normal direction greatly enhanced.
We study the energy level shifts of an accelerated multilevel atom in dipolecoupling to the derivative of a quantum massless scalar field and separately calcu-late the contributions of vacuum fluctuations and radiation reaction to the shifts.We find that, in contrast to the case of a monopole like interaction, both the vac- uum fluctuations and radiation reaction contributions are altered by acceleration,and they all contain non-thermal correction terms, our results suggest that the ef-fect of acceleration on the energy shifts is dependent on the type of the interactionbetween the atom and the quantum field.
The paper is organized as follows. We present a review of the formalism ofDDC in Chapter 1, and that of the works by others using the formalism of DDCon the spontaneous excitation and energy shifts of a two-level atom coupled toa scalar field in Chapter 2. Chapters 3-5 describe our work: the applications ofthe DDC formalism to discuss the spontaneous excitation and energy shifts of amultilevel accelerated atom interacting with the derivative of a scalar field. InChapter 6 we give a brief summary of our work and an outlook for possible futureresearch.
Jǖrgen Audretsch和Rainer Mǖller利用DDC方法研究了无边界闵氏时空中原子与无质量量子标量场的相互作用，讨论了量子真空中任意稳态运动原子能量的变化率，并计算了原子向平衡态的演化。他们的主要意图是定量区分和分析真空涨落和辐射反作用各自对匀加速基态原子自发激发的贡献，这有助于理解构成Unruh效应的物理基础。
陆世专和余洪伟运用Jǖrgen Audretsch和Rainer Mǖller的方法研究了边界存在时两能级加速原子与无质量量子标量场的相互作用，边界的出现修正了标量场的量子涨落，也改变了原子的辐射性质。通过计算惯性和匀加速运动原子的平均能量变化率，发现边界诱导的修正使激发态惯性原子的自发辐射率在边界附近振荡，这种振荡方式提供了一种用实验检验几何边界效应的可能性。边界的出现和原子加速导致真空涨落的改变，即使在真空，基态加速原子跃迁到激发态也有可能，这可以被认为是构成Unruh效应的真实物理过程。
Jǖgen Audretsch和Rainer Mǖller考虑了在Minkowski空间加速度对原子辐射能级移动的影响。他们研究了两能级原子和量子标量场的耦合，使用了Heisenberg图象方法，分别求出了真空涨落和辐射反作用对两能级原子Lamb移动的贡献，并对匀加速原子的能级移动和静止时的情况进行比较。
本文用Jǖrgen Audretsch和Rainer Mǖller的方法来研究与无质量量子标量场导数耦合的多能级加速原子的自发激发，并分别计算真空涨落和辐射反作用对平均原子能量变化率的贡献。我们发现，与原子和场之间的单极子类型的相互作用相比较，除了Unruh温度热库下的修正外，这里出现了与加速度的平方成正比的额外修正，加速度诱导的修正项显示出各向异性，对于各向同性的极化加速原子而言，纵向极化的贡献四倍于横向极化的贡献。边界的出现修正了量子场，也修正了与这些场相互作用的加速原子的自发激发率。在偶极子-导数耦合中我们研究了边界对匀加速多能级原子自发激发的影响，分别计算了修正的真空涨落和辐射反作用对原子自发激发率的贡献，结果显示边界修正了激发率，使得它成为原子与边界距离的函数。当原子越来越靠近边界时，边界效应越来越明显，平行于边界的原子极化对自发激发率的贡献被压制而垂直方向的贡献被增强。我们还研究了加速多能级原子的能级移动，分别计算了真空涨落和辐射反作用对能级移动的贡献。与单极子类型的相互作用相比，加速度改变了真空涨落和辐射反作用的贡献。我们的结果显示即使是考虑同样的量子标量场，平均原子能量变化率和能级移动的加速效应不仅依赖于与原子耦合的量子场，还依赖于相互作用的种类。
本文组织如下：第一章介绍DDC方法，第二章介绍已有的利用DDC方法研究与标量场相耦合的两能级原子的自发激发和能级移动，第三、四、五章介绍我们自己的工作——运用DDC方法讨论与标量场导数相耦合的多能级加速原子的自发激发和能级移动。在第六章是对我们自己工作的回顾与对未来研究的展望。
Mechanisms such as vacuum fluctuations, radiation reaction, or a combina-tion of them have been put forward to explain why spontaneous emission occurs.The ambiguity in physical interpretation arises from different choices of orderingof commuting operators of atom and field in a Heisenberg picture approach to theproblem. Significant progress has been made by Dalibard, Dupont-Roc, CohenTannoudji that there exists a symmetric operator ordering that the distinct con-tributions of vacuum fluctuations and radiation reaction to the rate of change ofan atomic observable are separately Hermitian. if one demands such an ordering,each contribution can possess an independent physical meaning. Such a procedureis generalized to the case of a small system S interacting with a large reservoir R,which is known as the formalism of DDC, and allows the separation of the twotypes of physical processes, those where R fluctuates and polarizes S (effects ofreservior fluctuations), those where S polarizes R (effects of self reaction).
Jǖrgen Audretsch and Rainer Mǖller have considered an atom in interactionwith a massless scalar quantum field. They have discussed the structure of therate of variation of the atomic energy for an arbitrary stationary motion of theatom through the quantum vacuum. Their main intention is to identify and toanalyze quantitatively the distinct contributions of vacuum fluctuations and radi-ation reaction to the spontaneous excitation of a uniformly accelerated atom inits ground state. This gives an understanding of the role of the different physicalprocesses underlying the Unruh effect. The atom's evolution into equilibrium forspontaneous excitation and spontaneous emission are calculated.
Shizhuan Lu and Hongwei Yu have studied a two-level atom in interactionwith a real massless scalar quantum field in a spacetime with a reflecting boundary.The presence of the boundary modifies the quantum fluctuations of the scalar field,which in turn modifies the radiative properties of atoms. They have calculatedthe rate of change of the mean atomic energy for both inertial motion and uniformacceleration. It is found that the modifications induced by the presence of aboundary make the spontaneous radiation rate of an excited inertial atom oscillatenear the boundary and this oscillatory behavior may offer a possible opportunityfor experimental tests for geometrical (boundary) effects in flat spacetime. Whilefor accelerated atoms, the transitions from ground states to excited states arefound to be possible even in a vacuum due to changes in the vacuum fluctuationsinduced by both the presence of the boundary and acceleration of atoms, and thiscan be regarded as an actual physical process underlying the Unruh effect.
Jǖrgen Audretsch and Rainer Mǖller have also considered the influence of ac-celeration on the radiative energy shifts of atoms in Minkowski space. They havestudied a two-level atom coupled to a scalar quantum field. Using a Heisenberg pic-ture approach, they are able to separate the contributions of vacuum fluctuationsand radiation reaction to Lamb shift of the two-level atom. The resulting energyshifts for the special case of a uniformly accelerated atom are then compared withthose of an atom at rest.
In this dissertation, we study the spontaneous excitation of an acceleratedmultilevel atom in dipole coupling to the derivative of a massless quantum scalarfield and separately calculate the contributions of the vacuum fluctuations andradiation reaction to the rate of change of the mean atomic energy of the atom. Itis found that, in contrast to the case where a monopole like interaction betweenthe atom and the field is assumed, there appear extra corrections proportional to the acceleration squared, in addition to corrections which can be viewed as aresult of an ambient thermal bath at the Unruh temperature, as compared withthe inertial case, and the acceleration induced correction terms show anisotropywith the contribution from longitudinal polarization being four times that from thetransverse polarization for isotropically polarized accelerated atoms. Our resultssuggest that the effect of acceleration on the rate of change of the mean atomicenergy is dependent not only on the quantum field to which the atom is coupled,but also on the type of the interaction even if the same scalar quantum field isconsidered.
The presence of boundaries modifies the modes of quantum fields, which mayin turn modifies the spontaneous excitation rate of accelerated atoms in interactionwith these fields. We study the effect of the presence of a reflecting boundary onthe spontaneous excitation of a uniformly accelerated polarized multilevel atominteracting with quantum scalar fields in a dipole-derivative coupling scheme. Weseparately calculate the contributions of modified vacuum fluctuations and theradiation reaction to the spontaneous excitation rate of the atom. Our results showthat the presence of the boundary modulates the excitation rate and makes it afunction of the atom's distance from the boundary. When the atom is placed closerand closer to the boundary, the influence of the boundary becomes more and moredrastic, with the contribution of the atom's polarization in the direction parallelto the boundary to the spontaneous excitation rate dramatically suppressed whilethat in the normal direction greatly enhanced.
We study the energy level shifts of an accelerated multilevel atom in dipolecoupling to the derivative of a quantum massless scalar field and separately calcu-late the contributions of vacuum fluctuations and radiation reaction to the shifts.We find that, in contrast to the case of a monopole like interaction, both the vac- uum fluctuations and radiation reaction contributions are altered by acceleration,and they all contain non-thermal correction terms, our results suggest that the ef-fect of acceleration on the energy shifts is dependent on the type of the interactionbetween the atom and the quantum field.
The paper is organized as follows. We present a review of the formalism ofDDC in Chapter 1, and that of the works by others using the formalism of DDCon the spontaneous excitation and energy shifts of a two-level atom coupled toa scalar field in Chapter 2. Chapters 3-5 describe our work: the applications ofthe DDC formalism to discuss the spontaneous excitation and energy shifts of amultilevel accelerated atom interacting with the derivative of a scalar field. InChapter 6 we give a brief summary of our work and an outlook for possible futureresearch.
引文
[1] J. R. Ackerhalt, P. L. Knight, and J. H. Eberly, Radiation reaction and Radiative Frequency Shifts. Phys. Rev. Lett. 1973, 30, 456-460.
[2] I. R. Senitzky, Radiation Reaction and Vacuum-Field Effects in Heisenberg Picture Quantum Electrodynamics. Phys. Rev. Lett. 1973, 31,955-958.
[3] J. R. Ackerhalt and J. H. Eberly, Quantum Electrodynamics and radiation reaction: Nonrelativistic Atomic Frenquency Shifts and Lifetime. Phys. Rev.D 1974, 10, 3350-3375.
[4] P. W. Milonni, J. R. Ackerhalt, and W. A. Smith, Interpretation of Radiative corrections in Spontaneous Emission. Phys. Rev. Lett. 1973, 31, 958-960.
[5] P. W. Milonni and W. A. Smith, Radiation reaction and vacuum Fluctuations in Spontaneous Emission. Phys. Rev. A. 1975, 11,814-824; P. W. Milonni, Phy. Scr. 1988, T21, 102.
[6] J. Dalibard, J. Dupont-Roc, and C. Cohen-Tannoudji, Vacuum Fluncutaions and Radiation Reaction: Identification of Their Respective contributions. J. Phys. 1982, 43, 1617-1638.
[7] J. Dalibard, J. Dupont-Roc, and C. Cohen-Tannoudji, Dynamics of a small System Coupled to a Reservoir: Reservoir Fluctuations and Self-Reaction. J. Phys. 1984, 45, 637-656.
[8] V. F. Weisskopf, Physics in the Twentieth Century-Selected essays. (The M. I. T. Press, Cambridge) 1972, 96-129.
[9] A. O. Barut, Fundations of Radiation Theory and Quantum Electrodynamics. 1980.
[10] T. A. Welton, Some Observable Effects of the Quantum-Mechanical Fluctuations of the Electromagnetic Field. Phys. Rev. 1948, 74, 1157-1167.
[11] J. Dupont-Roc, C. Fabre and C. Cohen-Tannoudji, Physical Interpretations for Radiative Corrections in the Nonrelativistic Limit. J. Phys. B. 1978, 11,563.
[12] G. W. Series, Optical Pumping and Atomic Line Shapes. edited by T. Skalinski(Panstwowe Wdawnictwo Naukowe, Warszawa) 1969, p. 25.
[13] P. K. Bullough, Coherence and Quantum Optics, edited by L. Mandel and E. Wolf(Plenum Press, New York). 1973 p. 121.
[14] H. J. Kimble and L. Mandel, Problem of Resonance Fluorescence and the Inadequacy of Spontaneous Emission as a Test of Quantum Electrodynamics. Phys. Rev. Lett. 1975, 34, 1485-1488.
[15] H. J. Kimble and L. Mandel, Theory of Resonance Fluorescence. Phys. Rev. A 1976, 13, 2123-2144.
[16] P. W. Milonni, Semiclassical and quantum-electrodynamical approaches in nonrelativistic radiation theory .Phys. Rep. 1976, 25, 1.
[17] J. B. French, V. F. Weisskopf, The Electromagnetic Shifts of Energy Levels. Phys. Rev. 1949, 75, 1240.
[18] J. D. Jackson, Classical Electrodynamics, 2nd edition (John Wiley and Sons, New York) 1975, section 17.
[19] E. J. Moniz and D. H. Sharp, Absence of Runaways and Divergent Self-Mass in Nonrelativistic Quantum Electrodynamics. Phys. Rev. D 1974, 10, 1133; Phys. Rev. D 1977, 15, 2850.
[20] V. F. Weisskopf, On the Self-Energy and the Electromagnetic Field of of the Electron. Phys. Rev 1939, 56, 72-85.
[21] L. Allen and J. H. Eberly, Optical Resonance and two-level atoms 1975.
[22] G. S. Agarwal, Springer Tracts in modern Physics, 1974, volume 70(Springer, Verlag, Berlin).
[23] C. Cohen-Tannoudji, Frontier in laser spectroscope, 1975, volume 1, Les houches session ⅩⅩⅦ,edited by R. Balian ,S. Haroche and S. Liberman(North Holland, Amsterdam), 1977.
[24] W. H. Louisell, Quantum Statistical Properties of Radiation. (John Wiley and Sone, New York), 1973.
[25] H. Grabert, On the equivalence of generalized Langevin equation and generalized master equation, Z. Phys. B 1977, 26, 79.
[26] P. Martin, Many Body Physics, Les Houches 1967, edit by C. De Witt and R. Balian(Gordon and Breach, New York) 1968.
[27] Jurgen Audretsch and Rainer Muller, Spontaneous excitation of an accelerated atom: The contributions of vacuum fluctuations and radiation reaction. Phys. Rev. A, 1994, 50, 1755.
[28] J. Audretsch and R. Muller, Radiative Energy Shifts of an Accelerated Two-Level System. Phys. Rev. A 1995, 52, 629-635.
[29] H. Yu and S. Lu, Spontaneous Excitation of an Accelerated Atom in a Spacetime with a Reflecting Plane Boundary. Phys. Rev. D 2005, 72, 064022.
[30] D. Meschede, W. Jhe, and E. A Hints, Radiative Properties of Atoms near a Conducting Plane: An Old Problem in a New Light. Phys. Rev. A, 1990, 41, 1587-1596.
[31] J. Audretsch and R. Muller, and M. Holzmann, Generalized Unrtth Effect and Lamb Shifts for Atoms on Arbitrary Stationary Trajectories. Classical Quantum Gravity, 1995, 12, 2927-2940.
[32] W. G. Unruh, Notes on Black-hole Evaporation. Phys. Rev. D 1976, 14, 870-892.
[33] R. H. Dicke, Coherence in Spontaneous Radiation Processes. Phys. Rev. 1954, 93, 99-110.
[34] P. W. Milonni, Why Spontaneous Emission?. Am. J. Phys. 1984, 52, 340-340.
[35] V. M. Fain, Soy. J. E. T. P, 1966, 882. V. M. Fain and Y. I. Khanin, Quantum Electronica. (M. I. T. Press, Cambridge) ,1969. B. Fain, I1 Nuovo Cimento 68B, 1982, 73.
[36] Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1972).
[37] H. B. G. Casimir, On the Attraction between Perfectly Conducting Plates. Proc. K. Ned. Akad. Wet. 1948, 51, 793.
[38] H. Yu and L. H. Ford, Lightcone Fluctuations in Two Flat Spacetime with Nontrivial Topology. Phys. Rev. D 1999, 60, 084023.
[39] H. Yu and L. H. Ford, Lightcone Fluctuations in Quantum Gravity and Extra Dimensions. Phys. Lett. B 2000, 496, 107-112.
[40] H. Yu and L. H. Ford, Light Fluctuations in Theories with Extra Dimenssions, arXiv, 2000, gr-qc/0004063.
[41] A. O. Barut and J. P. Dowling, Quantum Electrodynamics Based on Self-Fields: On the Origin of thermal Radiation Detected by an Accelerating Observer. Phys. Rev. A 1990, 41, 2277-2283.
[42] H. Yu and P. X. Wu, Quantum Fluctuations of the Light Cone in Fourdimensional Spacetime with Parallel Plane Boundaries. Phys. Rev. D 2003, 68, 084019.
[43] H. Yu and L. H. Ford, Vacuum Fluctuations and Brownian Motion of a Charged Test near a Reflecting Boundary. Phys. Rev. D 2004, 70, 065009.
[44] H. Yu and J. Chen, Brownian Motion of a Charged test Particle in Vacuum between Two Conduncing Plates. Phys. Rev. D 2004, 70, 125006-125010.
[45] D. Meschede, Radiating Atoms in Confined Space: From Spontaneous Emission to Micromasers. Phys. Rep. 1992, 211, 201.
[46] S. A. Fulling, Nonuniqueness of Canonical Field Quantization in Riemannian Space-Time. Phys. Rev. D 1973, 7, 2850-2862.
[47] N. D. Birrell and P. C. W. Davies, Quantum Field in Curved Space (Cambridge University Press, Cambridge, 1982).
[48] C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photo Interactious. Basic Processes and Applications. (Wiley, New York, 1992).
[49] G. Barton, Temperature Dependence of the Lamb Shift. Phys. Rev. A 1972, 5, 468-470.
[50] P. K. Knight, Effects of External Fields on the Lamb Shift. J.Phys. A 1972, 5, 417-425.
[51] J. W. Farley and W. H. Wing, Accurate Calculation of Dynamic Stark Shifts and Depopulation Rates of Rydberg Energy Levels Induced by Blackbody Radiation. Hydrogen, Helium, and Alkali-Metal Atoms. Phys. Rev. A 1981, 23, 2397-2424.
[52] H. A. Bethe,The Electromagnetic Shift of Energy Levels. Phys. Rev 1947, 72, 339.
[53] J. S. Bell and J. M. Leinaas, Nucl. Phys. B 1983, 212, 131; 1987, 284, 488.
[54] Passante, Radiative Level Shifts of an Accelerated Hydrogen Atom and Unruh Effect in Quantum Electrodynamics. Phys. Rev. A 1998, 57, 1590.
[55] Z. Zhu, H. Yu and S.Lu, Spontaneous Excitation of an Accelerated Hydrogen Atom Coupled with Electromagnetic Vacuum Fluctuations. Phys. Rev. D 2006, 73, 107501.
[56] Y. Zhu, and H. Yu, Spontaneous Excitation of an Aeeclerated Multilevel Atom in dipole Coupling to the derivative of a Scalar field. Class. Quantum. Grav 2007, 24, 95.
[57] M. Tan and H. Yu, Random Motion of a Charged Test Particle with a Constant Classical Velocity in a Spacetime with a Plane Boundary. Chin. Phys. Lett. 2005, 22, 2165.
[58] H. Yu, J. Chen and P. Wu, Brownian motion of a charged test particle near a reflecting boundary at finite temperature. JHEP 2006, 0602, 058.
[59] M. T. Jaekel and S. Reynaud, Fluctuations and Dissipation for a Mirror in Vacuum. Quantum. Opt 1992, 4, 39.
[60] G. Barton, On the Fluctuations of the Casimir Force. J. Phys. A 1991, 24, 991-1005.
[61] M. T. Jaekel and S. Reynaud, Motional Casimir Force. J. Phys. I(France) 1993, 3, 1.
[62] Y. Zhu, and H. Yu, Effects of a boundary on spontaneous excitation of an accelerated multilevel atom coupling with the derivative of a scalar field, Int. J. Mod. Phys. A (to be published).
[63] Y. Zhu, and H. Yu, Radiative energy shifts of an accelerated multilevel atom coupled to the derivative of a scalar field, Chin. Phys. Lett. 2007, 24, 878.
[64] P. Candelas. Vacuum Polarization in Schwarzschild Spacetime. Phys. Rev. D, 1980, 21, 2185-2202.
[65] P. C. W. Davies and V. Sahni. Quantum Gravitational Effects near Cosmic Strings. Class.Quantum. Gray, 1988,5,1-18.
[66] P. C. W. Davies, Z. X. Liu and A. C. Ottewill. Particle Detectors in the presence of Boundaries. Class. Quantum. Grav, 1989, 6, 1041-1051.
[67] N. B. Narozhny, A. M. Fedotov and V. D. Mur, Boundary Conditions in the Unruh Problem. Phys. Rev. D, 2002, 65, 025004
[2] I. R. Senitzky, Radiation Reaction and Vacuum-Field Effects in Heisenberg Picture Quantum Electrodynamics. Phys. Rev. Lett. 1973, 31,955-958.
[3] J. R. Ackerhalt and J. H. Eberly, Quantum Electrodynamics and radiation reaction: Nonrelativistic Atomic Frenquency Shifts and Lifetime. Phys. Rev.D 1974, 10, 3350-3375.
[4] P. W. Milonni, J. R. Ackerhalt, and W. A. Smith, Interpretation of Radiative corrections in Spontaneous Emission. Phys. Rev. Lett. 1973, 31, 958-960.
[5] P. W. Milonni and W. A. Smith, Radiation reaction and vacuum Fluctuations in Spontaneous Emission. Phys. Rev. A. 1975, 11,814-824; P. W. Milonni, Phy. Scr. 1988, T21, 102.
[6] J. Dalibard, J. Dupont-Roc, and C. Cohen-Tannoudji, Vacuum Fluncutaions and Radiation Reaction: Identification of Their Respective contributions. J. Phys. 1982, 43, 1617-1638.
[7] J. Dalibard, J. Dupont-Roc, and C. Cohen-Tannoudji, Dynamics of a small System Coupled to a Reservoir: Reservoir Fluctuations and Self-Reaction. J. Phys. 1984, 45, 637-656.
[8] V. F. Weisskopf, Physics in the Twentieth Century-Selected essays. (The M. I. T. Press, Cambridge) 1972, 96-129.
[9] A. O. Barut, Fundations of Radiation Theory and Quantum Electrodynamics. 1980.
[10] T. A. Welton, Some Observable Effects of the Quantum-Mechanical Fluctuations of the Electromagnetic Field. Phys. Rev. 1948, 74, 1157-1167.
[11] J. Dupont-Roc, C. Fabre and C. Cohen-Tannoudji, Physical Interpretations for Radiative Corrections in the Nonrelativistic Limit. J. Phys. B. 1978, 11,563.
[12] G. W. Series, Optical Pumping and Atomic Line Shapes. edited by T. Skalinski(Panstwowe Wdawnictwo Naukowe, Warszawa) 1969, p. 25.
[13] P. K. Bullough, Coherence and Quantum Optics, edited by L. Mandel and E. Wolf(Plenum Press, New York). 1973 p. 121.
[14] H. J. Kimble and L. Mandel, Problem of Resonance Fluorescence and the Inadequacy of Spontaneous Emission as a Test of Quantum Electrodynamics. Phys. Rev. Lett. 1975, 34, 1485-1488.
[15] H. J. Kimble and L. Mandel, Theory of Resonance Fluorescence. Phys. Rev. A 1976, 13, 2123-2144.
[16] P. W. Milonni, Semiclassical and quantum-electrodynamical approaches in nonrelativistic radiation theory .Phys. Rep. 1976, 25, 1.
[17] J. B. French, V. F. Weisskopf, The Electromagnetic Shifts of Energy Levels. Phys. Rev. 1949, 75, 1240.
[18] J. D. Jackson, Classical Electrodynamics, 2nd edition (John Wiley and Sons, New York) 1975, section 17.
[19] E. J. Moniz and D. H. Sharp, Absence of Runaways and Divergent Self-Mass in Nonrelativistic Quantum Electrodynamics. Phys. Rev. D 1974, 10, 1133; Phys. Rev. D 1977, 15, 2850.
[20] V. F. Weisskopf, On the Self-Energy and the Electromagnetic Field of of the Electron. Phys. Rev 1939, 56, 72-85.
[21] L. Allen and J. H. Eberly, Optical Resonance and two-level atoms 1975.
[22] G. S. Agarwal, Springer Tracts in modern Physics, 1974, volume 70(Springer, Verlag, Berlin).
[23] C. Cohen-Tannoudji, Frontier in laser spectroscope, 1975, volume 1, Les houches session ⅩⅩⅦ,edited by R. Balian ,S. Haroche and S. Liberman(North Holland, Amsterdam), 1977.
[24] W. H. Louisell, Quantum Statistical Properties of Radiation. (John Wiley and Sone, New York), 1973.
[25] H. Grabert, On the equivalence of generalized Langevin equation and generalized master equation, Z. Phys. B 1977, 26, 79.
[26] P. Martin, Many Body Physics, Les Houches 1967, edit by C. De Witt and R. Balian(Gordon and Breach, New York) 1968.
[27] Jurgen Audretsch and Rainer Muller, Spontaneous excitation of an accelerated atom: The contributions of vacuum fluctuations and radiation reaction. Phys. Rev. A, 1994, 50, 1755.
[28] J. Audretsch and R. Muller, Radiative Energy Shifts of an Accelerated Two-Level System. Phys. Rev. A 1995, 52, 629-635.
[29] H. Yu and S. Lu, Spontaneous Excitation of an Accelerated Atom in a Spacetime with a Reflecting Plane Boundary. Phys. Rev. D 2005, 72, 064022.
[30] D. Meschede, W. Jhe, and E. A Hints, Radiative Properties of Atoms near a Conducting Plane: An Old Problem in a New Light. Phys. Rev. A, 1990, 41, 1587-1596.
[31] J. Audretsch and R. Muller, and M. Holzmann, Generalized Unrtth Effect and Lamb Shifts for Atoms on Arbitrary Stationary Trajectories. Classical Quantum Gravity, 1995, 12, 2927-2940.
[32] W. G. Unruh, Notes on Black-hole Evaporation. Phys. Rev. D 1976, 14, 870-892.
[33] R. H. Dicke, Coherence in Spontaneous Radiation Processes. Phys. Rev. 1954, 93, 99-110.
[34] P. W. Milonni, Why Spontaneous Emission?. Am. J. Phys. 1984, 52, 340-340.
[35] V. M. Fain, Soy. J. E. T. P, 1966, 882. V. M. Fain and Y. I. Khanin, Quantum Electronica. (M. I. T. Press, Cambridge) ,1969. B. Fain, I1 Nuovo Cimento 68B, 1982, 73.
[36] Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1972).
[37] H. B. G. Casimir, On the Attraction between Perfectly Conducting Plates. Proc. K. Ned. Akad. Wet. 1948, 51, 793.
[38] H. Yu and L. H. Ford, Lightcone Fluctuations in Two Flat Spacetime with Nontrivial Topology. Phys. Rev. D 1999, 60, 084023.
[39] H. Yu and L. H. Ford, Lightcone Fluctuations in Quantum Gravity and Extra Dimensions. Phys. Lett. B 2000, 496, 107-112.
[40] H. Yu and L. H. Ford, Light Fluctuations in Theories with Extra Dimenssions, arXiv, 2000, gr-qc/0004063.
[41] A. O. Barut and J. P. Dowling, Quantum Electrodynamics Based on Self-Fields: On the Origin of thermal Radiation Detected by an Accelerating Observer. Phys. Rev. A 1990, 41, 2277-2283.
[42] H. Yu and P. X. Wu, Quantum Fluctuations of the Light Cone in Fourdimensional Spacetime with Parallel Plane Boundaries. Phys. Rev. D 2003, 68, 084019.
[43] H. Yu and L. H. Ford, Vacuum Fluctuations and Brownian Motion of a Charged Test near a Reflecting Boundary. Phys. Rev. D 2004, 70, 065009.
[44] H. Yu and J. Chen, Brownian Motion of a Charged test Particle in Vacuum between Two Conduncing Plates. Phys. Rev. D 2004, 70, 125006-125010.
[45] D. Meschede, Radiating Atoms in Confined Space: From Spontaneous Emission to Micromasers. Phys. Rep. 1992, 211, 201.
[46] S. A. Fulling, Nonuniqueness of Canonical Field Quantization in Riemannian Space-Time. Phys. Rev. D 1973, 7, 2850-2862.
[47] N. D. Birrell and P. C. W. Davies, Quantum Field in Curved Space (Cambridge University Press, Cambridge, 1982).
[48] C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photo Interactious. Basic Processes and Applications. (Wiley, New York, 1992).
[49] G. Barton, Temperature Dependence of the Lamb Shift. Phys. Rev. A 1972, 5, 468-470.
[50] P. K. Knight, Effects of External Fields on the Lamb Shift. J.Phys. A 1972, 5, 417-425.
[51] J. W. Farley and W. H. Wing, Accurate Calculation of Dynamic Stark Shifts and Depopulation Rates of Rydberg Energy Levels Induced by Blackbody Radiation. Hydrogen, Helium, and Alkali-Metal Atoms. Phys. Rev. A 1981, 23, 2397-2424.
[52] H. A. Bethe,The Electromagnetic Shift of Energy Levels. Phys. Rev 1947, 72, 339.
[53] J. S. Bell and J. M. Leinaas, Nucl. Phys. B 1983, 212, 131; 1987, 284, 488.
[54] Passante, Radiative Level Shifts of an Accelerated Hydrogen Atom and Unruh Effect in Quantum Electrodynamics. Phys. Rev. A 1998, 57, 1590.
[55] Z. Zhu, H. Yu and S.Lu, Spontaneous Excitation of an Accelerated Hydrogen Atom Coupled with Electromagnetic Vacuum Fluctuations. Phys. Rev. D 2006, 73, 107501.
[56] Y. Zhu, and H. Yu, Spontaneous Excitation of an Aeeclerated Multilevel Atom in dipole Coupling to the derivative of a Scalar field. Class. Quantum. Grav 2007, 24, 95.
[57] M. Tan and H. Yu, Random Motion of a Charged Test Particle with a Constant Classical Velocity in a Spacetime with a Plane Boundary. Chin. Phys. Lett. 2005, 22, 2165.
[58] H. Yu, J. Chen and P. Wu, Brownian motion of a charged test particle near a reflecting boundary at finite temperature. JHEP 2006, 0602, 058.
[59] M. T. Jaekel and S. Reynaud, Fluctuations and Dissipation for a Mirror in Vacuum. Quantum. Opt 1992, 4, 39.
[60] G. Barton, On the Fluctuations of the Casimir Force. J. Phys. A 1991, 24, 991-1005.
[61] M. T. Jaekel and S. Reynaud, Motional Casimir Force. J. Phys. I(France) 1993, 3, 1.
[62] Y. Zhu, and H. Yu, Effects of a boundary on spontaneous excitation of an accelerated multilevel atom coupling with the derivative of a scalar field, Int. J. Mod. Phys. A (to be published).
[63] Y. Zhu, and H. Yu, Radiative energy shifts of an accelerated multilevel atom coupled to the derivative of a scalar field, Chin. Phys. Lett. 2007, 24, 878.
[64] P. Candelas. Vacuum Polarization in Schwarzschild Spacetime. Phys. Rev. D, 1980, 21, 2185-2202.
[65] P. C. W. Davies and V. Sahni. Quantum Gravitational Effects near Cosmic Strings. Class.Quantum. Gray, 1988,5,1-18.
[66] P. C. W. Davies, Z. X. Liu and A. C. Ottewill. Particle Detectors in the presence of Boundaries. Class. Quantum. Grav, 1989, 6, 1041-1051.
[67] N. B. Narozhny, A. M. Fedotov and V. D. Mur, Boundary Conditions in the Unruh Problem. Phys. Rev. D, 2002, 65, 025004