Abstract:
Vacuum fluctuations provide a fundamental source of dissipation for systems coupled to quantum fields by radiation pressure. In the dynamical Casimir effect, accelerating neutral bodies in free space give rise to the emission of real photons while experiencing a damping force which plays the role of a radiation reaction force. Analog models where non-stationary conditions for the electromagnetic field simulate the presence of moving plates are currently under experimental investigation. A dissipative force might also appear in the case of uniform relative motion between two bodies, thus leading to a new kind of friction mechanism without mechanical contact. In this paper, we review recent advances on the dynamical Casimir and non-contact friction effects, highlighting their common physical origin. © 2011 Springer-Verlag Berlin Heidelberg.
Registro:
Documento: |
Artículo
|
Título: | Fluctuations, dissipation and the dynamical casimir effect |
Autor: | Dalvit, D.A.R.; Neto, P.A.M.; Mazzitelli, F.D. |
Filiación: | Theoretical Division, MS B213, Los Alamos National Laboratory, Los Alamos, NM 87545, United States Instituto de Física UFRJ, Caixa Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil Centro Atómico Bariloche, Comision Nacional de Energía Atómica, R8402AGP, Bariloche, Argentina Departamento de Física, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, 1428, Buenos Aires, Argentina
|
Año: | 2011
|
Volumen: | 834
|
Página de inicio: | 419
|
Página de fin: | 457
|
DOI: |
http://dx.doi.org/10.1007/978-3-642-20288-9_13 |
Título revista: | Lecture Notes in Physics
|
Título revista abreviado: | Lect. Notes Phys.
|
ISSN: | 00758450
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00758450_v834_n_p419_Dalvit |
Referencias:
- Barton, G., On the fluctuations of the Casimir force (1991) J. Phys. A: Math. Gen., 24, pp. 991-1005
- Barton, G., On the fluctuations of the Casimir force. 2: The stress-correlation function (1991) J. Phys. A: Math. Gen., 24, pp. 5533-5551
- Jaekel, M.-T., Reynaud, S., Quantum fluctuations of position of a mirror in vacuum (1993) J. Phys. (Paris) i, 3, pp. 1-20
- Dalvit, D.A.R., Maia Neto, P.A., Decoherence via the Dynamical Casimir Effect (2000) Phys. Rev. Lett., 84, pp. 798-801
- Maia Neto, P.A., Dalvit, D.A.R., Radiation pressure as a source ofdecoherence (2000) Phys. Rev. A., 62, p. 042103
- Callen, H.B., Welton, T.A., Irreversibility and generalized noise (1951) Phys. Rev., 83, pp. 34-40
- Ford, L.H., Vilenkin, A., Quantum radiation by moving mirrors (1982) Phys. Rev. D, 25, pp. 2569-2575
- Moore, G.T., Quantum theory ofelectromagnetic field in a variable-length one-dimensional cavity (1970) J. Math. Phys., 11, p. 2679
- Castagnino, M., Ferraro, R., The radiation from moving mirrors: The creation and absorption ofparticles (1984) Ann. Phys. (NY), 154, pp. 1-23
- Fulling, S.A., Davies, P.C.W., Radiation from a moving mirror in two dimensional space-time-conformal anomaly (1976) Proc. R. Soc. A, 348, pp. 393-414
- Hawking, S.W., Black-hole explosions (1974) Nature (London), 248, pp. 30-31
- Hawking, S.W., Particle creation by black-holes (1975) Commun. Math. Phys., 43, pp. 199-220
- Braginsky, V.B., Khalili, F.Ya., Friction and fluctuations produced by the quantum ground-state (1991) Phys. Lett, 161, pp. 197-201
- Jaekel, M.-T., Reynaud, S., Fluctuations and dissipation for a mirror in vacuum (1992) Quantum Opt., 4, pp. 39-53
- Braginsky, V.B., Vorontsov, U.Y.I., Quantum-mechanical limitations in macroscopic experiments and modern experimental techniques (1974) Usp. Fiz. Nauk., 114, pp. 41-53
- Caves, C., Defense of the standard quantum limit for free-mass position (1985) Phys. Rev. Lett., 54, pp. 2465-2468
- Jaekel, M.-T., Reynaud, S., Quantum limits in interferometric measurements (1990) Europhys. Lett., 13, pp. 301-306
- Kubo, R., Fluctuation-dissipation theorem (1966) Rep. Prog. Phys., 29, pp. 255-284
- Maia Neto, P.A., Reynaud, S., Dissipative force on a sphere moving in vacuum (1993) Phys. Rev. A, 47, pp. 1639-1646
- Barton, G., New aspects of the Casimir effect: Fluctuations and radiative reaction (1993) Cavity Quantum Electrodyamics Supplement: Advances in Atomic Molecular and Optical Physics, , Berman P., Academic Press, New York
- Maia Neto, P.A., MacHado, L.A.S., Radiation Reaction Force for a Mirror in Vacuum (1995) Braz. J. Phys., 25, pp. 324-334
- Golestanian, R., Kardar, M., Mechanical response of vacuum (1997) Physical Review Letters, 78 (18), pp. 3421-3425
- (1998) Phys. Rev. A, 58, pp. 1713-1722
- Volokitin, A.I., Persson, B.N.J., Near-field radiative heat transfer and noncontact friction (2007) Reviews of Modern Physics, 79 (4), pp. 1291-1329. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: RevModPhys.79.1291&metadataPrefix=oai_apsmeta_2, DOI 10.1103/RevModPhys.79.1291
- Pendry, J.B., Shearing the vacuum-quantum friction (1997) J. Phys.:Condens. Matter, 9, pp. 10301-10320
- Nussenzveig, H.M., (1972) Causality and Dispersion Relations., , Academic Press, New York
- Lambrecht, A., Jaekel, M.-T., Reynaud, S., Motion induced radiation from a vibrating cavity (1996) Physical Review Letters, 77 (4), pp. 615-618
- Maia Neto, P.A., Machado, L.A.S., Quantum radiation generated by a moving mirror in free space (1996) Physical Review A - Atomic, Molecular, and Optical Physics, 54 (4), pp. 3420-3427
- Montazeri, M., Miri, M., Radiation from a dynamically deforming mirror immersed in the electromagnetic vacuum (2008) Phys. Rev. A., 77, p. 053815
- Mundarain, D.F., Maia Neto, P.A., Quantum radiation in a plane cavity with moving mirrors (1998) Physical Review A - Atomic, Molecular, and Optical Physics, 57 (2), pp. 1379-1390
- Maia Neto, P.A., The dynamical Casimir effect with cylindrical waveguides (2005) Journal of Optics B: Quantum and Semiclassical Optics, 7 (3), pp. S86-S88. , DOI 10.1088/1464-4266/7/3/012, Nonstationary Casimir Effect and Quantum Systems with Moving Boundaries
- Pascoal, F., Celeri, L.C., Mizrahi, S.S., Moussa, M.H.Y., Dynamical Casimir effect for a massless scalar field between two concentric spherical shells (2008) Phys. Rev. A., 78, p. 032521
- Pascoal, F., Celeri, L.C., Mizrahi, S.S., Moussa, M.H.Y., Farina, C., Dynamical Casimir effect for a massless scalar field between two concentric spherical shells with mixed boundary conditions (2009) Phys. Rev. A., 80, p. 012503
- Eberlein, C., Theory of quantum radiation observed as sonoluminescence (1996) Physical Review A - Atomic, Molecular, and Optical Physics, 53 (4), pp. 2772-2787
- Mazzitelli, F.D., Millán, X.O., Photon creation in a spherical oscillating cavity (2006) Phys Rev. A., 73, p. 063829
- Dodonov, V.V., Klimov, A.B., Generation and detection of photons in a cavity with a resonantly oscillating boundary (1996) Physical Review A - Atomic, Molecular, and Optical Physics, 53 (4), pp. 2664-2682
- Crocce, M., Dalvit, D.A.R., Mazzitelli, F.D., Resonant photon creation in a three di-mensional oscillating cavity (2001) Phys. Rev. A., 64, p. 013808
- Crocce, M., Dalvit, D.A.R., Mazzitelli, F.D., Quantum electromagnetic field in a three dimensional oscillating cavity (2002) Phys. Rev. A., 66, p. 033811
- Crocce, M., Dalvit, D.A.R., Lombardo, F.C., Mazzitelli, F.D., Hertz potentials approach to the dynamical Casimir effect in cylindrical cavities of arbitrary section (2005) Journal of Optics B: Quantum and Semiclassical Optics, 7 (3), pp. S32-S39. , DOI 10.1088/1464-4266/7/3/005, Nonstationary Casimir Effect and Quantum Systems with Moving Boundaries
- Dalvit, D.A.R., Mazzitelli, F.D., Renormalization-group approach to the dynamical Casimir effect (1998) Physical Review A - Atomic, Molecular, and Optical Physics, 57 (3), pp. 2113-2119
- Lambrecht, A., Jaekel, M.-T., Reynaud, S., Frequency up-converted radiation from a cavity moving in vacuum (1998) Eur. Phys. J. D., 3, pp. 95-104
- Dalvit, D.A.R., Mazzitelli, F.D., Creation of photons in an oscillating cavity with two moving mirrors (1999) Physical Review A - Atomic, Molecular, and Optical Physics, 59 (4), pp. 3049-3059
- Jaekel, M.-T., Reynaud, S., Motional Casimir force (1992) J. Phys. I., 2, pp. 149-165
- Dezael, F.X., Lambrecht, A., Analogue Casimir radiation using an optical parametric oscillator (2010) Europhys. Lett., 89, p. 14001
- Dodonov, V.V., Dynamical Casimir effect in a nondegenerate cavity with losses and detuning (1998) Physical Review A - Atomic, Molecular, and Optical Physics, 58 (5), pp. 4147-4152
- Schaller, G., Schützhold, R., Plunien, G., Soff, G., Dynamical Casimir effect in a leaky cavity at finite temperature (2002) Phys. Rev. A., 66, p. 023812
- Kim, W.-J., Brownell, J.H., Onofrio, R., Detectability of dissipative motion in quantum vacuum via superradiance (2006) Phys. Rev. Lett., 96, p. 200402
- Yablonovitch, E., Accelerating reference frame for electromagnetic waves in a rapidly growing plasma: Unruh-Davies-Fulling-DeWitt radiation and the nonadiabatic Casimir effect (1989) Phys Rev. Lett., 62, pp. 1742-1745
- Yablonovitch, E., Heritage, J.P., Aspnes, D.E., Yafet, Y., Virtual photoconductivity (1989) Phys. Rev. Lett., 63, pp. 976-979
- Lozovik, Y.E., Tsvetus, V.G., Vinogradov, E.A., Femtosecond parametric excitation of electromagnetic field in a cavity (1995) JETP Lett., 61, pp. 723-729
- Lozovik, Y.E., Tsvetus, V.G., Vinogradov, E.A., Parametric excitation ofvacuum by use of femtosecond laser pulses (1995) Phys. Scr., 52, pp. 184-190
- Crocce, M., Dalvit, D.A.R., Lombardo, F., Mazzitelli, F.D., Model for resonant photon creation in a cavity with time dependent conductivity (2004) Phys. Rev. A., 70, p. 033811
- Mendonça, J.T., Guerreiro, A., (2005) Phys. Rev. A., 80, p. 043603
- Braggio, C., Bressi, G., Carugno, G., Del Noce, C., Galeazzi, G., Lombardi, A., Palmieri, A., Zanello, D., A novel experimental approach for the detection of the dynamical Casimir effect (2005) Europhysics Letters, 70 (6), pp. 754-760. , DOI 10.1209/epl/i2005-10048-8
- Braggio, C., Bressi, G., Carugno, G., Della Valle, F., Galeazzi, G., Ruoso, G., Character-ization of a low noise microwave receiver for the detection of vacuum photons (2009) Nucl. Instrum. Methods Phys. Res. A, 603, pp. 451-455
- Takashima, K., Hatakenaka, N., Kurihara, S., Zeilinger, A., Nonstationary boundary effect for a quantum flux in superconducting nanocircuits (2008) J. Phys. A., 41, p. 164036
- Castellanos-Beltran, M.A., Irwin, K.D., Hilton, G.C., Vale, L.R., Lehnert, K.W., Amplifi-cation and squeezing of quantum noise with a tunable Josephson metamaterial (2008) Nat Phys., 4, pp. 928-931
- Johansson, J.R., Johansson, G., Wilson, C.M., Nori, F., Dynamical Casimir effect in a superconducting coplanar waveguide (2009) Phys. Rev. Lett., 103, p. 147003
- Wilson, C.M., Duty, T., Sandberg, M., Persson, F., Shumeiko, V., Delsing, P., Photon Generation in An Electromagnetic Cavity with A Time-dependent Boundary, , arXiv: 1006.2540
- Carusotto, I., Balbinot, R., Fabbri, A., Recati, A., Density correlations and analog dynamical Casimir emission of Bogoliubov phonons in modulated atomic Bose-Einstein condensates (2010) Eur. Phys. J. D., 56, pp. 391-404
- Roberts, D., Pomeau, Y., Casimir-like force arising from quantum fluctuations in a slow-moving dilute Bose-Einstein condensate (2005) Phys. Rev. Lett., 95, p. 145303
- Jaekel, M.-T., Reynaud, S., Movement and fluctuations of the vacuum (1997) Reports on Progress in Physics, 60 (9), pp. 863-887
- Kardar, M., Golestanian, R., The "friction" of vacuum, and other fluctuation-induced forces (1999) Reviews of Modern Physics, 71 (4), pp. 1233-1245
- Dodonov, V.V., Nonstationary Casimir effect and analytical solutions for quantum fields in cavities with moving boundaries (2001) Adv. Chem. Phys., 119 (1), pp. 309-394. , MODERN NONLINEAR OPTICS
- Dodonov, V.V., Dynamical Casimir effect: Some theoretical aspects (2009) J. Phys.: Conf. Ser., 161, p. 012027
- Dodonov, V.V., (2010) Current Status of the Dynamical Casimir Effect, , arXiv: 1004.3301
- Fosco, C.D., Lombardo, F.C., Mazzitelli, F.D., Quantum dissipative effects in moving mirrors: A functional approach (2007) Phys. Rev. D., 76, p. 085007
- Barton, G., Eberlein, C., On quantum radiation from a moving body with finite refractive-index (1993) Ann. Phys. (New York), 227, pp. 222-274
- Alves, D.T., Farina, C., Maia Neto, P.A., Dynamical Casimir effect with Dirichlet and Neumann boundary conditions (2003) Journal of Physics A: Mathematical and General, 36 (44), pp. 11333-11342. , DOI 10.1088/0305-4470/36/44/011, PII S0305447003663031
- Alves, D.T., Granhen, E.R., Lima, M.G., Quantum radiation force on a moving mirror with Dirichlet and Neumann boundary conditions for a vacuum, finite temperature, and a coherent state (2008) Phys. Rev. D., 77, p. 125001
- Mintz, B., Farina, C., Neto, P.A.M., Rodrigues, R.B., Casimir forces for moving boundaries with Robin conditions (2006) Journal of Physics A: Mathematical and General, 39 (21), pp. 6559-6565. , DOI 10.1088/0305-4470/39/21/S54, PII S0305447006118910
- Dodonov, V.V., Klimov, A.B., Man'Ko, V.I., Generation of squeezed states in a resonator with a moving wall (1990) Phys. Lett. A., 149, pp. 225-228
- Dodonov, V.V., Klimov, A.B., Long-time asymptotics of a quantized electromagnetic-field in a resonator with oscillating boundary (1992) Phys. Lett. A., 167, pp. 309-313
- Mintz, B., Farina, C., Maia Neto, P.A., Rodrigues, R.B., Particle creation by a moving boundary with a Robin boundary condition (2006) Journal of Physics A: Mathematical and General, 39 (36), pp. 11325-11333. , DOI 10.1088/0305-4470/39/36/013, PII S0305447006248443, 013
- Jaekel, M.-T., Reynaud, S., Causality, stability and passivity for a mirror in vacuum (1992) Phys. Lett. A., 167, pp. 227-232
- Barton, G., Calogeracos, A., On the quantum electrodynamics of a dispersive mirror. 1: Mass shifts, radiation, and radiative reaction (1995) Ann. Phys. (New York), 238, pp. 227-267
- Verlot, P., Tavernarakis, A., Briant, T., Cohadon, P.-F., Heidmann, A., Scheme to probe optomechanical correlations between two optical beams down to the quantum level (2009) Phys. Rev. Lett., 102, p. 103601
- Schliesser, A., Arcizet, O., Riviere, R., Anetsberger, G., Kippenberg, T.J., Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit (2009) Nature Phys., 5, pp. 509-514
- Maia Neto, P.A., Vacuum radiation pressure on moving mirrors (1994) J. Phys. A: Math. Gen., 27, pp. 2167-2180
- Barton, G., North, C.A., Peculiarities of quantum radiation in three dimensions from moving mirrors with high refractive index (1996) Annals of Physics, 252 (1), pp. 72-114. , DOI 10.1006/aphy.1996.0125
- Gütig, R., Eberlein, C., Quantum radiation from moving dielectrics in two, three and more spatial dimensions (1998) J. Phys. A: Math. Gen., 31, pp. 6819-6838
- Barton, G., The quantum radiation from mirrors moving sideways (1996) Annals of Physics, 245 (2), pp. 361-388. , DOI 10.1006/aphy.1996.0013
- Pendry, J.B., Quantum friction-fact or fiction? (2010) New J. Phys., 12, p. 033028
- Volokitin, A.I., Persson, B.N.J., Theory of friction: The contribution from a fluctuating electromagnetic field (1999) Journal of Physics Condensed Matter, 11 (2), pp. 345-359
- Lifshitz, E.M., The theory ofmolecular attractive forces between solids (1956) Sov. Phys. JETP., 2, pp. 73-83
- Buhmann, S.Y., Welsch, D.-G., Dispersion forces in macroscopic quantum electrodynamics (2007) Progress in Quantum Electronics, 31 (2), pp. 51-130. , DOI 10.1016/j.pquantelec.2007.03.001, PII S0079672707000249
- Dedkov, G.V., Kyasov, A.A., Electromagnetic and fluctuation-electromagnetic forces of interaction of moving particles and nanoprobes with surfaces: A non-relativistic consideration (2002) Phys. Solid State., 44, pp. 1809-1832
- Hu, B.L., Roura, A., Shresta, S., Vacuum fluctuations and moving atom/detectors: From the Casimir-Polder to the Unruh-Davies-DeWitt-Fulling effect (2004) J. Opt. B: Quantum Semiclass. Opt., 6, pp. S698-S705
- Scheel, S., Buhmann, S.Y., Casimir-Polder forces on moving atoms (2009) Phys. Rev. A., 80, p. 042902
- Dodonov, V.V., Klimov, A.B., Nikonov, D.E., Quantum phenomena in resonators with moving walls (1993) J. Math. Phys., 34, p. 2742
- Petrov, N.P., The dynamical Casimir effect in a periodically changing domain: A dynamical systems approach (2005) Journal of Optics B: Quantum and Semiclassical Optics, 7 (3), pp. S89-S99. , DOI 10.1088/1464-4266/7/3/013, Nonstationary Casimir Effect and Quantum Systems with Moving Boundaries
- Ruser, M., Vibrating cavities: A numerical approach (2005) Journal of Optics B: Quantum and Semiclassical Optics, 7 (3), pp. S100-S115. , DOI 10.1088/1464-4266/7/3/014, Nonstationary Casimir Effect and Quantum Systems with Moving Boundaries
- Alves, D.T., Farina, C., Granhen, E.R., Dynamical Casimir effect in a resonant cavity with mixed boundary conditions (2006) Phys. Rev. A., 73, p. 063818
- Farina, C., Azevedo, D., Pascoal, F., Dynamical Casimir effect with Robin boundary conditions in a three dimensional open cavity (2010) Proceedings of QFEXT09, p. 334. , In: Milton, K.A., Bordag, M. (eds.) World Scientific, Singapore arXiv: 1001.2530
- Law, C.K., Resonance response of the quantum vacuum to an oscillating boundary (1994) Physical Review Letters, 73 (14), pp. 1931-1934
- Schutzhold, R., Plunien, G., Soff, G., Trembling cavities in the canonical approach (1998) Physical Review A - Atomic, Molecular, and Optical Physics, 57 (4), pp. 2311-2318
- Bender, C.M., Orszag, S.A., (1978) Advanced Mathematical Methods for Scientists and Engineers., , McGraw Hill New York
- Boyd, R., (2008) Nonlinear Optics. 3rd Edn., , Academic Press, Burlington USA
- Ji, J.-Y., Soh, K.-S., Cai, R.-G., Kim, S.P., Electromagnetic fields in a three-dimensional cavity and in a waveguide with oscillating walls (1998) J. Phys. A., 31, pp. L457-L462
- Dodonov, V.V., Resonance excitation and cooling of electromagnetic modes in a cavity with an oscillating wall (1996) Physics Letters, Section A: General, Atomic and Solid State Physics, 213 (5-6), pp. 219-225. , PII S037596019600120X
- Ruser, M., Numerical investigation of photon creation in a three-dimensional resonantly vibrating cavity: Transverse electric modes (2006) Phys. Rev. A., 73, p. 043811
- Hacyan, S., Jauregui, R., Soto, F., Villarreal, C., Spectrum ofelectromagnetic fluctuations in the Casimir effect (1990) J. Phys. A: Math. Gen., 23, p. 2401
- Dodonov, V.V., Dodonov, A.V., The nonstationary Casimir effect in a cavity with periodical time-dependent conductivity of a semiconductor mirror (2006) Journal of Physics A: Mathematical and General, 39 (21), pp. 6271-6281. , DOI 10.1088/0305-4470/39/21/S18, PII S0305447006114110
- Uhlmann, M., Plunien, G., Schützhold, R., Soff, G., Resonant cavity photon creation via the dynamical Casimir effect (2004) Phys.Rev. Lett., 93, p. 193601
- Naylor, W., Matsuki, S., Nishimura, T., Kido, Y., Dynamical Casimir effect for TE and TM modes in a resonant cavity bisected by a plasma sheet (2009) Phys. Rev. A., 80, p. 043835
- Dodonov, V.V., Photon distribution in the dynamical Casimir effect with an account of dissipation (2009) Phys. Rev. A., 80, p. 023814
- Lax, M., Quantum noise. IV. Quantum theory ofnoise sources (1966) Phys. Rev., 145, pp. 110-129
- Mendonça, J.T., Brodin, G., Marklund, M., Vacuum effects in a vibrating cavity: Time refraction, dynamical Casimir effect, and effective Unruh acceleration (2008) Phys. Lett. A., 372, pp. 5621-5624
- Arbet-Engels, V., Benvenuti, C., Calatroni, S., Darriulat, P., Peck, M.A., Valente, A.-M., Van'T Hof, C.A., Superconducting niobium cavities, a case for the film technology (2001) Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 463 (1-2), pp. 1-8. , DOI 10.1016/S0168-9002(01)00165-6, PII S0168900201001656
- Agnesi, A., Braggio, C., Bressi, G., Carugno, G., Galeazzi, G., Pirzio, F., Reali, G., Zanello, D., MIR status report: An experiment for the measurement of the dynamical Casimir effect (2008) J. Phys. A: Math. Gen., 41, p. 164024
- Segev, E., Abdo, B., Shtempluck, O., Buks, E., Yurke, B., Prospects of employing superconducting stripline resonators for studying the dynamical Casimir effect experimentally (2007) Phys. Lett. A., 370, pp. 202-206
Citas:
---------- APA ----------
Dalvit, D.A.R., Neto, P.A.M. & Mazzitelli, F.D.
(2011)
. Fluctuations, dissipation and the dynamical casimir effect. Lecture Notes in Physics, 834, 419-457.
http://dx.doi.org/10.1007/978-3-642-20288-9_13---------- CHICAGO ----------
Dalvit, D.A.R., Neto, P.A.M., Mazzitelli, F.D.
"Fluctuations, dissipation and the dynamical casimir effect"
. Lecture Notes in Physics 834
(2011) : 419-457.
http://dx.doi.org/10.1007/978-3-642-20288-9_13---------- MLA ----------
Dalvit, D.A.R., Neto, P.A.M., Mazzitelli, F.D.
"Fluctuations, dissipation and the dynamical casimir effect"
. Lecture Notes in Physics, vol. 834, 2011, pp. 419-457.
http://dx.doi.org/10.1007/978-3-642-20288-9_13---------- VANCOUVER ----------
Dalvit, D.A.R., Neto, P.A.M., Mazzitelli, F.D. Fluctuations, dissipation and the dynamical casimir effect. Lect. Notes Phys. 2011;834:419-457.
http://dx.doi.org/10.1007/978-3-642-20288-9_13