We study a stochastic version of the dynamical Casimir effect, computing the particle creation inside a cavity produced by a random motion of one of its walls. We first present a calculation perturbative in the amplitude of the motion. We compare the stochastic particle creation with the deterministic counterpart. Then, we go beyond the perturbative evaluation using a stochastic version of the multiple scale analysis, that takes into account stochastic parametric resonance. We stress the relevance of the coupling between the different modes induced by the stochastic motion. In the single-mode approximation, the equations are formally analogous to those that describe the stochastic particle creation in a cosmological context, that we rederive using multiple scale analysis.

CEICO Institute of Physics of the Czech Academy of Sciences Na Slovance 1999 2 18221 Prague Czech Republic

Centro Atómico Bariloche and Instituto Balseiro Comisión Nacional de Energía Atómica Bariloche R8402AGP Argentina

Department of Physics University of Chicago Chicago IL 60637 USA

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Moore G.T. Quantum theory of the electromagnetic field in a variable-length one dimensional cavity. J. Math. Phys. 1970;11:2679. doi: 10.1063/1.1665432. DOI

Dodonov V.V. Current status of the dynamical Casimir effect. Phys. Scr. 2010;82:038105. doi: 10.1088/0031-8949/82/03/038105. DOI

Dalvit D.A.R., Neto P.A.M., Mazzitelli F.D. Fluctuations, dissipation and the dynamical Casimir effect. Lect. Notes Phys. 2011;834:419.

Nation P.D., Johansson J.R., Blencowe M.P., Nori F. Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits. Rev. Mod. Phys. 2012;84:1. doi: 10.1103/RevModPhys.84.1. DOI

Dodonov V.V. Fifty years of the dynamical Casimir effect. Physics. 2020;2:67–104. doi: 10.3390/physics2010007. DOI

Parker L. Particle creation in expanding universes. Phys. Rev. Lett. 1968;21:562. doi: 10.1103/PhysRevLett.21.562. DOI

Parker L. Quantized fields and particle creation in expanding universes I. Phys. Rev. 1969;183:1057. doi: 10.1103/PhysRev.183.1057. DOI

Parker L. Quantized fields and particle creation in expanding universes II. Phys. Rev. D. 1971;3:346. doi: 10.1103/PhysRevD.3.346. DOI

Birrell N.D., Davies P.C.W. Quantum Fields in Curved Space. Cambridge University Press; Cambridge, UK: 1984.

Parker L.E., Toms D. Quantum Field Theory in Curved Spacetime: Quantized Field and Gravity. Cambridge University Press; Cambridge, UK: 2009.

Hu B.L., Shiokawa K. Wave propagation in stochastic space-times: Localization, amplification and particle creation. Phys. Rev. D. 1998;57:3474–3483. doi: 10.1103/PhysRevD.57.3474. DOI

Amin M.A., Baumann D. From Wires to Cosmology. JCAP. 2016;2:45. doi: 10.1088/1475-7516/2016/02/045. DOI

Choudhury S., Mukherjee A., Chauhan P., Bhattacherjee S. Quantum Out-of-Equilibrium Cosmology. Eur. Phys. J. C. 2019;79:320. doi: 10.1140/epjc/s10052-019-6751-2. DOI

Lozano E., Mazzitelli F.D. The role of noise in the early Universe. Int. J. Mod. Phys. D. 2021;30:2150117. doi: 10.1142/S0218271821501170. DOI

Dodonov A.V., Dodonov E.V., Dodonov V.V. Photon generation from vacuum in nondegenerate cavities with regular and random periodic displacements of boundaries. Phys. Lett. A. 2003;317:378. doi: 10.1016/j.physleta.2003.08.065. DOI

Settineri A., Macri V., Garziano L., Stefano O.D., Nori F., Savasta S. Conversion of mechanical noise into correlated photon pairs: Dynamical Casimir effect from an incoherent mechanical drive. Phys. Rev. A. 2019;100:022501. doi: 10.1103/PhysRevA.100.022501. DOI

Roman-Ancheyta R., Ramos-Prieto I., Perez-Leija A., Busch K., Leon-Montiel R.D. Dynamical Casimir effect in stochastic systems: Photon harvesting through noise. Phys. Rev. A. 2017;96:032501. doi: 10.1103/PhysRevA.96.032501. DOI

Razavy M., Terning J. Quantum radiation in a one-dimensional cavity with moving boundaries. Phys. Rev. D. 1985;31:307. doi: 10.1103/PhysRevD.31.307. PubMed DOI

Crocce M., Dalvit D.A.R., Mazzitelli F.D. Resonant photon creation in a three-dimensional oscillating cavity. Phys. Rev. A. 2001;64:013808. doi: 10.1103/PhysRevA.64.013808. DOI

Crocce M., Dalvit D.A.R., Mazzitelli F.D. Quantum electromagnetic field in a three-dimensional oscillating cavity. Phys. Rev. A. 2002;66:033811. doi: 10.1103/PhysRevA.66.033811. DOI

Bender C.M., Orszag S.A. Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill; New York, NY, USA: 1978.

Papanicolau G., Keller J.B. Stochastic differential equations with applications to random harmonic oscillators and wave propagation in random media. SIAM J. Appl. Math. 1971;21:287. doi: 10.1137/0121032. DOI

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. J. Opt. B Quantum Semiclass. Opt. 2005;7:S32. doi: 10.1088/1464-4266/7/3/005. DOI

Ji J.Y., Jung H.H., Park J.W., Soh K.S. Production of photons by the parametric resonance in the dynamical Casimir effect. Phys. Rev. A. 1997;56:4440. doi: 10.1103/PhysRevA.56.4440. DOI

Calzetta E.A., Hu B.L.B. Nonequilibrium Quantum Field Theory. Cambridge University Press; Cambridge, UK: 2008.

Zanchin V., Maia A., Jr., Craig W., Brandenberger R.H. Reheating in the presence of noise. Phys. Rev. D. 1998;57:4651. doi: 10.1103/PhysRevD.57.4651. DOI

Wilson C.M., Johansson G., Pourkabirian A., Simonen M., Johansson J.R., Duty T., Nori F., Delsing P. Observation of the dynamical Casimir effect in a superconducting circuit. Nature. 2011;479:376. doi: 10.1038/nature10561. PubMed DOI