Particle radiation produced by accelerated systems and their analogy with damped oscillators


  • Miguel Angel Estévez Juárez Instituto de Física, Benemérita Universidad Autónoma de Puebla
  • Emerson Sadurní Instituto de Física, Benemérita Universidad Autónoma de Puebla.



Unruh Effect, Rindler coordinates, Klein-Gordon equation in curved space, micro electro-mechanical oscillator


The Unruh effect predicts how uniformly accelerated observers will perceive a change in the vacuum state. This shows that the concept of particle number depends on the acceleration of the reference frame. Although this is a result of quantum field theory, its experimental verification is still questioned, mainly due to the high accelerations required. In this work we study a quantum oscillator with only one complex coordinate and a damping term acting as perturbation, which has all the characteristics of the Unruh effect in second quantization for an accelerated observer. The Bogoliubov transformation connecting the two different vacuum states is obtained. This leads to an explicit formula for the particle occupation number as a function of energy and acceleration. Furthermore, it is shown that our analogue system contains an effective temperature that depends on the observer's sudden acceleration, seen as a friction force. The purpose of this work is to demonstrate that quanta production (particles or energy packets) is inevitable under the premises of quantum field theory.

Author Biography

Emerson Sadurní, Instituto de Física, Benemérita Universidad Autónoma de Puebla.

Professor  Dr. E. Sadurní, Theoretical  and Mathematical Physics.


L. Crispino, A. Higuchi, and G. Matsas, The Unruh effect and its applications, Rev. Mod. Phys. 80 (2008),

W. Unruh, Notes on black-hole evaporation, Phys. Rev.D 14 (1976), 870

J. Krim, Friction at the nano-scale, Physics World 18 (1976) 31,

J. Franco-Villafañe et al., First Experimental Realization of the Dirac Oscillator, Phys. Rev. Lett. 111 (2013),

E. Sadurní, T. Seligman, and F. Mortessagne, Playing relativistic billiards beyond graphene, New J. Phys. 12 (2010) 053014,

S. Bittner et al., Bound states in sharply bent waveguides: Analytical and experimental approach, Phys. Rev. E 87 (2013),

E. Sadurní and W. P. Schleich, Conformal mapping and bound states in bent waveguides, AIP Conference Proceedings 1323 (2010),

W. Rindler, Hyperbolic Motion in Curved Space Time, Phys. Rev. 119 (1960) 2082,

P. Caldirola, Forze non conservative nella meccanica quantistica, Il Nuovo Cimento 18 (1941) 393-400,

D. Truax, Baker-Campbell-Hausdorff relations and unitarity of SU(2) and SU(1,1) squeeze operators, Phys. Rev. D 31 (1985) 1988,




How to Cite

Estévez Juárez MA, Sadurní E. Particle radiation produced by accelerated systems and their analogy with damped oscillators. Supl. Rev. Mex. Fis. [Internet]. 2023 Sep. 18 [cited 2024 Jul. 17];4(2):021101 1-. Available from: