Dynamic Casimir Phenomena

red ballRotating Steady State: A dielectric sphere rotating with angular frequency Ω

yellow ballConsider waves of frequency  ω and angular state m :

Lab frame:           

Object frame:         

yellow ball "Generation of waves by a rotating body," Ya B. Zel'dovich, JETP Lett. 14, 180 (1971); 

yellow ball If  ω'and  ω have opposite signs:

 yellow ball  Amplitude of (classical) scattered wave exceeds incoming wave (Super-radiance).

 yellow ball  Conjectured (quantum) spontaneous emission with no incoming wave.

yellow ball "Spontaneous emission by rotating objects: A scattering approach,"

M.F. Maghrebi, R.L. Jaffe, & M. Kardar, PRL108, 230403 (2012). 

yellow ballNumber of photons in a mode of frequency   ω and angular state m,

generated by object rotating with angular velocity Ω  is:

        

yellow ballE.g., net power for a rotating cylinder:  

BBT  (url)

red ball Accelerating bodies in vacuum may experience friction, and emit radiation.

yellow ball "Quantum Theory of the Electromagnetic Field in a Variable-Length One-Dimensional Cavity,"

G. T. Moore, J. Math. Phys. 11, 2679 (1970)

yellow ball "Radiation from a Moving Mirror in Two Dimensional Space-Time: Conformal Anomaly,"

S. A. Fulling and P. C. W. Davies, Proc. R. Soc. London, Ser. A 348, 393 (1976).

...

yellow ball "Observation of the dynamical Casimir effect in a superconducting circuit,"

Wilson, Johansson, Pourkabirian, Simoen, Johansson, Duty, F. Nori & P. Delsing, Nature 479, 376 (2011).

yellow ball"Observation of self-amplifying Hawking radiation in an analogue black-hole laser,"

J. Steinhauer, Nature Phys. 10, 864 (2014). 

red ball Force fluctuations: Dissipation implies fluctuations; all forces discussed so far are averages of a fluctuating quantity.

yellow ballAs a simple consequences of such fluctuations consider the wanderings of

a classical particle of mass m in a quantum bath.

yellow ballThere is no net force on the particle, but it disperses due to force fluctuations:

yellow ballLangevin equation for an otherwise free particle,

yellow ball In the commonly used Caldeira-Legget formalism, the force is linearly coupled to the bath,

However, a linear coupling is forbiddent for a neutral, but polarizable, particle.

yellow ball With linear coupling, a free field theory implies a Gaussian distribution for φ,

hence the force and the displacement are also Gaussian distributed, entirely described by the variance

yellow ball For a neutral particle (no linear coupling), the quadratic force is not Gaussian distributed; leading to cumulants

consistent with a power-law probability distribution, reminiscent of Levy flights:

yellow ballPotential realizations for solitons in Bose-Einstein condensate.