**Dynamic Casimir Phenomena**

**Rotating Steady State: **A dielectric sphere rotating with angular frequency *Ω*

Consider waves of frequency

ωand angular statem:Lab frame:

Object frame:

"Generation of waves by a rotating body," Ya B. Zel'dovich, JETP Lett.

14, 180 (1971);If

ω'andωhave opposite signs:Amplitude of (classical) scattered wave exceeds incoming wave (

Super-radiance).Conjectured (quantum) spontaneous emission with no incoming wave.

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

M.F. Maghrebi, R.L. Jaffe, & M. Kardar, PRL

108, 230403 (2012).Number of photons in a mode of frequency

ωand angular statem,generated by object rotating with angular velocity

Ωis:

E.g., net power for a rotating cylinder:

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

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

G. T. Moore, J. Math. Phys.

11, 2679 (1970)"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).

...

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

Wilson, Johansson, Pourkabirian, Simoen, Johansson, Duty, F. Nori & P. Delsing, Nature

479, 376 (2011).

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

J. Steinhauer, Nature Phys.

10, 864 (2014).

As a simple consequences of such fluctuations consider the wanderings of

a classical particle of mass

min a quantum bath.There is no net force on the particle, but it disperses due to force fluctuations:

Langevin equation for an otherwise free particle,

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.

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

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:

Potential realizations for solitons in Bose-Einstein condensate.