Thermalization and Unruh Radiation for a Uniformly Accelerated Charged Particle
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1 July 2010, Azumino Thermalization and Unruh Radiation for a Uniformly Accelerated Charged Particle 張森 Sen Zhang S. Iso and Y. Yamamoto
2 Unruh effect and Unruh radiation Vacuum: ~ ~ Bogoliubov transformation Unruh Effect: Vacuum for inertial observer thermal state for accelerating observer Hawking Radiation: Vacuum of free falling observer Asymptotic observer
3 Unruh effect and Unruh radiation Unruh Effect: Vacuum for inertial observer thermal state for accelerating observer Unruh Temperature: (10 7 K) How to See? Unruh Radiation: radiation due to fluctuation of electron Chen, Tajima 99 Schutzhold, Schaller, Habs 06
4 Previous Results Chen, Tajima 99 Schutzhold, Schaller, Habs 06 Radiation from fluctuation Larmor radiation Dimensionless laser strength parameter (a 0 ~100 for patawatt-class laser) Unruh radiation is very small compare to Larmor radiation. The angular distribution is quite different. The discussion is intuitive and smart But more systematic derivation is required Unruh radiation are treated in a complete different way from Larmor radiation. How does the path of the uniformly accelerated particle fluctuate? The interference effect were not considered.
5 Plan Charged particle How does it fluctuate actually? Stochastic equation (general formalism for fluctuation) Accelerating case Equipartition theorem Agrees Chen Tajima s proporsal Unruh Radiation Radiation from fluctuations in transverse directions Angular distribution Interference effect But several problems
6 Particle
7 Stochastic Equation Real Process Random motion Focus on Particle Motion absorption and radiation Brownian motion
8 Stochastic Equation Scalar for simplicity: Equation of motion: Solution: fluctuation dissipation Effective equation for a particle interacting with some quantum field
9 expansion: Non-local Renormalized mass Self-force from Larmor radiation (ALD) P. R. Johnson and B. L. Hu
10 Fluctuation around uniformly accelerated motion for transverse direction: Equation of fluctuations Acceleration (1 kev) Transverse direction Longitudinal direction
11 Transverse Fluctuation Neglecting term: Relaxation Time: Including term: Two point function: Derivative expansion
12 Equipartition Theorem Equipartition theorem thermal
13 Action: Solution: Stochastic equation: Universal Equipartition theorem
14 Longitudinal Fluctuation Transform variables for the accelerated observer : Problem of coordinates: The expectation values change, but the Bogoliubov transformation is same Problem on constant electric field: Different longitudinal coordinates means different acceleration Difficult to say if the longitudinal is same to the transverse Fluctuation in longitudinal direction for uniformly accelerated obserber: Very different from transverse direction
15 Radiation
16 Interference effect What Chen-Tajima calculated Nonzero Depend on
17 Inteference Effect - Unruh Detector 2D: no radiation Raine, Sciama, Grove 91 s Unruh Detector 4D: radiate during thermalization, but no radiation if the detector state is thermal state at first Shih-Yuin Lin & B. L. Hu Eom:
18 Interference term G R Cancels the radiation from inhomogeneous part
19 Interference effect - charged particle For transverse fluctuation:
20 Energy momentum tensor: Larmor Radiation: Unruh Radiation
21 Summary and Future Work An uniformly accelerated particle satisfies a stochastic equation. The transverse momentum fluctuations satisfy the equipartition theorem for both scalar field and gauge field. Longitudinal direction is more complicated. Radiations due to the fluctuations are calculated partly. The interference effect are important. There may be a problem on validity of approximation which relates to the UV divergence. Treatment based on QED will be required. Longitudinal contribution, Angular distribution, QED case
22 UV divergence Four poles Photon travelling time in Compton wave length Relaxation time (thermalization time) : does not contribute for but is dominant for. Cancelled by the interference term, in the calculation of radiation due to transverse fluctuations Unruh radiation depends on physics beyond the semi-classical analysis in our framework. Treatment based on QED will be required.
23 Problem of Radiation Dumping Abraham-Lorentz-Dirac Force: Energy momentum conservation on-shell condition Runaway Solution Landau-Lifshitz equation: No back reaction for uniformly accelerated electron!? What can we say about this problem using QED?
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