Thermalization and Unruh Radiation for a Uniformly Accelerated Charged Particle July 2010, Azumino...
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Transcript of Thermalization and Unruh Radiation for a Uniformly Accelerated Charged Particle July 2010, Azumino...
Thermalization and Unruh Radiation for a Uniformly Accelerated Charged Particle
July 2010, Azumino
張 森Sen Zhang
S. Iso and Y. Yamamoto
Unruh effect and Unruh radiation
~
Vacuum:
~
Hawking Radiation:
Bogoliubov transformation
Vacuum of free falling observer
Vacuum for inertial observer
thermal state for accelerating observer
Unruh Effect:
Asymptotic observer
Vacuum for inertial observer
(107K)
thermal state for accelerating observer
Unruh Effect:
Unruh Temperature:
How to See?Unruh Radiation: radiation due to fluctuation of electron
Schutzhold, Schaller, Habs ‘06Chen, Tajima ‘99
Unruh effect and Unruh radiation
Radiation from fluctuation
Larmor radiation
Previous Results
The discussion is intuitive and smart …
But more systematic derivation is required
Schutzhold, Schaller, Habs ‘06Chen, Tajima ‘99
Dimensionless laser strength parameter(a0 ~ 100 for patawatt-class laser)
Unruh radiation is very small compare to Larmor radiation. The angular distribution is quite different.
・ 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.
Plan• Charged particle
• Unruh Radiation
Stochastic equation (general formalism for fluctuation)
Accelerating case
Equipartition theorem Agrees Chen Tajima’s proporsal
How does it fluctuate actually?
Radiation from fluctuations in transverse directions
Angular distribution
Interference effect
But several problems …
Particle
Stochastic Equation
Focus on Particle Motion
Real Process Random motion
absorption and radiation Brownian motion
Stochastic Equation
Equation of motion:
Solution:
fluctuation
dissipation
Effective equation for a particle interacting with some quantum field
Scalar for simplicity:
Self-force from Larmor radiation (ALD)
P. R. Johnson and B. L. Hu
expansion:
Non-local
Renormalized mass
Fluctuation around uniformly accelerated motion for transverse direction:
Acceleration (1 keV)
Equation of fluctuations
Transverse direction
Longitudinal direction
Two point function:
Derivative expansion
Transverse Fluctuation
Relaxation Time:
Neglecting term:
Including term:
Equipartition Theorem
Equipartition theorem
thermal
Action:
Solution:
Stochastic equation:
Equipartition theorem
Universal
Longitudinal FluctuationTransform 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
Radiation
Interference effect
Depend on
What Chen-Tajima calculated
Nonzero
Unruh Detector
2D: no radiationRaine, Sciama, Grove 91’s
4D: radiate during thermalization, but no radiation if the detector state is thermal state at first
Shih-Yuin Lin & B. L. Hu
Eom:
Inteference Effect - Unruh Detector
Interference term
GR
Cancels the radiation from inhomogeneous part
Interference effect - charged particle
For transverse fluctuation:
Energy momentum tensor:
Larmor Radiation:
Unruh Radiation
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 …
Four poles
Relaxation time (thermalization time)
Photon travelling time in Compton wave length
: does not contribute for but is dominant for .
Unruh radiation depends on physics beyond the semi-classical analysis
in our framework. Treatment based on QED will be required.
UV divergence
Cancelled by the interference term, in the calculationof radiation due to transverse fluctuations
Problem of Radiation Dumping
Energy momentum conservation
Abraham-Lorentz-Dirac Force:
Runaway Solution
Landau-Lifshitz equation:
No back reaction for uniformly accelerated electron !?
on-shell condition
What can we say about this problem using QED?