1. Energy loss in abelian medium M. Kirakosyan, Lebedev Institute A. Leonidov, Lebedev Institute and ITEP Quarks 2008 28.05.2008

2. Energy loss of fast particle in random inhomogeneous medium Density fluctuations induce fluctuations of dielectric permittivity Abelian approximation Motivation: Early stage of high energy nuclear collisions is inevitably strongly inhomogeneous on the event-by-event basis.

3. Turbulent energy density in nuclear collisions: M. Guylassy, D. Rischke, B. Zhang, Nuclear Physics A613 (1997), 397

4. Event-by-event versus average: M. Guylassy, D. Rischke, B. Zhang, Nuclear Physics A613 (1997), 397

5. Maxwell equation for monochromatic electric field: Permittivity includes spatially random component: Gaussian ensemble:

6. Polarization operator in Bourret approximation: Dielectric permittivity: Average Green function through Dyson equation:

7. Analytical expression for polarization operator: Exponential correlation function Bourret approximation:

8. Ratio of imaginary and real parts of permittivity

9. Mean electric field: Uniformly moving particle: Energy loss per unit path length:

10. Spectral density of stochastic energy loss Transverse losses larger at high energies!

11. Dependence of spectral density of energy loss on the magnitude of fluctuations Transverse losses more important for large fluctuations!

12. Conclusions Randomness of the medium strongly influences energy losses Nontrivial dependencies of transverse and longitudinal losses on energy and fluctuation’s magnitude Applications to physics of heavy ion collisions look promising!