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Causal Baryon Diffusion and Colored Noise. Joe Kapusta University of Minnesota. Collaborator: Clint Young. Sources of Fluctuations in High Energy Nuclear Collisions. Initial state fluctuations Hydrodynamic fluctuations due to finite particle number

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causal baryon diffusion and colored noise

Causal Baryon Diffusion and Colored Noise

Joe Kapusta

University of Minnesota

Collaborator: Clint Young

sources of fluctuations in high energy nuclear collisions

Sources of Fluctuations in High Energy Nuclear Collisions

Initial state fluctuations

Hydrodynamic fluctuations due to finite particle number

Energy and momentum deposition by jets traversing the medium

Freeze-out fluctuations

why the need for causality
Why the need for causality?

The diffusion equation propagates information

instantaneously. No good for hydrodynamic

modeling of high energy nuclear collisions!

What should the current

be modified to?

why colored noise
Why colored noise?

Add noise to the current; in the local rest frame:

This is white noise (Fourier transform is a

constant). It is OK for hydrodynamics if

noise is treated as a perturbation, but creates

havoc if it is treated nonperturbatively as

there will be a dependence on the

coarse-grained cell size.

slide7

Fluctuation-Dissipation Theorem

Response function

Density correlator

Noise

cattaneo equation
Cattaneo Equation

(Infinite group velocity is not an issue; Brillouin.)

summary
Summary
  • We have studied and compared the baryon

current in 1st, 2nd and 3rd order dissipative

fluid dynamics.

  • We computed the response function, baryon

autocorrelation function, and noise.

  • One needs at least 2nd order for finite propagation speed, and at least 3rd order for finite correlation lengths and times for noise.
slide16
These results can readily be implemented in numerical hydrodynamic codes. (I-44)
  • Baryon transport and noise should be important even if the net baryon number is zero, and may play a crucial role near a critical point.
  • Microscopic calculations are needed to compute the time constants (probably functions of temperature and density).
  • Noise happens!

Supported by the Office Science, U.S. Department of Energy.