TY - JOUR

T1 - On the dynamics of statistical fluctuations in heavy ion collisions

AU - Hofmann, Helmut

AU - Siemens, Philip J.

N1 - Funding Information:
t Work supported in part by the Deutsche Forschungsgemeinschaft. tt Most of the work has been performed during this author's atgy at the NieL Bohr Institute, Co-

PY - 1977/1/10

Y1 - 1977/1/10

N2 - We show how statistical fluctuations can be treated within the collective approach to heavy ion reactions. In the classical limit, the equation of motion for the distribution d in the collective variables Qμ and their conjugate momenta Pμ turns out to be a Fokker-Planck equation. We briefly describe the connection of this equation to one of the Smoluchowski type for a distribution in Qμ only, often used in heavy ion physics. For anharmonic motion our general Fokker-Planck equation is simplified to be linear in the deviations of the Qμ mand Pμ from their mean values. The solution of this equation is discussed in terms of a simple Gaussian. The parameters of this Gaussian are determined completely by the first and second moments in Qμ mand Pμ. The equations for the first moments are identical to the Newton equations including frictional forces. Those for the second moments are linear differential equations of first order and hence easily solvable. The whole derivation is completely analogous to that for the Newton equation reported recently. Here the starting point is the quantum mechanical von Neumann equation rather than the Heisenberg equations. As an intermediate result we obtain and discuss briefly a quantal equation for the reduced density operator d which includes frictional effects.

AB - We show how statistical fluctuations can be treated within the collective approach to heavy ion reactions. In the classical limit, the equation of motion for the distribution d in the collective variables Qμ and their conjugate momenta Pμ turns out to be a Fokker-Planck equation. We briefly describe the connection of this equation to one of the Smoluchowski type for a distribution in Qμ only, often used in heavy ion physics. For anharmonic motion our general Fokker-Planck equation is simplified to be linear in the deviations of the Qμ mand Pμ from their mean values. The solution of this equation is discussed in terms of a simple Gaussian. The parameters of this Gaussian are determined completely by the first and second moments in Qμ mand Pμ. The equations for the first moments are identical to the Newton equations including frictional forces. Those for the second moments are linear differential equations of first order and hence easily solvable. The whole derivation is completely analogous to that for the Newton equation reported recently. Here the starting point is the quantum mechanical von Neumann equation rather than the Heisenberg equations. As an intermediate result we obtain and discuss briefly a quantal equation for the reduced density operator d which includes frictional effects.

UR - http://www.scopus.com/inward/record.url?scp=0011662697&partnerID=8YFLogxK

U2 - 10.1016/0375-9474(77)90464-X

DO - 10.1016/0375-9474(77)90464-X

M3 - Article

AN - SCOPUS:0011662697

SN - 0375-9474

VL - 275

SP - 464

EP - 486

JO - Nuclear Physics, Section A

JF - Nuclear Physics, Section A

IS - 2

ER -