Range of validity of transport equations
Range of validity of transport equations
复制标题
输运方程的有效性范围
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
S. Borsányi
中科院分区：
文献类型：
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作者：
J. Berges;S. Borsányi
Transport equations can be derived from quantum field theory assuming a loss of information about the details of the initial state and a gradient expansion. While the latter can be systematically improved, the assumption about a memory loss is not known to be controlled by a small expansion parameter. We determine the range of validity of transport equations for the example of a scalar g{sup 2}{phi}{sup 4} theory. We solve the nonequilibrium time evolution using the three-loop 2PI effective action. The approximation includes off-shell and memory effects and assumes no gradient expansion. This is compared to transport equations to lowest order (LO) and beyond (NLO). We find that the earliest time for the validity of transport equations is set by the characteristic relaxation time scale t{sub damp}=-2{omega}/{sigma}{sub {rho}}{sup (eq)}, where -{sigma}{sub {rho}}{sup (eq)}/2 denotes the on-shell imaginary-part of the self-energy. This time scale agrees with the characteristic time for partial memory loss, but is much shorter than thermal equilibration times. For times larger than about t{sub damp} the gradient expansion to NLO is found to describe the full results rather well for g{sup 2}(less-or-similar sign)1.
Transport equations can be derived from quantum field theory assuming a loss of information about the details of the initial state and a gradient expansion. While the latter can be systematically improved, the assumption about a memory loss is not known to be controlled by a small expansion parameter. We determine the range of validity of transport equations for the example of a scalar g{sup 2}{phi}{sup 4} theory. We solve the nonequilibrium time evolution using the three-loop 2PI effective action. The approximation includes off-shell and memory effects and assumes no gradient expansion. This is compared to transport equations to lowest order (LO) and beyond (NLO). We find that the earliest time for the validity of transport equations is set by the characteristic relaxation time scale t{sub damp}=-2{omega}/{sigma}{sub {rho}}{sup (eq)}, where -{sigma}{sub {rho}}{sup (eq)}/2 denotes the on-shell imaginary-part of the self-energy. This time scale agrees with the characteristic time for partial memory loss, but is much shorter than thermal equilibration times. For times larger than about t{sub damp} the gradient expansion to NLO is found to describe the full results rather well for g{sup 2}(less-or-similar sign)1.