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对1+1和2+1维空间上定向聚合问题的数值模拟结果显示,任意有限温度下的横向涨落和自由能涨落在聚合尺度t较大时都将趋于零温度时强耦合下的结果:Δx∝tν和ΔF∝tω(d=1+1时,ν=2/3,ω=1/3;d=2+1时,ν≈0.6,ω≈0.2).有限温度下,由于1+1维和2+1维空间上的比热C(T,t)∝t和1+1维空间上的熵涨落ΔS∝t1/2,1+1维空间上的系综能量涨落和内能涨落以及2+1维空间上的系综能量涨落均趋于t1/2而远强于自由能涨落.在2+1维空间上,定向聚合问题有发生相变的迹象:当熵涨落达到其最大值时,单位聚合尺度的熵涨落和内能涨落在聚合尺度t→∞时,可能会由低温下趋于有限值(零温度除外)转变为高温下趋于零
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关键词:
- 定向聚合 /
- 表面生长现象 /
- Kardar-Parisi-Zhang方程
Numerical Simulations for directed polymers in 1+1 and 2+1 dimensions show that the transverse fluctuations and free energy fluctuations tend to the strong coupling limit: Δx∝tν,ΔF∝tω (ν=2/3,ω=1/3 for d=1+1; ν≈0.6, ω≈0.2 for d=2+1) at any finite temperature as their behaviors at zero temperature for the long length t of polymer. At finite temperatures, as a result of that the specific heat in both 1+1 dimensions and 2+1 dimensions scales as t and the entropy fluctuations in 1+1 dimensions scale as t1/2 , the ensemble energy fluctuations in both 1+1 and 2+1 dimensions and the internal energy fluctuations in 1+1 dimensions are more pronounced than the free energy fluctuations and scale as t1/2. There is an indication of a phase transition in 2+1 dimensions. It is plausible that the entropy fluctuations and the internal fluctuations per unit length polymers for t→∞ will become zero value at high temperatures from nonzero values at low temperatures at some temperature T=TC where the entropy fluctuation reaches maximum.-
Keywords:
- directed polymers /
- surface growth phenomena /
- KPZ equation
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