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[求助]
自相關(guān)函數(shù)為什么最終會(huì)接近于0
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| 一般的自相關(guān)函數(shù)有類似的表達(dá)式:A(t)=/.其中,B(t)為t時(shí)刻的物理量,如速度、均方末端距、偶極矩等等,有的是矢量,有的是標(biāo)量。<>為系綜平均。當(dāng)t很小的時(shí)候,A(t)接近于1,這個(gè)很好理解。但為什么當(dāng)t很大的時(shí)候,A(t)接近于0?請(qǐng)大家?guī)蛶兔Γx謝! |
專家顧問(wèn) (正式寫手)
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專家經(jīng)驗(yàn): +49 |
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Not always zero. It depends on the ensemble average . At t=infinity, = ^2, so if is not equal to zero, then A(t) won't go to zero at infinite time. For velocity-velocity auto TCF or dipole-dipole TCF in uniform liquid, it should decay to zero since =0. However, at some interfaces or in confinement, the dipole-dipole TCF might not decay to zero since molecule's orientations are not uniformly distributed. |
木蟲 (著名寫手)

專家顧問(wèn) (正式寫手)
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專家經(jīng)驗(yàn): +49 |
專家顧問(wèn) (正式寫手)
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專家經(jīng)驗(yàn): +49 |
專家顧問(wèn) (正式寫手)
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專家經(jīng)驗(yàn): +49 |
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I mean, you should refer to some Stat Mech textbooks for the definition of ensemble and ensemble average. Briefly speaking an ensemble is a set of points chosen in phase space, different ensembles have different probability distributions ( in NVE it's uniform and in NVT it's Boltzmann distribution). With these probability distributions you can calculating the ensemble average by sampling over the ensemble. In an MD simulation, after the system has reached equilibrium, you just sample N copies of quantity A, add them together and divide by N, and that is the ensemble average. |
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