純量場論之切黏滯係數

Abstract

本論文研究了切黏滯係數 (η) 對熵 (s) 之比值 η/s 在純量場論中之富有現象。藉由研究弱耦合多分量之純量場論，我們發現 η/s 隨溫度變化之行為， 不同於一般所認為之普適行為: 即在多數系統中， 該比值在發生 (二階) 相變之溫度時達到其局域最小值。在只考慮個別(弱)交互作用二分量純量場論中 ─ 其一分量在低溫凝結而另一分量處於對稱相， 即使系統發生相變， η/s 仍可以隨溫度單調遞減。在Modified O(N) 模型中， η/s 可以同時因共振和相變而產生 “雙谷” 行為，或是隨溫度單調遞減，或是如同發生在多數其他系統， 在相變溫度時達到其極小值。

The rich phenomena of the shear viscosity (η) to entropy density (s) ratio, η/s, in scalar field theories are studied. Unlike the speculated universal behavior – η/s reaches its local minimum at the (second order) phase transition temperature – in a wide class of systems, we find unusual behaviors for η/s in temperature by studying weakly coupled multi-component scalar field theories. In two-component weakly self-interacting real scalar fields theories with one of them condensing at low temperatures while the other remains in the symmetric phase, η/s can decrease monotonically in temperature despite the phase transition1. In the modified O(N) model, η/s can have a “double dip” behavior due to resonances and the phase transition, or η/s can either decrease monotonically in temperature or, as seen in many other systems, reach a minimum at the phase transition2.