arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0711.3435hep-th
收藏

强耦合标量场理论中比熵的量子束缚

Quantum Bound on the Specific Entropy in Strong-Coupled Scalar Field Theory

M. Aparicio Alcalde, G. Menezes, N. F. Svaiter

备注：
Accepted for publication in Physical Review D
发表信息：
Phys.Rev.D77:125024,2008
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

本文利用欧氏路径积分方法和泛函方法，讨论了强耦合区的$(g_{0} ϕ^{p})_{d}$自相互作用标量场理论。我们假设宏观边界的存在下，限制在一个超立方体的侧$L$领域。我们还认为系统在温度$β^{-1}$处处于热平衡。对于空间上有界的自由场，贝肯斯坦界指出比熵满足不等式$\frac{S}{E} < 2 πR$，其中$R$代表外接系统的最小球体的半径。利用强耦合微扰展开，我们得到了系统的重整化平均能量$E$和熵$S$，达到$(g_{0})^{-\frac{2}{p}}$阶，给出了比熵在某些情况下也满足量子束缚的解析证明.定义$ε_d^{(r)}$为单位长度自由理论的重整化零点能，无量纲量$ξ=\fracβ{L}$、$h_1(d)$和$h_2(d)$为$d$的正解析函数，在高温情况下，得到比熵满足$\frac{S}{E} < 2πR \frac{h_1(d)}{h_2(d)} ξ$ .当考虑到比熵的低温行为时，我们有$\frac{S}{E} <2πR \frac{h_1(d)}{ε_d^{(r)}}ξ^{1-d}$。因此，重整化零点能量的符号可以使这个量子束缚无效。如果重整化零点能是一个正的量，在中温和低温极限，存在量子束缚。

英文摘要：

Using the Euclidean path integral approach with functional methods, we discuss the $(g_{0} ϕ^{p})_{d}$ self-interacting scalar field theory, in the strong-coupling regime. We assume the presence of macroscopic boundaries confining the field in a hypercube of side $L$. We also consider that the system is in thermal equilibrium at temperature $β^{-1}$. For spatially bounded free fields, the Bekenstein bound states that the specific entropy satisfies the inequality $\frac{S}{E} < 2 πR$, where $R$ stands for the radius of the smallest sphere that circumscribes the system. Employing the strong-coupling perturbative expansion, we obtain the renormalized mean energy $E$ and entropy $S$ for the system up to the order $(g_{0})^{-\frac{2}{p}}$, presenting an analytical proof that the specific entropy also satisfies in some situations a quantum bound. Defining $ε_d^{(r)}$ as the renormalized zero-point energy for the free theory per unit length, the dimensionless quantity $ξ=\fracβ{L}$ and $h_1(d)$ and $h_2(d)$ as positive analytic functions of $d$, for the case of high temperature, we get that the specific entropy satisfies $\frac{S}{E} < 2πR \frac{h_1(d)}{h_2(d)} ξ$. When considering the low temperature behavior of the specific entropy, we have $\frac{S}{E} <2πR \frac{h_1(d)}{ε_d^{(r)}}ξ^{1-d}$. Therefore the sign of the renormalized zero-point energy can invalidate this quantum bound. If the renormalized zero point-energy is a positive quantity, at intermediate temperatures and in the low temperature limit, there is a quantum bound.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑