论文标题
部分可观测时空混沌系统的无模型预测
Superconductivity near a quantum critical point in the extreme retardation regime
论文作者
论文摘要
我们在量子临界时研究费米，并以表格$ v（ω_l）=（g/|ω_l|）^γ$极度迟缓的相互作用进行研究，其中$ω_l$是传输的Matsubara频率。该系统在临界温度$ t = t_c $下经历正常的perconductor相变。顺序参数是Eliashberg理论中的频率依赖性间隙函数$δ（ω_n）$。通常，这种相互作用极为智障，价格为$γ\ gg 1 $，除非在低温下$γ> 3 $就足够了。我们评估了普通状态的特定热量，$ t_c $，特定热量的跳跃，$δ（ω_n）$接近$ t_c $和landau自由能。我们的答案在限制$γ\至\ infty $中渐近。在低温下，我们证明了自由能的全局最小值是非排效的，并确定阶参数，自由能和特定热量。这些答案对于$ t \ to0 $和$γ> 3 $都是准确的。我们还发现并调查了$γ$模型的不稳定：$ t \ to0 $的负比热，而刚好超过$ t_c $。
We study fermions at quantum criticality with extremely retarded interactions of the form $V(ω_l)=(g/|ω_l|)^γ$, where $ω_l$ is the transferred Matsubara frequency. This system undergoes a normal-superconductor phase transition at a critical temperature $T=T_c$. The order parameter is the frequency-dependent gap function $Δ(ω_n)$ as in the Eliashberg theory. In general, the interaction is extremely retarded for $γ\gg 1$, except at low temperatures $γ>3$ is sufficient. We evaluate the normal state specific heat, $T_c$, the jump in the specific heat, $Δ(ω_n)$ near $T_c$, and the Landau free energy. Our answers are asymptotically exact in the limit $γ\to\infty$. At low temperatures, we prove that the global minimum of the free energy is nondegenerate and determine the order parameter, the free energy, and the specific heat. These answers are exact for $T\to0$ and $γ>3$. We also uncover and investigate an instability of the $γ$ model: negative specific heat at $T\to0$ and just above $T_c$.
