具有非对称势的量子晶体中的相变
A Phase Transition in a Quantum Crystal with Asymmetric Potentials
摘要：
考虑了以简立方晶格$\mathbb{Z}^d$为标度的平移不变相互作用量子非谐振子系统。非调和势是一般类型的，这特别意味着它可能没有对称性。对于这个系统，我们证明了在$d\geq 3$提供的外场一定值下，全局极化（在热力学极限下得到）变得不连续，并且粒子质量和相互作用强度足够大.证明是基于代表性的本地吉布斯状态的路径措施，从而使用红外估计和Garsia-Rodemich-Rumsey不等式。
英文摘要：
A translation invariant system of interacting quantum anharmonic oscillators indexed by the elements of a simple cubic lattice $\mathbb{Z}^d$ is considered. The anharmonic potential is of general type, which in particular means that it might have no symmetry. For this system, we prove that the global polarization (obtained in the thermodynamic limit) gets discontinuous at a certain value of the external field provided $d\geq 3$, and the particle mass as well as the interaction intensity are big enough. The proof is based on the representation of local Gibbs states in terms of path measures and thereby on the use of the infrared estimates and the Garsia-Rodemich-Rumsey inequality.
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