Department of Physics, Ben Gurion University of the Negev, Beer Sheva 84105, Israel.
Phys Rev Lett. 2013 Sep 13;111(11):115302. doi: 10.1103/PhysRevLett.111.115302. Epub 2013 Sep 9.
We study various realizations of collective coordinates, e.g., the position of a particle, the charge of a Coulomb box, or the phase of a Bose or a superconducting condensate, coupled to Luttinger liquids with N flavors. We find that for a Luttinger parameter (1/2)<K<1 there is a phase transition from a delocalized phase into a phase with a periodic potential at strong coupling. In the delocalized phase the dynamics is dominated by an effective mass, i.e., diffusive in imaginary time, while on the transition line it becomes dissipative. At K=(1/2) there is an additional transition into a localized phase with no diffusion at zero temperature.
我们研究了各种集体坐标的实现方式，例如粒子的位置、库仑盒的电荷或玻色或超导凝聚体的相位，这些坐标与具有 N 个味道的 Luttinger 液体耦合。我们发现，对于 Luttinger 参数 (1/2)<K<1，在强耦合下，从非局域相到具有周期性势的相存在相变。在非局域相中，动力学由有效质量主导，即在虚时间中扩散，而在相变线上则是耗散的。在 K=(1/2)处，存在向零温度下没有扩散的局域相的附加转变。
