Constructing KMS states from infinite-dimensional spectral triples

We construct KMS-states from $\mathrm{Li}_1$-summable semifinite spectral triples and show that in several important examples the construction coincides with well-known direct constructions of KMS-states for naturally defined flows. Under further summability assumptions the constructed KMS-state can be computed in terms of Dixmier traces. For closed manifolds, we recover the ordinary Lebesgue integral. For Cuntz-Pimsner algebras with their gauge flow, the construction produces KMS-states from traces on the coefficient algebra and recovers the Laca-Neshveyev correspondence. For a discrete group acting on its Stone-\v{C}ech boundary, we recover the Patterson-Sullivan measures on the Stone-\v{C}ech boundary for a flow defined from the Radon-Nikodym cocycle.Comment: 66 page

Three-dimensional structure of a string-fluid complex plasma

Three-dimensional structure of complex (dusty) plasmas was investigated under long-term microgravity conditions in the International-Space-Station-based Plasmakristall-4 facility. The microparticle suspensions were confined in a polarity-switched dc discharge. The experimental results were compared to the results of the molecular dynamics simulations with the interparticle interaction potential represented as a superposition of isotropic Yukawa and anisotropic quadrupole terms. Both simulated and experimental data exhibited qualitatively similar structural features indicating the bulk liquid-like order with the inclusion of solid-like strings aligned with the axial electric field. Individual strings were identified and their size spectrum was calculated. The decay rate of the size spectrum was found to decrease with the enhancement of string-like structural features

Slowing of acoustic waves in electrorheological and string-fluid complex plasmas

The PK-4 laboratory consists of a direct current plasma tube into which microparticles are injected, forming a complex plasma. The microparticles acquire many electrons from the ambient plasma and are thus highly charged and interact with each other. If ion streams are present, wakes form downstream of the microparticles, which lead to an attractive term in the potential between the microparticles, triggering the appearance of microparticle strings and modifying the complex plasma into an electrorheological form. Here we report on a set of experiments on compressional waves in such a string fluid in the PK-4 laboratory during a parabolic flight and on board the International Space Station. We find a slowing of acoustic waves and hypothesize that the additional attractive interaction term leads to slower wave speeds than in complex plasmas with purely repulsive potentials. We test this hypothesis with simulations, and compare with theory