Discovering Congested Routes Using Vehicle Trajectories in Road Networks

Bok, Kyoung Soo; He, Li; Lim, Jong Tae; Yoo, Jae Soo

doi:10.1155/2015/420689

Cited by 4 publications

(1 citation statement)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…higher energy branch of excitations which has not yet been discovered. A brief report of this work has already been published 20 .…”

Section: Periodic Variation Of Loop-current Ordermentioning

confidence: 99%

Pseudogap and Fermi arcs in underdoped cuprates

Varma

2019

Phys. Rev. B

View full text Add to dashboard Cite

The proposed loop-current order in cuprates cannot give the observed pseudogap and the Fermiarcs because it preserves translation symmetry. A modification to a periodic arrangement of the four possible orientations of the order parameter with a large period of between about 12 to 30 lattice constants is proposed and shown in a simple and controlled calculation to give one-particle spectra with every feature as in the ARPES experiments. The results follow from (1) the currents at the boundaries of the periodic domains with similar topology as the Affleck-Marston flux phase, and (2) the mixing introduced by the boundary currents between the states near the erstwhile Fermi-surface and the ghost Fermi-surfaces which are displaced from it by mini-reciprocal vectors. The proposed idea can be ruled out or verified by high resolution diffraction or imaging experiments. It does not run afoul of the variety of different experiments consistent with the loop-current order as well as the theory of the marginal Fermi-liquid and d-wave superconductivity based on quantumcritical fluctuations of the loop current order. 1 arXiv:1903.04699v2 [cond-mat.str-el] The cuprate phase diagram [1] has presented three new phenomena in physics, two new normal states -the strange metal and the pseudogap with Fermi-arcs [2, 3], and the high temperature d-wave superconducting phase. It is now generally accepted that the pseudogap occurs below a phase transition at T * (x) ending at a quantum-critical point as a function of doping x = x c , as was predicted [4]. The strange metal region occurs on the other side of T * (x) and ends in a gradual cross-over to a Fermi-liquid phase. The Fermi-liquid normal phase further supports the existence of a quantum-critical point. Superconductivity occurs in a region of x around the quantum-critical point. This paper is concerned with the unanswered questions about the one-particle spectra in the pseudogap state in the cuprate metals. An angle-dependent gap is observed in ARPES experiments [2, 3] at the erstwhile Fermi-surface (measured above T * (x)) decreasing in magnitude from the (0, π) directions ending in a Fermi-arc -a region with zero gap over a finite angle centered in the (π, π) directions. In the same region of the phase diagram, a tiny closed Fermi-surface, about 2% of that expected by calculated band-structure, is observed in magneto-oscillation experiments at low temperatures and high enough magnetic fields [5]. Refined experiments [6] suggest that such small Fermi-surfaces occur near the diagonal directions where ARPES observes Fermi-arcs. T * (x) does mark the onset of the loop-current ordered state [7] which breaks time-reversal symmetries as well as reflection and rotation symmetries. Seven different experimental techniques [8-17] which test different aspects of such symmetries, are consistent with the occurrence of such a state below T * (x). Quantum critical fluctuations [18] of this state coupled to fermions give in a systematic theory the marginal fermi-liquid [19] universally observed in...

show abstract

“…higher energy branch of excitations which has not yet been discovered. A brief report of this work has already been published 20 .…”

Section: Periodic Variation Of Loop-current Ordermentioning

confidence: 99%