Study on Vital Node of Distribution Networks

Elementary Excitations, Spectral Weights and Experimental Signatures of a Supersolid and a Fulde-Ferrell-Larkin-Ovchinnikov State

“…6. So the reentrant lattice SS discussed in 43,50,51 is different from the bulk 4 He SS state discussed in this paper, although both kinds of supersolids share some interesting common properties. In both cases, the SF to SS transition is driven by the closing of the gap of the roton minimum, so the transition could be first or second order at mean field level.…”

“…So the theory developed in this paper on bulk 4 He is different from the lattice theory developed in 43,50 . As shown in the appendix A and in 50,51 , one common fact of both supersolids is that both are due to vacancies or interstitials. Lattice supersolids can also be described by doping the adjacent CDW either by vacancies or interstitials, so are classified as two types SS − v and SS − i.…”

“…So the coupling constant g in Helium 4 plays a similar role as the chemical potential µ in the lattice models, the gap ∆(p) in the NS-PH which tunes the distance from the NS-PH to the SF plays a similar role as the gap in the CDW which tunes the distance from the CDW to the superfluid . It was shown in 51 , the lattice supersolids existing at commensurate 1/2 filling factors in frustrated lattices such as triangular lattice is just the coexistence of SS-v and SS-i. Combined with the results in 50 , we conclude that 4 He supersolid can exist both in bulk and on substrate, while although H 2 supersolid may not exist in the bulk, but it may exist on wisely chosen substrates.…”

“…Of course, both experiments may due to phase separations instead of the SS phase. very recently, the author studied various kinds od supersolids in frustrated lattices such as triangular and kagome lattices 51 . By comparing Eqns.1, 2,3 in the continuum with the Eqn.B1 on the lattice, one can see the crucial difference between a lattice system with a continuous system: Eqn 1 stands for a spontaneously formed lattice with phonon excitations.…”

“…The filling factor is controlled by an external chemical potential. At integer filling factors or half filling factor, there are particle-hole symmetry (PH) for excitations which ensures the number of particles is equal to that of vacancies and adding interstitials is equivalent to adding vacancies respectively 50,51 . While in the latter, the lattice results from a spontaneous translational symmetry breaking driven by the pressure as shown in the Fig.…”