Asymptotic scattering and duality in the one-dimensional three-state quantum Potts model on a lattice

We determine numerically the single-particle and the two-particle spectrum of the three-state quantum Potts model on a lattice by using the density matrix renormalization group method, and extract information on the asymptotic (small momentum) S-matrix of the quasiparticles. The low energy part of the finite size spectrum can be understood in terms of a simple effective model introduced in a previous work, and is consistent with an asymptotic S-matrix of an exchange form below a momentum scale p*. This scale appears to vanish faster than the Compton scale, mc, as one approaches the critical point, suggesting that a dangerously irrelevant operator may be responsible for the behaviour observed on the lattice.

Equilibration of quantum gases

Finding equilibration times is a major unsolved problem in physics with few analytical results. Here we look at equilibration times for quantum gases of bosons and fermions in the regime of negligibly weak interactions, a setting which not only includes paradigmatic systems such as gases confined to boxes, but also Luttinger liquids and the free superfluid Hubbard model. To do this, we focus on two classes of measurements: (i) coarse-grained observables, such as the number of particles in a region of space, and (ii) few-mode measurements, such as phase correlators.Weshow that, in this setting, equilibration occurs quite generally despite the fact that the particles are not interacting. Furthermore, for coarse-grained measurements the timescale is generally at most polynomial in the number of particles N, which is much faster than previous general upper bounds, which were exponential in N. For local measurements on lattice systems, the timescale is typically linear in the number of lattice sites. In fact, for one-dimensional lattices, the scaling is generally linear in the length of the lattice, which is optimal. Additionally, we look at a few specific examples, one of which consists ofNfermions initially confined on one side of a partition in a box. The partition is removed and the fermions equilibrate extremely quickly in time O(1 N).

Transcription of TIR1-Controlled Genes Can be Regulated within 10 Min by an Auxin-Induced Process. Can TIR1 be the Receptor?

ABP1 and TIR1/AFBs are known as auxin receptors. ABP1 is linked to auxin responses several of which are faster than 10 min. TIR1 regulates auxin-induced transcription of early auxin genes also within minutes. We use transcription of such TIR1-dependent genes as indicator of TIR1 activity to show the rapid regulation of TIR1 by exogenous auxin. To this end, we used quantification of transcription of a set of fifteen early auxin-induced reporter genes at t = 10 and t = 30 min to measure this as a TIR1-dependent auxin response. We conducted this study in 22 mutants of auxin transporters (pin5, abcb1, abcb19, and aux1/lax3), protein kinases and phosphatases (ibr5, npr1, cpk3, CPK3-OX, d6pk1, d6pkl1-1, d6pkl3-2, d6pkl1-1/d6pkl2-2, and d6pkl1-1/d6pkl3-2), of fatty acid metabolism (fad2-1, fad6-1, ssi2, lacs4, lacs9, and lacs4/lacs9) and receptors (tir1, tir1/afb2, and tir1/afb3) and compared them to the wild type. After 10 min auxin application, in 18 out of 22 mutants mis-regulated expression of at least one reporter was found, and in 15 mutants transcription of two-to-three out of five selected auxin reporter genes was mis-regulated. After 30 min of auxin application to mutant plants, mis-regulation of reporter genes ranged from one to 13 out of 15 tested reporter genes. Those genes chosen as mutants were themselves not regulated in their expression by auxin for at least 1 h, excluding an influence of TIR1/AFBs on their transcription. The expression of TIR1/AFB genes was also not modulated by auxin for up to 3 h. Together, this excludes a feedback or feedforward of these mutant genes/proteins on TIR1/AFBs output of transcription in this auxin-induced response. However, an auxin-induced response needed an as yet unknown auxin receptor. We suggest that the auxin receptor necessary for the fast auxin-induced transcription modulation could be, instead, ABP1. The alternative hypothesis would be that auxin-induced expression of a protein, initiated by TIR1/AFBs receptors, could initiate these responses and that this unknown protein regulated TIR1/AFB activities within 10 min.