Theory of finite temperature crossovers near quantum critical points close to, or above, their upper-critical dimension

A systematic method for the computation of finite temperature ($T$) crossover functions near quantum critical points close to, or above, their upper-critical dimension is devised. We describe the physics of the various regions in the $T$ and critical tuning parameter ($t$) plane. The quantum critical point is at $T=0$, $t=0$, and in many cases there is a line of finite temperature transitions at $T = T_c (t)$, $t < 0$ with $T_c (0) = 0$. For the relativistic, $n$-component $\phi^4$ continuum quantum field theory (which describes lattice quantum rotor ($n \geq 2$) and transverse field Ising ($n=1$) models) the upper critical dimension is $d=3$, and for $d<3$, $\epsilon=3-d$ is the control parameter over the entire phase diagram. In the region $|T - T_c (t)| \ll T_c (t)$, we obtain an $\epsilon$ expansion for coupling constants which then are input as arguments of known {\em classical, tricritical,} crossover functions. In the high $T$ region of the continuum theory, an expansion in integer powers of $\sqrt{\epsilon}$, modulo powers of $\ln \epsilon$, holds for all thermodynamic observables, static correlators, and dynamic properties at all Matsubara frequencies; for the imaginary part of correlators at real frequencies ($\omega$), the perturbative $\sqrt{\epsilon}$ expansion describes quantum relaxation at $\hbar \omega \sim k_B T$ or larger, but fails for $\hbar \omega \sim \sqrt{\epsilon} k_B T$ or smaller. An important principle, underlying the whole calculation, is the analyticity of all observables as functions of $t$ at $t=0$, for $T>0$; indeed, analytic continuation in $t$ is used to obtain results in a portion of the phase diagram. Our method also applies to a large class of other quantum critical points and their associated continuum quantum field theories.Comment: 36 pages, 4 eps figure

Quantum field theory of metallic spin glasses

We introduce an effective field theory for the vicinity of a zero temperature quantum transition between a metallic spin glass (``spin density glass'') and a metallic quantum paramagnet. Following a mean field analysis, we perform a perturbative renormalization-group study and find that the critical properties are dominated by static disorder-induced fluctuations, and that dynamic quantum-mechanical effects are dangerously irrelevant. A Gaussian fixed point is stable for a finite range of couplings for spatial dimensionality $d > 8$, but disorder effects always lead to runaway flows to strong coupling for $d \leq 8$. Scaling hypotheses for a {\em static\/} strong-coupling critical field theory are proposed. The non-linear susceptibility has an anomalously weak singularity at such a critical point. Although motivated by a perturbative study of metallic spin glasses, the scaling hypotheses are more general, and could apply to other quantum spin glass to paramagnet transitions.Comment: 16 pages, REVTEX 3.0, 2 postscript figures; version contains reference to related work in cond-mat/950412

The PIN domain endonuclease Utp24 cleaves pre-ribosomal RNA at two coupled sites in yeast and humans

During ribosomal RNA (rRNA) maturation, cleavages at defined sites separate the mature rRNAs from spacer regions, but the identities of several enzymes required for 18S rRNA release remain unknown. PilT N-terminus (PIN) domain proteins are frequently endonucleases and the PIN domain protein Utp24 is essential for early cleavages at three pre-rRNA sites in yeast (A0, A1 and A2) and humans (A0, 1 and 2a). In yeast, A1 is cleaved prior to A2 and both cleavages require base-pairing by the U3 snoRNA to the central pseudoknot elements of the 18S rRNA. We found that yeast Utp24 UV-crosslinked in vivo to U3 and the pseudoknot, placing Utp24 close to cleavage at site A1. Yeast and human Utp24 proteins exhibited in vitro endonuclease activity on an RNA substrate containing yeast site A2. Moreover, an intact PIN domain in human UTP24 was required for accurate cleavages at sites 1 and 2a in vivo, whereas mutation of another potential site 2a endonuclease, RCL1, did not affect 18S production. We propose that Utp24 cleaves sites A1/1 and A2/2a in yeast and human cells

Fractal chemical kinetics: Reacting random walkers

Computer simulations on binary reactions of random walkers ( A + A → A ) on fractal spaces bear out a recent conjecture: ( ρ −1 − ρ 0 −1 ) ∞ t f , where ρ is the instantaneous walker density and ρ 0 the initial one, and f = d s /2, where d s is the spectral dimension. For the Sierpinski gaskets: d =2, 2 f =1.38 ( d s =1.365); d =3, 2 f =1.56 ( d s =1.547); biased initial random distributions are compared to unbiased ones. For site percolation: d = 2, p =0.60, 2 f = 1.35 ( d s =1.35); d=3, p =0.32, 2 f =1.37 ( d s =1.4); fractal-to-Euclidean crossovers are also observed. For energetically disordered lattices, the effective 2 f (from reacting walkers) and d s (from single walkers) are in good agreement, in both two and three dimensions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45149/1/10955_2005_Article_BF01012924.pd

Synthesis, Spectroscopic Investigations, and Molecular-structures of 1-phenyl-1-chalcogeno-4-methyl-4-chloro-1-lambda(5),4-phosphastanninanes, Me(cl)sn(ch2-ch2)2p(e)ph(e = O,S,Se)

A series of 1-phenyl-1-chalcogeno-4-methyl-4-chloro-1lambda5,4-phosphastanninanes Me(Cl)Sn(CH2-CH2)2P(E)Ph with E = S, Se, O (7-9) has been synthesized by chlorodemetalation of the related tetraorganotin derivatives Me2Sn(CH2-CH2)2P(E)Ph (1-3) with Me2SnCl2. Sn-119, P-31, and H-1 NMR studies in nonpolar solvents show that 7-9 exhibit a P=E...Sn coordination which is intramolecular for 7 and 8 (E = S, Se) and intermolecular for 9 (E = O). In donor solvents the intramolecular interaction of 7 and 8 is no longer present. The molecular structures of 7-9 were determined by X-ray analysis. The structure determination of 7 gave the monoclinic space group P2(1)/c (a = 12.256(15), b = 9.293(6), c = 12.622(13) angstrom; beta = 96.64(10)degrees; V = 1427.9(25) angstrom3; Z = 4; R = 0.040). 8 crystallizes in the orthorhombic space group Pccn (a = 22.703(3), b = 16.910(22), c = 7.523(4) angstrom; V = 2888.1(51) angstrom3; Z = 8; R = 0.053). 9 has the triclinic space group P1 (a = 7.606(3), b = 10.179(2), c = 9.883(2) angstrom; alpha = 117.97(2), beta = 96.58(3), gamma = 87.80(3)degrees; V = 671.2(3) angstrom3; Z = 2; R = 0.0395). In the solid state 7-9 also exhibit pentacoordination at the tin with the ligand polyhedron approaching an ideal trigonal bipyramid in the order 7 < 8 < 9. 9 exists as dimers with intermolecular P=O...Sn contacts and a chair conformation for the 1lambda5,4-phosphastanninane ring system, whereas 7 and 8 are monomeric with intramolecular P=E...Sn coordination and a boat conformation of the six-membered ring