Dynamical Monte Carlo investigation of spin reversals and nonequilibrium magnetization of single-molecule magnets

In this paper, we combine thermal effects with Landau-Zener (LZ) quantum tunneling effects in a dynamical Monte Carlo (DMC) framework to produce satisfactory magnetization curves of single-molecule magnet (SMM) systems. We use the giant spin approximation for SMM spins and consider regular lattices of SMMs with magnetic dipolar interactions (MDI). We calculate spin reversal probabilities from thermal-activated barrier hurdling, direct LZ tunneling, and thermal-assisted LZ tunnelings in the presence of sweeping magnetic fields. We do systematical DMC simulations for Mn$_{12}$ systems with various temperatures and sweeping rates. Our simulations produce clear step structures in low-temperature magnetization curves, and our results show that the thermally activated barrier hurdling becomes dominating at high temperature near 3K and the thermal-assisted tunnelings play important roles at intermediate temperature. These are consistent with corresponding experimental results on good Mn$_{12}$ samples (with less disorders) in the presence of little misalignments between the easy axis and applied magnetic fields, and therefore our magnetization curves are satisfactory. Furthermore, our DMC results show that the MDI, with the thermal effects, have important effects on the LZ tunneling processes, but both the MDI and the LZ tunneling give place to the thermal-activated barrier hurdling effect in determining the magnetization curves when the temperature is near 3K. This DMC approach can be applicable to other SMM systems, and could be used to study other properties of SMM systems.Comment: Phys Rev B, accepted; 10 pages, 6 figure

Determination of the X(3872) Meson Quantum Numbers

The Large Hadron Collider beauty (LHCb) is one of the several experiments located at the ring of the Large Hadron Collider (LHC) in Geneva. The LHCb detector is a single arm forward spectrometer and is designed to perform high precision measurements of Charge Parity (CP) violation parameters and rare decays of the beauty and charm hadrons. The detector was successfully operated at a center-of-mass energy of 7 TeV in 2010 and 2011 and at 8 TeV in 2012. Over 3 fb-1 of data has been collected by the LHCb. The LHCb experiment is also well suited for studies on hadron spectroscopy. Besides the well established mesons consisting of quark-antiquark pairs (qq-bar), it has been proposed that exotic qqq-barq-bar mesons could exist. One of the candidates for a four-quark state is the charmonium-like state X(3872) which was first observed by the Belle experiment in 2003. This narrow state has a mass of about 3872 MeV which is located in a region of excited charmonium states (cc-bar). However its mass does not match to any theoretically predicted charmonium state. In order to investigate the nature of this anomalous state, we analyze its quantum number which is the key for its interpretation. The X(3872) events are reconstructed from B+-\u3eX(3872)K+, where X(3872)-\u3epi+ pi- J/psi , J/psi-\u3emu+mu-; based on 1 fb-1 of 2011 data collected by LHCb detector. We implement a method which is guaranteed by statistics to be the most powerful way to discriminate between spin hypotheses; namely unbinned likelihood ratio test using full angular phase-space. The 5-dimensional analysis shows that 1++ hypothesis is preferred with overwhelming significance. The only alternative assignment allowed by the previous measurements, JPC = 2-+, is rejected with a confidence level equivalent to more than eight Gaussian standard deviations. This result favors exotic explanations of the X(3872) state, such as a mesonic molecule or a tetraquark

Convergence of Sewing Conformal Blocks

In recent work, Damiolini-Gibney-Tarasca showed that for a $C_2$-cofinite rational CFT-type vertex operator algebra $\mathbb V$, sheaves of conformal blocks are locally free and satisfy the factorization property. In this article, we use analytic methods to prove that sewing conformal blocks is convergent, solving a conjecture proposed by Zhu and Huang.Comment: 62 pages, reference added. The assumptions of CFT-type and rationality are completely removed in the main results. Logarithmic modules are treated. A new proof is written for multiple sewing (Sec. 13) since the original inductive proof does not apply to logarithmic modules. (Note that our results do not cover the pseudotraces of intertwining operators.