Asymptotic Freedom, Dimensional Transmutation, and an Infra-red Conformal Fixed Point for the δ\delta-Function Potential in 1-dimensional Relativistic Quantum Mechanics

We consider the Schr\"odinger equation for a relativistic point particle in an external 1-dimensional $\delta$-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudo-differential operator $H = \sqrt{p^2 + m^2}$. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infra-red conformal fixed point. Thus it can be used to illustrate non-trivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics

Fate of Accidental Symmetries of the Relativistic Hydrogen Atom in a Spherical Cavity

The non-relativistic hydrogen atom enjoys an accidental $SO(4)$ symmetry, that enlarges the rotational $SO(3)$ symmetry, by extending the angular momentum algebra with the Runge-Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson-Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius $R$ with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter $\gamma$, in general the accidental $SO(4)$ symmetry is lifted. However, for $R = (l+1)(l+2) a$ (where $a$ is the Bohr radius and $l$ is the orbital angular momentum) some degeneracy remains when $\gamma = \infty$ or $\gamma = \frac{2}{R}$. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of $R$ and $\gamma$.Comment: 27 pages, 7 figure

Majorana Fermions in a Box

Majorana fermion dynamics may arise at the edge of Kitaev wires or superconductors. Alternatively, it can be engineered by using trapped ions or ultracold atoms in an optical lattice as quantum simulators. This motivates the theoretical study of Majorana fermions confined to a finite volume, whose boundary conditions are characterized by self-adjoint extension parameters. While the boundary conditions for Dirac fermions in $(1+1)$-d are characterized by a 1-parameter family, $\lambda = - \lambda^*$, of self-adjoint extensions, for Majorana fermions $\lambda$ is restricted to $\pm i$. Based on this result, we compute the frequency spectrum of Majorana fermions confined to a 1-d interval. The boundary conditions for Dirac fermions confined to a 3-d region of space are characterized by a 4-parameter family of self-adjoint extensions, which is reduced to two distinct 1-parameter families for Majorana fermions. We also consider the problems related to the quantum mechanical interpretation of the Majorana equation as a single-particle equation. Furthermore, the equation is related to a relativistic Schr\"odinger equation that does not suffer from these problems.Comment: 23 pages, 2 figure

Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians

We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant

Multiple segmental and selective isotope labeling of large RNA for NMR structural studies

Multiple segmental and selective isotope labeling of RNA with three segments has been demonstrated by introducing an RNA segment, selectively labeled with 13C9/15N2/2H(1′, 3′, 4′, 5′, 5′′)-labeled uridine residues, into the central position of the 20 kDa ε-RNA of Duck Hepatitis B Virus. The RNA molecules were produced via two efficient protocols: a two-step protocol, which uses T4 DNA ligase and T4 RNA ligase 1, and a one-pot protocol, which uses T4 RNA ligase 1 alone. With T4 RNA ligase 1 all not-to-be-ligated termini are usually protected to prevent formation of side products. We show that such labor-intensive protection of termini is not required, provided segmentation sites can be chosen such that the segments fold into the target structure or target-like structures and thus are not trapped into stable alternate structures. These sites can be reliably predicted via DINAMelt. The simplified NMR spectrum provided evidence for the presence of a U28 H3-imino resonance, previously obscured in the fully labeled sample, and thus of the non-canonical base pair U28:C37. The demonstrated multiple segmental labeling protocols are generally applicable to large RNA molecules and can be extended to more than three segments

Visualizing spatially correlated dynamics that directs RNA conformational transitions

RNAs fold into three- dimensional ( 3D) structures that subsequently undergo large, functionally important, conformational transitions in response to a variety of cellular signals(1-3). RNA structures are believed to encode spatially tuned flexibility that can direct transitions along specific conformational pathways(4,5). However, this hypothesis has proved difficult to examine directly because atomic movements in complex biomolecules cannot be visualized in 3D by using current experimental methods. Here we report the successful implementation of a strategy using NMR that has allowed us to visualize, with complete 3D rotational sensitivity, the dynamics between two RNA helices that are linked by a functionally important trinucleotide bulge over timescales extending up to milliseconds. The key to our approach is to anchor NMR frames of reference onto each helix and thereby directly measure their dynamics, one relative to the other, using 'relativistic' sets of residual dipolar couplings ( RDCs)(6,7). Using this approach, we uncovered super- large amplitude helix motions that trace out a surprisingly structured and spatially correlated 3D dynamic trajectory. The two helices twist around their individual axes by approximately 536 and 1106 in a highly correlated manner ( R = 0.97) while simultaneously ( R = 0.81 - 0.92) bending by about 94 degrees. Remarkably, the 3D dynamic trajectory is dotted at various positions by seven distinct ligand- bound conformations of the RNA. Thus even partly unstructured RNAs can undergo structured dynamics that directs ligand- induced transitions along specific predefined conformational pathways.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62506/1/nature06389.pd

Chiral Magnetic Effect on the Lattice

We review recent progress on the lattice simulations of the chiral magnetic effect. There are two different approaches to analyze the chiral magnetic effect on the lattice. In one approach, the charge density distribution or the current fluctuation is measured under a topological background of the gluon field. In the other approach, the topological effect is mimicked by the chiral chemical potential, and the induced current is directly measured. Both approaches are now developing toward the exact analysis of the chiral magnetic effect.Comment: to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

Yield of soybean genotypes identified through GGE biplot and path analysis.

Genotype x environment (GxE) interaction is an important source of variation in soybean yield, which can significantly influence selection in breeding programs. This study aimed to select superior soybean genotypes for performance and yield stability, from data from multienvironment trials (METs), through GGE biplot analysis that combines the main effects of the genotype (G) plus the genotype-by-environment (G×E) interaction. As well as, through path analysis, determine the direct and indirect influences of yield components on soybean grain yield, as a genotype selection strategy

Molecular Dynamics and Quantum Mechanics of RNA: Conformational and Chemical Change We Can Believe In

Structure and dynamics are both critical to RNA’s vital functions in biology. Numerous techniques can elucidate the structural dynamics of RNA, but computational approaches based on experimental data arguably hold the promise of providing the most detail. In this Account, we highlight areas wherein molecular dynamics (MD) and quantum mechanical (QM) techniques are applied to RNA, particularly in relation to complementary experimental studies