Parallel axis theorem for free-space electron wavefunctions

We consider the orbital angular momentum of a free electron vortex moving in a uniform magnetic field. We identify three contributions to this angular momentum: the canonical orbital angular momentum associated with the vortex, the angular momentum of the cyclotron orbit of the wavefunction, and a diamagnetic angular momentum. The cyclotron and diamagnetic angular momenta are found to be separable according to the parallel axis theorem. This means that rotations can occur with respect to two or more axes simultaneously, which can be observed with superpositions of vortex states

Dimethyl 2,2'-di-nitro-biphenyl-4,4'-di-carboxyl-ate.

The title compound, C16H12N2O8, exhibits two near-planar aromatic ester groups with ar-yl-ester dihedral angles of 2.1 (2) and 4.2 (3)°. The dihedral angle between the aromatic rings is 58.0 (1)°. The two nitro groups are tilted slightly from the plane of the aromatic rings, making dihedral angles of 14.1 (1) and 8.2 (2)°. In the crystal, mol-ecules are connected by weak C-H⋯O inter-actions, forming a three-dimensional network

Uranium(III) coordination chemistry and oxidation in a flexible small-cavity macrocycle

U(III) complexes of the conformationally flexible, small-cavity macrocycle trans-calix[2]benzene[2]pyrrolide (L)2–, [U(L)X] (X = O-2,6-tBu2C6H3, N(SiMe3)2), have been synthesized from [U(L)BH4] and structurally characterized. These complexes show binding of the U(III) center in the bis(arene) pocket of the macrocycle, which flexes to accommodate the increase in the steric bulk of X, resulting in long U–X bonds to the ancillary ligands. Oxidation to the cationic U(IV) complex [U(L)X][B(C6F5)4] (X = BH4) results in ligand rearrangement to bind the smaller, harder cation in the bis(pyrrolide) pocket, in a conformation that has not been previously observed for (L)2–, with X located between the two ligand arene rings

Modified Laplace transformation method at finite temperature: application to infra-red problems of N component ϕ4\phi^4 theory

Modified Laplace transformation method is applied to N component $\phi^4$ theory and the finite temperature problem in the massless limit is re-examined in the large N limit. We perform perturbation expansion of the dressed thermal mass in the massive case to several orders and try the massless approximation with the help of modified Laplace transformation. The contribution with fractional power of the coupling constant is recovered from the truncated massive series. The use of inverse Laplace transformation with respect to the mass square is crucial in evaluating the coefficients of fractional power terms.Comment: 16pages, Latex, typographical errors are correcte

Lie Groups and mechanics: an introduction

The aim of this paper is to present aspects of the use of Lie groups in mechanics. We start with the motion of the rigid body for which the main concepts are extracted. In a second part, we extend the theory for an arbitrary Lie group and in a third section we apply these methods for the diffeomorphism group of the circle with two particular examples: the Burger equation and the Camassa-Holm equation

Chemical Equilibration in Hadronic Collisions

We study chemical equilibration in out-of-equilibrium Quark-Gluon Plasma using the first principles method of QCD effective kinetic theory, accurate at weak coupling. In longitudinally expanding systems--relevant for relativistic nuclear collisions--we find that for realistic couplings chemical equilibration takes place after hydrodynamization, but well before local thermalization. We estimate that hadronic collisions with final state multiplicities ${dN_\text{ch}}/{d\eta}\gtrsim 10^2$ live long enough to reach approximate chemical equilibrium, which is consistent with the saturation of strangeness enhancement observed in proton-proton, proton-nucleus and nucleus-nucleus collisions.Comment: 7 pages, 3 figures, see also our companion paper arXiv:1811.03068, v2 small changes, published versio

Crystal structure of dimethyl 9H-carbazole-2,7-di-carb-oxy-late.

In the title compound, C16H13NO4, the carbazole ring system is almost planar with non-H atoms possessing a mean deviation from planarity of 0.037 Å. The two ester groups are orientated trans to one another and tilted slightly from the mean plane of the carbazole ring system, making dihedral angles of 8.12 (6) and 8.21 (5)°. In the crystal, mol-ecules are linked by pairs of N-H⋯O hydrogen bonds forming inversion dimers. The dimers are linked by parallel slipped π-π inter-actions, forming slabs propagating along the b-axis direction [inter-centroid distance = 3.6042 (8) Å, inter-planar distance = 3.3437 (5) Å, slippage = 1.345 Å]

Stopping distance for high energy jets in weakly-coupled quark-gluon plasmas

We derive a simple formula for the stopping distance for a high-energy quark traveling through a weakly-coupled quark gluon plasma. The result is given to next-to-leading-order in an expansion in inverse logarithms ln(E/T), where T is the temperature of the plasma. We also define a stopping distance for gluons and give a leading-log result. Discussion of stopping distance has a theoretical advantage over discussion of energy loss rates in that stopping distances can be generalized to the case of strong coupling, where one may not speak of individual partons.Comment: 20 pages, 4 figures [change from v1: fixed embarrassing reference error

Is the angular momentum of an electron conserved in a uniform magnetic field?

We show that an electron moving in a uniform magnetic field possesses a time-varying ``diamagnetic'' angular momentum. Surprisingly this means that the kinetic angular momentum of the electron may vary with time, despite the rotational symmetry of the system. This apparent violation of angular momentum conservation is resolved by including the angular momentum of the surrounding fields