29,192 research outputs found
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
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
Modified Laplace transformation method at finite temperature: application to infra-red problems of N component theory
Modified Laplace transformation method is applied to N component
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
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]
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
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
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
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