2,316 research outputs found
Information Geometry, Inference Methods and Chaotic Energy Levels Statistics
In this Letter, we propose a novel information-geometric characterization of
chaotic (integrable) energy level statistics of a quantum antiferromagnetic
Ising spin chain in a tilted (transverse) external magnetic field. Finally, we
conjecture our results might find some potential physical applications in
quantum energy level statistics.Comment: 9 pages, added correct journal referenc
From Lagrangian to Quantum Mechanics with Symmetries
We present an old and regretfully forgotten method by Jacobi which allows one
to find many Lagrangians of simple classical models and also of nonconservative
systems. We underline that the knowledge of Lie symmetries generates Jacobi
last multipliers and each of the latter yields a Lagrangian. Then it is shown
that Noether's theorem can identify among those Lagrangians the physical
Lagrangian(s) that will successfully lead to quantization. The preservation of
the Noether symmetries as Lie symmetries of the corresponding Schr\"odinger
equation is the key that takes classical mechanics into quantum mechanics.
Some examples are presented.Comment: To appear in: Proceedings of Symmetries in Science XV, Journal of
Physics: Conference Series, (2012
Elliptic Phases: A Study of the Nonlinear Elasticity of Twist-Grain Boundaries
We develop an explicit and tractable representation of a twist-grain-boundary
phase of a smectic A liquid crystal. This allows us to calculate the
interaction energy between grain boundaries and the relative contributions from
the bending and compression deformations. We discuss the special stability of
the 90 degree grain boundaries and discuss the relation of this structure to
the Schwarz D surface.Comment: 4 pages, 2 figure
On a generalization of Jacobi's elliptic functions and the Double Sine-Gordon kink chain
A generalization of Jacobi's elliptic functions is introduced as inversions
of hyperelliptic integrals. We discuss the special properties of these
functions, present addition theorems and give a list of indefinite integrals.
As a physical application we show that periodic kink solutions (kink chains) of
the double sine-Gordon model can be described in a canonical form in terms of
generalized Jacobi functions.Comment: 18 pages, 9 figures, 3 table
Modular Solutions to Equations of Generalized Halphen Type
Solutions to a class of differential systems that generalize the Halphen
system are determined in terms of automorphic functions whose groups are
commensurable with the modular group. These functions all uniformize Riemann
surfaces of genus zero and have --series with integral coefficients.
Rational maps relating these functions are derived, implying subgroup relations
between their automorphism groups, as well as symmetrization maps relating the
associated differential systems.Comment: PlainTeX 36gs. (Formula for Hecke operator corrected.
The oxidation of CO on RuO<sub>2</sub>(110) at room temperature
RuO2(110) surfaces were prepared by exposing Ru(0001) to 10(7) L of O-2 at 700 K. Postexposure of O-2 at 300 K resulted in an additional oxygen species (O-cus) adsorbed on coordinatively unsaturated Ru atoms (Ru-cus). The surface was then exposed to CO at 300 K and studied by thermal desorption spectroscopy (TDS) and high-resolution electron energy loss spectroscopy (HREELS). It is demonstrated that CO is oxidized at 300 K through reaction with both the O-cus as well as with surface O-atoms held in bridge positions (O-bridge). Although-at room temperature-CO adsorbs intermediately on the Ru-cus atoms, it is stable only at the Ru atoms underneath the O-bridge after the latter has been reacted off. At room temperature only surface oxygen takes part in the CO oxidation and the oxygen-depleted surface can be restored by O-2 exposure, so that under steady-state flow conditions an oxygen-deficient surface will exist whose stoichiometry will be determined by the ratio of partial pressures
Little groups of irreps of O(3), SO(3), and the infinite axial subgroups
Little groups are enumerated for the irreps and their components in any basis
of O(3) and SO(3) up to rank 9, and for all irreps of C, C, C, D and D. The results are obtained
by a new chain criterion, which distinguishes massive (rotationally
inequivalent) irrep basis functions and allows for multiple branching paths,
and are verified by inspection. These results are relevant to the determination
of the symmetry of a material from its linear and nonlinear optical properties
and to the choices of order parameters for symmetry breaking in liquid
crystals.Comment: 28 pages and 3 figure
Efficient algorithms for rigid body integration using optimized splitting methods and exact free rotational motion
Hamiltonian splitting methods are an established technique to derive stable
and accurate integration schemes in molecular dynamics, in which additional
accuracy can be gained using force gradients. For rigid bodies, a tradition
exists in the literature to further split up the kinetic part of the
Hamiltonian, which lowers the accuracy. The goal of this note is to comment on
the best combination of optimized splitting and gradient methods that avoids
splitting the kinetic energy. These schemes are generally applicable, but the
optimal scheme depends on the desired level of accuracy. For simulations of
liquid water it is found that the velocity Verlet scheme is only optimal for
crude simulations with accuracies larger than 1.5%, while surprisingly a
modified Verlet scheme (HOA) is optimal up to accuracies of 0.4% and a fourth
order gradient scheme (GIER4) is optimal for even higher accuracies.Comment: 2 pages, 1 figure. Added clarifying comments. Accepted for
publication in the Journal of Chemical Physic
General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions
In a recent paper we presented analytic expressions for the axis potential,
the disk metric, and the surface mass density of the global solution to
Einstein's field equations describing a rigidly rotating disk of dust. Here we
add the complete solution in terms of ultraelliptic functions and quadratures.Comment: 5 pages, published in 1995 [Phys. Rev. Lett. 75 (1995) 3046
Sur les nombres premiers complexes que l'on dit considérer dans la théorie des résidus de cinquième, huitième et douzième puissance
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