Search results for "Hamiltonian"
showing 10 items of 662 documents
Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems
2001
We consider a class of Hamiltonians with three degrees of freedom that can be mapped into quasi-periodically driven pendulums. The purpose of this paper is to determine the threshold of the break-up of invariant tori with a specific frequency vector. We apply two techniques: the frequency map analysis and renormalization-group methods. The renormalization transformation acting on a Hamiltonian is a canonical change of coordinates which is a combination of a partial elimination of the irrelevant modes of the Hamiltonian and a rescaling of phase space around the considered torus. We give numerical evidence that the critical coupling at which the renormalization transformation starts to diverg…
STRUCTURAL INSTABILITY IN FERROELECTRICS: SUPERIMPOSING HAMILTONIAN AND STOCHASTIC DYNAMICS
2008
ABSTRACT Structural instability of ferroelectrics distinguished by appearance of coexisting phases and spatial inhomogeneity is at variance with the predictions of statistics in the canonical ensemble. A more refined description includes ergodicity breaking which become apparent at critical temperature when the system resides in metastable state and its development lead to one of possible minimum energy states. In this study the domain growth and switching is reproduced within the framework of Fokker-Planck approach. The mathematical technique is developed for empiric Landau Hamiltonians and improved for application to first principles effective Hamiltonians with supercells and elementary l…
The chiral anomaly in non-leptonic weak interactions
1992
7 páginas.-- arXiv:hep-ph/9205210v1
New measurements and global analysis of chloromethane in the region from 0 to 1800cm−1
2003
Abstract New high resolution Fourier transform spectra of pure 12CH335Cl and 12CH337Cl isotopomers of chloromethane have been recorded in Wuppertal covering the region from 600 to 3800 cm−1. New rotational transitions within the v2=1, v5=1, and v3=2 states have been measured at Lille. A first global analysis of the lower four band systems of the molecule (700–1800 cm−1) is reported. The model was based on an effective Hamiltonian and dipole moment expressed in terms of irreducible tensor operators. A common set of 125 effective hamiltonian parameters (sixth order) has been adjusted to fit simultaneously some 11 000 IR data for each of the isotopomers including 153 mm wave data for 12 CH3 35…
Stability and Chaos
2010
In this chapter we study a larger class of dynamical systems that include but go beyond Hamiltonian systems. We are interested, on the one hand, in dissipative systems, i.e. systems that lose energy through frictional forces or into which energy is fed from exterior sources, and, on the other hand, in discrete, or discretized, systems such as those generated by studying flows by means of the Poincare mapping. The occurence of dissipation implies that the system is coupled to other, external systems, in a controllable manner. The strength of such couplings appears in the set of solutions, usually in the form of parameters. If these parameters are varied it may happen that the flow undergoes …
Polarization and modal attractors in conservative counterpropagating four-wave interaction
2005
An experimental and theoretical study of the resonant four-wave interaction scheme in the counterpropagating configuration reveals the existence of a novel attraction process in Hamiltonian systems. We show analytically that it is the specificity of the boundary conditions inherent in the counterpropagating configuration that makes attraction dynamics possible in spite of the reversible nature of the four-wave interaction. In the context of optics, this novel dynamical feature could be the basic mechanism of a universal polarizer performing total polarization conversion of unpolarized light with, in principle, 100% efficiency.
Exercises, Hints and Selected Solutions
2016
1.1. Prove the formula (1.8a) in Sect. 1.3, $$\displaystyle{ \int \mathrm{d}^{n}x\; =\int _{ 0}^{+\infty }\!\!\!\mathrm{d}r\;r^{n-1}\int _{ 0}^{2\pi }\!\!\!\mathrm{d}\phi \prod _{ k=1}^{n-2}\int _{ 0}^{\pi }\!\!\!\mathrm{d}\theta _{ k}\sin ^{k}(\theta _{ k}) }$$ (1.1) by means of induction.
Canonical Adiabatic Theory
2001
In the present chapter we are concerned with systems, the change of which—with the exception of a single degree of freedom—should proceed slowly. (Compare the pertinent remarks about \(\varepsilon\) as slow parameter in Chap. 7) Accordingly, the Hamiltonian reads: $$\displaystyle{ H = H_{0}{\bigl (J,\varepsilon p_{i},\varepsilon q_{i};\varepsilon t\bigr )} +\varepsilon H_{1}{\bigl (J,\theta,\varepsilon p_{i},\varepsilon q_{i};\varepsilon t\bigr )}\;. }$$ (12.1) Here, \((J,\theta )\) designates the “fast” action-angle variables for the unperturbed, solved problem \(H_{0}(\varepsilon = 0),\) and the (p i , q i ) represent the remaining “slow” canonical variables, which do not necessarily have…
Perturbative treatment of spin-orbit coupling within spin-free exact two-component theory.
2014
This work deals with the perturbative treatment of spin-orbit-coupling (SOC) effects within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e). We investigate two schemes for constructing the SFX2C-1e SOC matrix: the SFX2C-1e+SOC [der] scheme defines the SOC matrix elements based on SFX2C-1e analytic-derivative theory, hereby treating the SOC integrals as the perturbation; the SFX2C-1e+SOC [fd] scheme takes the difference between the X2C-1e and SFX2C-1e Hamiltonian matrices as the SOC perturbation. Furthermore, a mean-field approach in the SFX2C-1e framework is formulated and implemented to efficiently include two-electron SOC effects. Systematic approximations …
Spectroscopy of XY2Z2 (C2v) Molecules: A Tensorial Formalism Adapted to the O(3)⊃Td⊃C2v Chain. Application to the Ground State of SO2F2
2002
Abstract A tensorial formalism adapted to the case of quasi-spherical XY 2 Z 2 asymmetric tops such as SO 2 F 2 has been developed as an extension of the usual one for the tetrahedral molecules. We use the O (3)⊃ T d ⊃ C 2 v group chain. All the coupling coefficients and formulas for the computation of matrix elements are given for this chain. Such relations are then deduced in the C 2 v group itself. We also present a development of the Hamiltonian, dipole moment, and polarizability operators for the molecules under consideration using this formalism. These operators are involved in the calculation of the energies and intensities of rovibrational transitions and are essential for spectrum …