Search results for "Hamiltonian"
showing 10 items of 662 documents
Optical pulling and pushing forces in bilayer PT-symmetric structures
2018
Photons are massless, yet can exert force on small particles. This $r\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n$ $p\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}e$, though discussed by Kepler, still needs investigation for modern systems. This study reveals that the optical force exerted on a parity-time-symmetric bilayer with balanced gain and loss can be $a\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}y\phantom{\rule{0}{0…
The bi-Hamiltonian theory of the Harry Dym equation
2002
We describe how the Harry Dym equation fits into the the bi-Hamiltonian formalism for the Korteweg-de Vries equation and other soliton equations. This is achieved using a certain Poisson pencil constructed from two compatible Poisson structures. We obtain an analogue of the Kadomtsev-Petviashivili hierarchy whose reduction leads to the Harry Dym hierarchy. We call such a system the HD-KP hierarchy. We then construct an infinite system of ordinary differential equations (in infinitely many variables) that is equivalent to the HD-KP hierarchy. Its role is analogous to the role of the Central System in the Kadomtsev-Petviashivili hierarchy.
Equation-of-motion coupled-cluster methods for atoms and molecules in strong magnetic fields.
2017
A program for the direct calculation of excitation energies of atoms and molecules in strong magnetic fields is presented. The implementation includes the equation-of-motion coupled-cluster singles-doubles (EOM-CCSD) method for electronically excited states as well as its spin-flip variant. Differences to regular EOM-CCSD implementations are due to the appearance of the canonical angular-momentum operator in the Hamiltonian causing the wave function to become complex. The gauge-origin problem is treated by the use of gauge-including atomic orbitals. Therefore, a modified Davidson method for diagonalizing complex non-Hermitian matrices is used. Excitation energies for selected atoms and mole…
Jet-cooled FTIR spectroscopy and analysis of the C–O stretch fundamental of Ni(CO)4
2008
Rovibrational spectra of the C–O stretch band (ν5) of Ni(CO)4 have been recorded at 0.006 cm− 1 resolution by coupling a low pressure continuous supersonic jet with a high resolution interferometer. The spectrum has been analysed thanks to the STDS software (see http://icb.u-bourgogne.fr/OMR/SMA/SHTDS/) that implements the tensorial formalism developed in the Dijon group for tetrahedral molecules. We obtain a very satisfying simulation thanks to an effective Hamiltonian expanded up to order 3. The asymmetry of the high-J lines is due to a small tetrahedral splitting and is well reproduced. The root mean square deviation is 0.96 × 10− 3 cm− 1. The Coriolis constant is somewhat larger than fo…
Tensorial Development of the Rovibronic Hamiltonian and Dipole Moment Operators for XY3Z Molecules with a Degenerate Electronic State. Preliminary Ap…
2009
Abstract We present a development of the Hamiltonian and transition moment operators of XY3Z ( C 3 v ) symmetric tops molecules in a degenerate electronic state with the aid of a tensorial formalism developed in a recent paper [A. El Hilali, V. Boudon, M. Loete, J. Mol. Spectrosc. 239 (2006) 41–50]. Electronic operators are defined from group theory properties. They provide a new approach to build an effective rovibronic Hamiltonian as well as an effective dipole moment operator for rovibronic transition of XY3Z molecules. This model is studied qualitatively thanks to the tensorial algebra properties. Expressions of the matrix elements are derived for these operators. A first simple applica…
Electronic structure of Rf+ (Z=104) from ab initio calculations
2021
We report calculation of the energy spectrum and the spectroscopic properties of the superheavy element ion: ${\mathrm{Rf}}^{+}$. We use the four-component relativistic Dirac-Coulomb Hamiltonian and the multireference configuration interaction model to tackle the complex electronic structure problem that combines strong relativistic effects and electron correlation. We determine the energies of the ground and the low-lying excited states of ${\mathrm{Rf}}^{+}$, which originate from the $7{s}^{2}6{d}^{1},\phantom{\rule{0.28em}{0ex}}7{s}^{1}6{d}^{2},\phantom{\rule{0.28em}{0ex}}7{s}^{2}7{p}^{1}$, and $7{s}^{1}6{d}^{1}7{p}^{1}$ configurations. The results are discussed vis-\`a-vis the lighter h…
When does Wenzel's extension of Young's equation for the contact angle of droplets apply? A density functional study.
2020
he contact angle of a liquid droplet on a surface under partial wetting conditions differs for a nanoscopically rough or periodically corrugated surface from its value for a perfectly flat surface. Wenzel's relation attributes this difference simply to the geometric magnification of the surface area (by a factor $r_{\rm w}$), but the validity of this idea is controversial. We elucidate this problem by model calculations for a sinusoidal corrugation of the form $z_{\rm wall}(y) = \Delta\cos(2\pi y/\lambda)$ , for a potential of short range $\sigma_{\rm w}$ acting from the wall on the fluid particles. When the vapor phase is an ideal gas, the change of the wall-vapor surface tension can be co…
Breakdown of the Reduction of the Rovibrational Hamiltonian: The Case of S18O2F2
2009
Abstract The ground state rotational spectrum of the near-spherical top molecule S18O2F2 (sulfuryl fluoride) has been measured from 50 to 700 GHz. As for the parent isotopologue, S16O2F2 [K. Sarka, J. Demaison, L. Margules, I. Merke, N. Heineking, H. Burger, H. Ruland, J. Mol. Spectrosc. 200 (2000) 55–64], it was necessary to use a non-reduced Hamiltonian in order to obtain a satisfactory fit. It was possible to determine six quartic centrifugal distortion constants (instead of five for a standard asymmetric top) and five sextic constants (one of them not existing in the reduced Hamiltonian) could also be determined. This ground state level has also been analysed thanks to a tensorial forma…
Cost-Effective Treatment of Scalar Relativistic Effects for Multireference Systems: A CASSCF Implementation Based on the Spin-free Dirac-Coulomb Hami…
2016
We present an implementation of the complete active space-self-consistent field (CASSCF) method specifically designed to be used in four-component scalar relativistic calculations based on the spin-free Dirac-Coulomb (SFDC) Hamiltonian. Our implementation takes full advantage of the properties of the SFDC Hamiltonian that allow us to use real algebra and to exploit point-group and spin symmetry to their full extent while including in a rigorous way scalar relativistic effects in the treatment. The SFDC-CASSCF treatment is more expensive than its non-relativistic counterpart only in the orbital optimization step, while exhibiting the same computational cost for the rate-determining full conf…
Rovibrational Interactions in the Local-Mode Limit: The (n000) Stretching Overtone Bands of Spherical Tops
1995
Abstract We present a tensorial formalism adapted to the study of the ( n 000) rovibrational stretching states of spherical tops in the local mode limit. A local symmetrized rovibrational basis is built to take explicitly into account the fact that, in these states, the local symmetry is C 3ν rather than T d . Likewise, we introduce local rovibrational operators to build an effective Hamiltonian for these states. We then test our model by fitting the energy levels of 28 SiH 4 for 3 ≤ n ≤ 5.