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In this paper, an energy-preserving difference scheme is proposed for solving the space fractional Klein-Gordon equation based on the Hamiltonian form of the equation. First, we study some properties of the fractional Laplacian operator and reformulate the equation as an infinite-dimension canonical Hamiltonian system. Then, we use the fractional centered difference formula to discrete the equation and derive a semi-discrete Hamiltonian system that can conserve the semi-discrete energy. Subsequently, a fully-discrete scheme is obtained by applying the averaged vector field method to the semi-discrete system. The resulting scheme's unconditional point-wise error estimate is discussed by using the "cut-off" technique. Furthermore, a fast solver is presented to reduce the computational complexity of the scheme based on the fast Fourier transformation technique in practical computation. Finally, some numerical experiments are displayed to demonstrate the efficiency and conservation of the constructed scheme in long time simulation. • We reformulate the fractional Klein-Gordon equation as a canonical Hamiltonian system. • We explore an energy-preserving scheme based on the AVF method to solve the fractional Klein-Gordon equation. • Without any restriction on the grid ratio, the proposed scheme is convergent with order O (h 2 + τ 2) in L ∞ -norm. • A fast algorithm is used to reduce the computational complexity in practical computation. [ABSTRACT FROM AUTHOR]

The generator coordinatemethod in the Gaussian overlap approximation (GOA) is applied to a description of the nuclear quadrupole collective states. The full five-dimensional quadrupole tensor is used as a set of the generator coordinates. The integral Hill-Wheeler equation is reduced to a differential equation by using the Fourier transforms of the overlap and energy kernels. The differential Bohr Hamiltonian obtained this way is compared with that derived by the usual approach to the collective Hamiltonian in the GOA which does contain an additional approximation. The method of calculating the quantities which determine the Bohr Hamiltonian from the set of deformation-dependent intrinsic states is demonstrated. In particular, it appears that the moments of inertia at the quadrupole rotations are of the Yoccoz type. [ABSTRACT FROM AUTHOR]

Abstract: Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of the phase-space: no linear structure is necessary. It is shown that the “fractional Fourier transform” provides a simple example of this construction. As an application of this technique we show that for any linear Hamiltonian system, its quantum dynamics can be obtained exactly as the lift of the corresponding classical dynamics by means of the above transformation. Moreover, it can be deduced from the free quantum evolution. This way new, unknown symmetries of the Schrödinger equation can be constructed. It is also argued that the above construction defines in a natural way a connection in the bundle of quantum states, with the base space describing all their possible representations. The non-flatness of this connection would be responsible for the non-existence of a quantum representation of the complete algebra of classical observables. [Copyright &y& Elsevier]

These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The BV--formalism is introduced through an odd Fourier transform and the algebraic aspects of integration theory are stressed. As a main application we consider the perturbation theory for certain finite dimensional integrals within BV-formalism. As an illustration we present a proof of the isomorphism between the graph complex and the Chevalley-Eilenberg complex of formal Hamiltonian vectors fields. We briefly discuss how these ideas can be extended to the infinite dimensional setting. These notes should be accessible to both physicists and mathematicians. [ABSTRACT FROM AUTHOR]

Abstract: The Fourier-transform absorption spectrum of -enriched nitrous oxide has been recorded at the Doppler limited resolution in the spectral range 3500–9000cm−1. 6523 Transitions of were observed and assigned based on the global effective Hamiltonian model. The band-by-band analysis led to the determination of the ro-vibrational parameters of a total of 65 bands. Among these bands, 39 are newly observed, and the rotational analysis of 26 others were significantly extended and improved. [Copyright &y& Elsevier]

Abstract: The rotational spectra of three isotopomers of the Ar–dimethyl sulfide (DMS) complex – normal, 34S, and 13C species – were measured in the frequency region from 3.7 up to 24.1GHz by Fourier transform microwave spectroscopy. The normal species yielded 43 a-type and 79 c-type transitions. No Ar tunneling splitting was observed, while many transitions were split by the internal rotation of the two methyl tops of the DMS unit. In cases where the K-type splitting was close to that due to methyl internal-rotation, several forbidden transitions were observed that followed b-type selection rules. All of the observed transition frequencies were analyzed simultaneously using a phenomenological Hamiltonian also used in previously published work describing the Ar–dimethyl ether (DME) and Ne–DME complexes. The rotational and centrifugal distortion constants and the potential barrier height to methyl-top internal rotation, V 3, were determined. The rotational constants were consistent with an Ar–DMS center of mass (cm) distance of 3.796 (3)Å and a S–cm–Ar angle of 104.8 (2)°. The V 3 potential barrier obtained, 736.17 (32)cm−1, was 97.8% of the DMS monomer barrier. By assuming a Lennard–Jones-type potential, the dissociation energy was estimated to be 2.4kJ mol−1, which was close to the value for Ar–DME, 2.5kJmol−1. [Copyright &y& Elsevier]

Abstract: The adiabatic separation of large-amplitude torsional motion from small-amplitude vibrations is applied as an aid in interpreting the results of fully coupled quantum calculations on a model methanol Hamiltonian. Comparison is made with prior work on nitromethane [D. Cavagnat, L. Lespade, J. Chem. Phys. 106 (1997) 7946]. Even though the torsional potentials are very different, both molecules show a transition from adiabatic to diabatic behavior when the CH stretch is excited to νCH =4 or higher. In the adiabatic approximation, the effective torsional potentials for the various CH stretch vibrational states do not cross, but the CH vibrational amplitude moves from one bond to the next as a function of torsional angle. In the diabatic approximation, the effective torsional potentials do cross, but the distribution of the CH vibrational amplitude remains approximately constant in the vicinity of the crossing. The transition to diabatic behavior is promoted by the normal mode to local mode transition, and the relevant adiabatic and diabatic effective torsional potentials are determined by the torsion–vibration coupling. The torsion–vibration couplings in the four overtone manifolds considered (methanol OH, CH, nitromethane CH, and hydrogen peroxide OH) are large, reaching 265–500cm−1 by νXH =6, and are of generally similar magnitude. The largest torsion–vibration couplings involve the first Fourier term in the torsional angle (cosγ for the CH stretch in methanol and the OH stretch in HOOH), whereas higher Fourier terms (cos2γ in nitromethane and cos3γ for the OH stretch of methanol) result in somewhat weaker coupling. Nonadiabatic matrix elements in methanol couple the torsional and vibrational energies and they exhibit a slow fall-off with coupling order. [Copyright &y& Elsevier]

Abstract: Stimulated by recent THz measurements of the methanol spectrum in one of our laboratories, undertaken in support of NASA programs related to the Herschel Space Observatory (HSO) and the Atacama Large Millimeter Array (ALMA), we have carried out a global analysis of available microwave and high-resolution infrared data for the first three torsional states (ν t =0, 1, 2), and for J values up to 30. This global fit of approximately 5600 frequency measurements and 19000 Fourier transform far infrared (FTFIR) wavenumber measurements to 119 parameters reaches the estimated experimental measurement accuracy for the FTFIR transitions, and about twice the estimated experimental measurement accuracy for the microwave, submillimeter-wave, and terahertz transitions. The present fit is essentially a continuation of our earlier work, but we have greatly expanded our previous data set and have added a large number of new torsion–rotation interaction terms to the Hamiltonian in our previously used computer program. The results, together with a number of calculated (but unmeasured) transitions, including their line strength, estimated uncertainty, and lower state energy, are made available in the supplementary material as a database formatted to be useful for astronomical searches. Some discussion of several open spectroscopic problems, e.g., (i) an improved notation for the numerous parameters in the torsion–rotation Hamiltonian, (ii) possible causes of the failure to fit frequency measurements to the estimated measurement uncertainty, and (iii) pitfalls to be avoided when intercomparing apparently identical parameters from the internal axis method and the rho axis method are also given. [Copyright &y& Elsevier]

High-resolution Fourier transform and sub-millimetre torsion-rotation spectra of D[sub 2] O[sub 2] have been recorded between 20 and 1200 cm[sup –1] . Spectra involving the torsional levels (n,τ) = (0,1), (0,3), (1,1), (1,3), (2,1), (2,3), and (3,1) have been observed and assigned.The Hamiltonian that has been used with success in the analysis of H[sub 2] O[sub 2] surprisingly proved to be inadequate for D[sub 2] O[sub 2] because the smaller torsional spacings give rise to some near resonances with |Δ K[sub a] | = 3 that do not occur in H[sub 2] O[sub 2] . Once this extra interaction was included the spectra have been fitted fairly well. The observed levels are too far below the cis-torsional barrier for the staggering of the even and odd K values to be observed. PACS Nos.: 3310, 3320B, 3320E, 3520J, 3520PLe spectre de torsion-rotation de D[sub 2] O[sub 2] a été enregistré entre 20 et 1200 cm[sup –1] par spectroscopie de Fourier à haute résolution et par techniques sub-millimétriques. L'analyse de ces spectres a été menée à bien permettant d'attribuer les niveaux de torsion (n,τ) = (0,1), (0,3), (1,1), (1,3), (2,1), (2,3) et (3,1). Le modéle d'Hamiltonian qui avait été utilisé avec succés pour reproduire les niveaux d'énergie de H[sub 2] O[sub 2] s'est révélé de façon surprenante inadéquat dans le cas de D[sub 2] O[sub 2] du fait d'espacements torsionnels plus faibles pour cette dernière molécule: en fait pour D[sub 2] O[sub 2] sont observées des résonances en (|Δ K[sub a] | = 3) qui n'existent pas dans le cas de H[sub 2] O[sub 2] . L'introduction dans l'Hamiltonien des termes prenant en compte ces interactions a permis de reproduire les spectres observés de façon tout a fait satisfaisante. Enfin il faut noter que les niveaux observés sont situés a des energies trop faibles par rapport à celle de la barrière de torsion cis pour que le deplacement des niveaux pairs et impairs en K, du a cette barrière, soit observé. [ABSTRACT FROM AUTHOR]

A general analytical theory of temporal relaxation processes in isolated quantum systems with many degrees of freedom is elaborated, which unifies and substantially amends several previous approximations. Specifically, the Fourier transform of the initial energy distribution is found to play a key role, which is furthermore equivalent to the so-called survival probability in case of a pure initial state. The main prerequisite is the absence of any notable transport currents, caused for instance by some initially unbalanced local densities of particles, energy, and so on. In particular, such a transportless relaxation scenario naturally arises when both the system Hamiltonian and the initial non-equilibrium state do not exhibit any spatial inhomogeneities on macroscopic scales. A further requirement is that the relaxation must not be notably influenced by any approximate (but not exact) constant of motion or metastable state. The theoretical predictions are compared with various experimental and numerical results from the literature. [ABSTRACT FROM AUTHOR]