Spectroscopic interpretation: The high vibrations of CDBrClF

Jung, Christof; Mejía‐Monasterio, Carlos; Taylor, Howard S.

doi:10.1063/1.1644795

Cited by 19 publications

(28 citation statements)

References 17 publications

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“…The symmetrized form is more convenient when considering the semiclassical limit, as will become clear in the next paragraph. Hamiltonians of this kind have been used in molecular physics in order to describe and assign vibrational spectra [13,16]. In the molecular case they describe all kinds of vibrational degrees of freedom like stretches, bends, torsions etc.…”

Section: The Modelmentioning

confidence: 99%

“…Therefore we need a fast and easy method to transfer statements about the reduced system into the corresponding statements about the original system. We have called this procedure the lift in the previous work on molecular systems [14][15][16]. Let us assume a trajectory of the reduced system is given and we want to reconstruct the corresponding trajectory of the original system.…”

Section: Classical Dynamics and Coupling Schemesmentioning

confidence: 99%

“…In this section, we show examples of wave functions belonging to the various classes of motion described in the previous section. Our method of classification has been developed in [13][14][15][16] especially for Hamiltonians given quantum mechanically in raising and lowering operators and classically in action-angle variables. An analysis in a similar spirit of wave functions in the usual position space is rather common in molecular physics, two representative examples are [29,30].…”

Section: Classification Of Semiclassical Wave Functionsmentioning

confidence: 99%

“…In this paper we present a semiclassical technique to analyze the spectral properties of a Bose-Einstein condensate. This method has already been used to describe the vibrational spectra of molecules [13][14][15][16] and provides an intuitive picture for the at first sight uninterpretable spectra. In this sense, the dynamics of a Bose-Einstein condensate in a triple well potential is analogous to the vibrations of a tri-atomic molecule.…”

Section: Introductionmentioning

confidence: 99%

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Semiclassical approach to Bose-Einstein condensates in a triple well potential

Mossmann

Jung

2006

Phys. Rev. A

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We present an approach for the analysis of Bose-Einstein condensates in a few mode approximation. This method has already been used to successfully analyze the vibrational modes in various molecular systems and offers a perspective on the dynamics in many particle bosonic systems. We discuss a system consisting of a Bose-Einstein condensate in a triple well potential. Such systems correspond to classical Hamiltonian systems with three degrees of freedom. The semiclassical approach allows a simple visualization of the eigenstates of the quantum system referring to the underlying classical dynamics. From this classification we can read off the dynamical properties of the eigenstates such as particle exchange between the wells and entanglement without further calculations. In addition, this approach offers insights into the validity of the mean-field description of the many particle system by the Gross-Pitaevskii equation, since we make use of exactly this correspondence in our semiclassical analysis. We choose a three mode system in order to visualize it easily and, moreover, to have a sufficiently interesting structure, although the method can also be extended to higher dimensional systems.⌽ ͑r ជ͒ = ͚ n,m n,m ͑r ជ͒â n,m , ͑2͒where we assume that the basis functions ͕ n,m ͖ of the oneparticle Hilbert space are exponentially localized in space and real, as is the case for the Wannier functions ͓22͔. The index n describes basis functions in different wells and we *Electronic address: mossmann@fis.unam.mx PHYSICAL REVIEW A 74, 033601 ͑2006͒

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Section: The Modelmentioning

confidence: 99%

Section: Classical Dynamics and Coupling Schemesmentioning

confidence: 99%

Section: Classification Of Semiclassical Wave Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Semiclassical approach to Bose-Einstein condensates in a triple well potential

Mossmann

Jung

2006

Phys. Rev. A

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“…6 Spectra become distorted due to the influence of resonances, 7 and the different peaks can be hierarchically organized in terms of polyads. 8,9 This reflects the importance of the intramolecular energy transfer processes taking place inside the molecule. 10 At very high excitation energies, the interactions become too large and the picture based on normal mode states is no longer valid.…”

mentioning

confidence: 99%

Homoclinic motions in the vibrational spectra of floppy systems: The LiCN molecule

Borondo

Vergini

Wisniacki

et al. 2005

The Journal of Chemical Physics

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Recent experimental and theoretical methods allowed the efficient investigation of highly excited rovibrational states of molecular systems. At these levels of excitation the correspondence principle holds, and then classical mechanics can provide intuitive views of the involved processes. In this respect, we have recently shown that for completely hyperbolic systems, homoclinic motions, which are known to organize the classical chaotic region in Hamiltonian systems, imprint a clear signature in the corresponding highly excited quantum spectra. In this Communication we show that this result also holds in mixed systems, by considering an application to the floppy LiNC∕LiCN molecular system.

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On the nature of highly vibrationally excited states of thiophosgene#

Keshavamurthy

2012

J Chem Sci

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In this work an analysis of the highly vibrationally excited states of thiophosgene (SCCl2) is made in order to gain insights into some of the experimental observations and spectral features. The states analyzed herein lie in a spectrally complex region where strong mode mixings are expected due to the overlap of several strong anharmonic Fermi resonances. Two recent techniques, a semiclassical angle space representation of the eigenstates and the parametric variation of the eigenvalues (levelvelocities) are used to identify eigenstate sequences exhibiting common localization characteristics. Preliminary results on the influence of highly excited out-of-plane bending modes on the nature of the eigenstates suggest a possible bifurcation in the system. I. INTRODUCIONUnderstanding the nature of the highly excited molecular eigenstates is equivalent to deciphering the mechanism of intramolecular vibrational energy redistribution (IVR) occuring in the molecule [1]. However, the assignment of eigenstates is far from simple. The existence of and interplay of several strong anharmonic resonances result in complicated spectral patterns and highly mixed states. Nevertheless, eigenstates of molecular systems rarely exhibit the extreme scenario of being completely ergodic or completely regular [2]. A generic situation, even at fairly high energies, is the coexistence of several classes of eigenstates with differing degree of mixing being interspersed among each other [3,4]. More interestingly, the interspersed states can show several sequences associated with certain identifiable common localization characteristics. In other words, although a full set of quantum numbers do not exist for labeling such states, there are reasons to believe that a sufficient number of approximate quantum numbers do exist to understand, and hence assign, the eigenstates. Since the approximate quantum numbers arise out of the local dynamics due to specific resonances, relevant at the energies of interest, the assignment is inherently dynamical in nature. In a nutshell, several decades of work have shown that dynamical assignments can be done reliably only if the structure of the corresponding classical phase space is well understood [5].This work is concerned with the dynamical assignment of the eigenstates of thiophosgene SCCl 2 . The Hamiltonian of interest is a highly accurate spectroscopic Hamiltonian obtained [6] by Gruebele and Sibert via a canonical Van Vleck perturbation analysis of the experimentally derived normal mode potential surface [7]. The Hamiltonian can be expressed as H = H 0 + V res withThe zeroth-order anharmonic Hamiltonian is H 0 , whose eigenstates are the feature states and V res accounts for the important anharmonic resonances responsible for the IVR dynamics. In the rest of the paper the various resonances will be refered to by simply indicating the modes. For instance, the first resonance term in V res above will be refered to as the 526-resonance. The hermitian adjoints of the operators are denoted by c.c., and the op...

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Spectroscopic interpretation: The high vibrations of CDBrClF

Cited by 19 publications

References 17 publications

Semiclassical approach to Bose-Einstein condensates in a triple well potential

Semiclassical approach to Bose-Einstein condensates in a triple well potential

Homoclinic motions in the vibrational spectra of floppy systems: The LiCN molecule

On the nature of highly vibrationally excited states of thiophosgene#

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