The quantum theory of local modes in a coupled system of nonlinear oscillators

Bernstein, L.; Eilbeck, J. C.; Scott, Alwyn C.

doi:10.1088/0951-7715/3/2/004

Cited by 96 publications

(143 citation statements)

References 30 publications

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“…For each of the four (ψ a , ψ b ) conditions on great circles given in (33)(34)(35)(36), there is a family of critical points. Each family corresponds to a new type of mode, applying the reasoning of section 3 as follows.…”

Section: Resultsmentioning

confidence: 99%

“…(33)(34)(35)(36), the relative phase angle and the dihedral angle are locked at either 0 or π/2. The association with ψ a is particularly evident in the animations but can also be discerned in the still frames of Figure 5.…”

Section: Resultsmentioning

confidence: 99%

“…A simplification comes from the observation that with the discrete ψ a , ψ b values, (28) can be rewritten as For the entire accessible range of J a , J b , and when ψ a , ψ b are constrained to values in (33)(34)(35)(36), the factor between the curly brackets was numerically verified to be always nonzero. Therefore (28) has the very simple solution After substitution for J b ) 0, the remaining condition (27) becomes an easily solved quadratic equation.…”

Section: Implementation Of the Bifurcation Analysismentioning

confidence: 99%

See 2 more Smart Citations

Bending Dynamics of Acetylene: New Modes Born in Bifurcations of Normal Modes

Tyng

Kellman

2006

J. Phys. Chem. B

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W This paper contains enhanced objects available on the Internet at http://pubs.acs.org/jpcbfk.Semiclassical techniques are used to analyze highly excited pure bending vibrational dynamics from spectra of C 2 H 2 . An analytic bifurcation approach is developed, based on critical points of a classical version of the quantum fitting Hamiltonian. At high energy four new types of anharmonic modes are born in bifurcations of the normal modes: local, orthogonal, precessional, and counter-rotator. Visual insight into their nature is obtained with the help of computer-generated three-dimensional animations. The connection between the local mode and the acetylene-vinylidene isomerization "reaction mode" is considered.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Implementation Of the Bifurcation Analysismentioning

confidence: 99%

See 1 more Smart Citation

Bending Dynamics of Acetylene: New Modes Born in Bifurcations of Normal Modes

Tyng

Kellman

2006

J. Phys. Chem. B

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“…This system arises in the study of molecular vibrations in one-dimensional chains such as benzene and certain molecular crystals [5,26,25,24,2]. With site energies scaled out through a gauge transformation the reduced Hamiltonian operator iŝ (ii) The quantum Ablowitz-Ladik (QAL) equation…”

Section: (I) the Quantum Discrete Nonlinear Schrödinger (Qdnls) Equationmentioning

confidence: 99%

Quantum lattice solitons

Scott

Eilbeck

Gilhøj

1994

Physica D: Nonlinear Phenomena

124

177

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The number state method is used to study soliton bands for three anharmonic quantum lattices: i) The discrete nonlinear Schrödinger equation, ii) The Ablowitz-Ladik system, and iii) A fermionic polaron model. Each of these systems is assumed to have f -fold translational symmetry in one spatial dimension, where f is the number of freedoms (lattice points). At the second quantum level (n = 2) we calculate exact eigenfunctions and energies of pure quantum states, from which we determine binding energy (E b ), effective mass (m * ) and maximum group velocity (Vm) of the soliton bands as functions of the anharmonicity in the limit f → ∞. For arbitrary values of n we have asymptotic expressions for E b , m * , and Vm as functions of the anharmonicity in the limits of large and small anharmonicity. Using these expressions we discuss and describe wave packets of pure eigenstates that correspond to classical solitons.

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“…Semiclassical expressions for the tunneling splittings of the eigenvalues have been derived [8,9] in context of the spin-system in eqn. (2) below (see also [10,11] for a perturbative treatment of the splittings and [12] for a detailed analysis of the quantum spectrum).…”

Section: Introductionmentioning

confidence: 99%

Semiclassical quantization of anN-particle Bose-Hubbard model

Graefe

Korsch

2007

Phys. Rev. A

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A semiclassical Bohr-Sommerfeld approximation is derived for an N -particle, two-mode BoseHubbard system modeling a Bose-Einstein condensate in a double-well potential. This semiclassical description is based on the 'classical' dynamics of the mean-field Gross-Pitaevskii equation and is expected to be valid for large N . We demonstrate the possibility to reconstruct quantum properties of the N -particle system from the mean-field dynamics. The resulting semiclassical eigenvalues and eigenstates are found to be in very good agreement with the exact ones, even for small values of N , both for subcritical and supercritical particle interaction strength where tunneling has to be taken into account.

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The quantum theory of local modes in a coupled system of nonlinear oscillators

Abstract: The discrete self-trapping (DST) equation describes a coupled system of anharmonic oscillators that can be quantised in a remarkably simple manner. Here the DST system is used to describe the relationship between quantum and classical descriptions of local modes of vibration in a molecule.

Cited by 96 publications

References 30 publications

Bending Dynamics of Acetylene: New Modes Born in Bifurcations of Normal Modes

Bending Dynamics of Acetylene: New Modes Born in Bifurcations of Normal Modes

Quantum lattice solitons

Semiclassical quantization of anN-particle Bose-Hubbard model

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