Tunnelling of a large spin: mapping onto a particle problem

Scharf, G.; Wreszinski, Walter F.; van,; Hemmen, J. Leo van

doi:10.1088/0305-4470/20/13/032

Cited by 74 publications

(67 citation statements)

References 5 publications

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“…Its relation to previous calculations is discussed there. From the viewpoint of this article, the interesting comparison is with Scharf, Wreszinski, and van Hemmen [28]. These authors only consider the case where α and γ are fixed as S → ∞, so that θ 0 = O(1/S).…”

Section: Illustrative Examplesmentioning

confidence: 99%

Tunnel splittings for one-dimensional potential wells revisited

Garg

2000

American Journal of Physics

114

132

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The WKB and instanton answers for the tunnel splitting of the ground state in a symmetric double well potential are both reduced to an expression involving only the functionals of the potential, without the need for solving any auxilliary problems. This formula is applied to simple model problems. The prefactor for the splitting in the text book by Landau and Lifshitz is amended so as to apply to the ground and low lying excited states.

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Section: Illustrative Examplesmentioning

confidence: 99%

Tunnel splittings for one-dimensional potential wells revisited

Garg

2000

American Journal of Physics

114

132

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“…Previous work in this direction concentrated on the symmetric case, where the permutational symmetry of the system with respect to an interchange of the two modes simplifies an analysis. 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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“…From the theoretical point of view, spin tunneling has been treated mainly by the use of a WKB method adapted to spin systems [9,10], by using Feyman's path integral treatment of quantum mechanics [11,12], and also by using su(2) coherent states [13] in order to establish a correspondence between the spectrum of the spin system with the energy levels of a particle moving in an effective potential [14].…”

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confidence: 99%

Quantum description of spin tunneling in magnetic molecules

Galetti

2007

Physica A: Statistical Mechanics and its Applications

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Abstract.A new approach is used that allows to describe the magnetic molecules main properties in a direct and simple way. Results obtained for the F e 8 cluster show good agreement with the experimental data.PACS numbers: 03.65. Ca, 75.45+j, 75.60Jp Submitted to: J. Phys. C: Solid State Phys.In recent years, with the experimental advances in the measurement of magnetic molecular clusters properties, it has emerged a new frontier in this area. One of the interesting aspects that came out of these studies is the possibility of measuring spin tunneling in mesoscopic systems what corresponds, in a standard quantum description, to the tunneling of the collective degree of freedom corresponding to the magnetization direction through a potential barrier separating two minima of an effective potential associated with the spatial orientation [1,2,3,4,5,6,7,8].From the theoretical point of view, spin tunneling has been treated mainly by the use of a WKB method adapted to spin systems [9,10], by using Feyman's path integral treatment of quantum mechanics [11,12], and also by using su(2) coherent states [13] in order to establish a correspondence between the spectrum of the spin system with the energy levels of a particle moving in an effective potential [14].In the present letter we intend to show that still another approach may be used for describing spin tunneling -in angle representation -in such a way that analytic expressions for the characteristic parameters of the magnetic molecular clusters can be obtained; in particular, the results for the spectrum and energy barrier heights are directly obtained and the spin tunneling process can be easily interpreted.The starting point of the present approach is the introduction of a quantum phenomenological Hamiltonian describing the spin system, written in terms of angular momentum operators obeying the standard commutation relations, and that reflects

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Tunnelling of a large spin: mapping onto a particle problem

Cited by 74 publications

References 5 publications

Tunnel splittings for one-dimensional potential wells revisited

Tunnel splittings for one-dimensional potential wells revisited

Semiclassical quantization of anN-particle Bose-Hubbard model

Quantum description of spin tunneling in magnetic molecules

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