Supersymmetry and eigensurface topology of the planar quantum pendulum

Schmidt, Burkhard; Friedrich, Břetislav

doi:10.3389/fphy.2014.00037

Cited by 15 publications

(41 citation statements)

References 38 publications

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“…A similar situation arises for the planar pendulum, Fig. 7, where again the conditions of quasi-solvability (integer values of κ) coincide with the loci of genuine (odd κ) or avoided (even κ) intersections of the higher states; note that the latter occur only for a large-enough ζ [32,57]. We note that the algebraic solutions found may serve as benchmarks for numerical analysis and the polynomial Ansatz they suggest could be useful for numerical calculations beyond quasi-solvability, i.e., for non-integer values of the topological index κ.…”

Section: Discussionmentioning

confidence: 56%

“…The non-physical choice of M = 1/2 for a symmetric top makes it possible to retrieve all our previous results concerning the quasi-solvability of the planar pendulum (in the trigonometric case) and the Razavy system (in the hyperbolic case), as reported in Refs. [32,57].…”

Section: Planar Pendulum Razavy Systemmentioning

confidence: 99%

“…Our previous work [32,57] examined the spatial symmetry classes and irreducible representations Γ t,h of both the planar pendulum and the Razavy systems. Table X lists…”

Section: Planar Pendulum Razavy Systemmentioning

confidence: 99%

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Symmetric tops in combined electric fields: Conditional quasisolvability via the quantum Hamilton-Jacobi theory

et al. 2018

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We make use of the Quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasisolvability of the quantum symmetric top subject to combined electric fields (symmetric top pendulum). We derive the conditions of quasi-solvability of the time-independent Schrödinger equation as well as the corresponding finite sets of exact analytic solutions. We do so for this prototypical trigonometric system as well as for its anti-isospectral hyperbolic counterpart. An examination of the algebraic and numerical spectra of these two systems reveals mutually closely related patterns.The QHJ approach allows to retrieve the closed-form solutions for the spherical and planar pendula and the Razavy system that had been obtained in our earlier work via Supersymmetric Quantum Mechanics as well as to find a cornucopia of additional exact analytic solutions. * bretislav.friedrich@fhi-berlin.mpg.de † burkhard.schmidt@fu-berlin.de arXiv:1802.07939v1 [math-ph]

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Section: Discussionmentioning

confidence: 56%

Section: Planar Pendulum Razavy Systemmentioning

confidence: 99%

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Symmetric tops in combined electric fields: Conditional quasisolvability via the quantum Hamilton-Jacobi theory

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“…Also worthy of exploring is the dependence of the triple-field effects on the tilt angles among the three field vectors [21,71]. Relevant to both is the topology of the eigenenergy surfaces spanned by the η el , η m , and η opt interaction parameters that may result in conical intersections [63,64], another subject of our forthcoming study. , , ) I listed in tables A1 -A5, see [72].…”

Section: Discussionmentioning

confidence: 99%

Directional properties of polar paramagnetic molecules subject to congruent electric, magnetic and optical fields

Sharma

Friedrich

2015

New J. Phys.

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We show that congruent electric, magnetic and non-resonant optical fields acting concurrently on a polar paramagnetic (and polarizable) molecule offer possibilities to both amplify and control the directionality of the ensuing molecular states that surpass those available in double-field combinations or in single fields alone. At the core of these triple-field effects is the lifting of the degeneracy of the projection quantum number M by the magnetic field superimposed on the optical field and a subsequent coupling of the members of the 'doubled' (for states with ≠ M 0) tunneling doublets due to the optical field by even a weak electrostatic field. 3 2 molecule in its electronic ground state) and, therefore, correspondingly larger magnetic dipole moments. The recently discovered LiHe van der Waals molecule [67, 68], a polar and paramagnetic halo species, would also benefit from the study of its OPEN ACCESS

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“…Eqs. (45), (46), with the classical trajectories, as given by Eqs. (43) and (44), that gives rise to the rich pattern of the canals and ridges seen in Fig.…”

Section: Purely Orienting Interactionmentioning

confidence: 99%

Dynamics of polar polarizable rotors acted upon by unipolar electromagnetic pulses: From the sudden to the adiabatic regime

Mirahmadi

Schmidt

Karra

et al. 2018

The Journal of Chemical Physics

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We study, analytically as well as numerically, the dynamics that arises from the interaction of a polar polarizable rigid rotor with single unipolar electromagnetic pulses of varying length, ∆τ , with respect to the rotational period of the rotor, τ r . In the sudden, non-adiabatic limit, ∆τ τ r , we derive analytic expressions for the rotor's wavefunctions, kinetic energies, and field-free evolution of orientation and alignment. We verify the analytic results by solving the corresponding timedependent Schrödinger equation numerically and extend the temporal range of the interactions considered all the way to the adiabatic limit, ∆τ τ r , where general analytic solutions beyond the field-free case are no longer available. The effects of the orienting and aligning interactions as well as of their combination on the post-pulse populations of the rotational states are visualized as functions of the orienting and aligning kick strengths in terms of populations quilts. Quantum carpets that encapsulate the evolution of the rotational wavepackets provide the space-time portraits of the resulting dynamics. The population quilts and quantum carpets reveal that purely orienting, purely aligning, or even-break combined interactions each exhibit a sui generis dynamics. In the intermediate temporal regime, we find that the wavepackets as functions of the orienting and aligning kick strengths show resonances that correspond to diminished kinetic energies at particular values of the pulse duration. * burkhard.schmidt@fu-berlin.de † bretislav.friedrich@fhi-berlin.mpg.de arXiv:1806.11329v3 [quant-ph] 9 Aug 2018 basis set for expanding the time-dependent wavefunction, with the resultwhere E J = J(J + 1). Note that the expansion coefficients, C J J 0 ,M 0 , are time-independent, in consequence of the fact that the time dependence in Eq. (10) only arises from the e −iJ 2 τ term.The final form of the wavefunction in the sudden limit is given by (for a detailed derivationare the Clebsch-Gordan coefficients and only c J is a function of the kick strengths, cf. Eq. (A5).Throughout the remainder of this paper, we restrict ourselves to the case when the free rotor is initially in its ground state, J 0 = M 0 = 0. As a result, the C J J 0 ,M 0 coefficients in Eq. (11) reduce toThe coefficients C J J 0 ,M 0 arising in Eq. (11) can be found by expanding the time-independent term in Eq. (10) in terms of spherical harmonics,with Γ the gamma function; we applied the Legendre duplication formula [49] to achieve the final form of Eq. (A4).By making use of Eq. (A2) and Eq. (A5) we can evaluateC J J 0 ,M 0 in Eq. (A1) as follows,where J 1 M 1 , J 2 M 2 |J 3 M 3 are the Clebsch-Gordan coefficients, which vanish unless |J −J 0 | ≤ J ≤ J + J 0 and J + J + J 0 is an even integer [49]. Finally, we obtainIn all the analytic results presented in this paper, Eqs. (A5) and (A7) were found to converge satisfactorily for κ and J up to 80 and 50, respectively (e.g. for P η = P ζ = 8 the 80th term of the sum over k in Eq. (A5) is close to 10 −30 for C 50 0,0 ≈ 1...

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Supersymmetry and eigensurface topology of the planar quantum pendulum

Cited by 15 publications

References 38 publications

Symmetric tops in combined electric fields: Conditional quasisolvability via the quantum Hamilton-Jacobi theory

Symmetric tops in combined electric fields: Conditional quasisolvability via the quantum Hamilton-Jacobi theory

Directional properties of polar paramagnetic molecules subject to congruent electric, magnetic and optical fields

Dynamics of polar polarizable rotors acted upon by unipolar electromagnetic pulses: From the sudden to the adiabatic regime

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