Calculation of the determinant of shape invariant operators

Jafarizadeh, M. A.; Fakhri, H.

doi:10.1016/s0375-9601(97)00211-9

Cited by 20 publications

(22 citation statements)

References 8 publications

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“…We shall calculate the tunneling rate by applying the dilute-instanton approximation to first order inh [14], on the corresponding Duru-Kleinert path integral [12]. Its prefactor is calculated by the heat kernel method [15], using the shape invariance symmetry [16]. This paper is organized as follows: In section 2, the Duru-Kleinert path integral formula and Duru-Kleinert equivalence of corresponding actions is briefly reviewed.…”

Section: Introductionmentioning

confidence: 99%

Tunneling inΛdecaying cosmologies and the cosmological constant problem

et al. 1999

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The tunneling rate, with an exact prefactor, is calculated to first order in ប for an empty closed Friedmann-Robertson-Walker universe with a decaying cosmological term ⌳ϳR Ϫm (R is the scale factor and m is a parameter 0рmр2). This model is equivalent to a cosmology with the equation of state p ϭ(m/3Ϫ1) . The calculations are performed by applying the dilute-instanton approximation on the corresponding Duru-Kleinert path integral. It is shown that the highest tunneling rate occurs for mϭ2 corresponding to the cosmic string matter universe. The most probable cosmological term obtained, such as the one obtained by Strominger, accounts for a possible solution to the cosmological constant problem. ͓S0556-2821͑99͒03016-7͔ PACS number͑s͒: 98.80.Hw *

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Section: Introductionmentioning

confidence: 99%

Tunneling inΛdecaying cosmologies and the cosmological constant problem

et al. 1999

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“…Actually, on the one hand, the shape invariance plays a very important role in the solvability of these potentials. 3,5 On the other hand, it is rather crucial in the determination of the determinant of the Hamiltonian operator associated with these shape invariant potentials. 2,4 Also shape invariance symmetry is almost responsible for the generation of the coherent and squeezed states via the shape invariant potential.…”

Section: Discussionmentioning

confidence: 99%

Isospectral deformation of some shape invariant potentials

Jafarizadeh

Esfandyari

Panahi-Talemi

2000

Journal of Mathematical Physics

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Here we generalize the isospectral deformation of the discrete eigenspectrum of Eleonsky and Korolev ͓Phys. Rev. A 55, 2580 ͑1997͔͒ to continuous eigenspectrum of some well-known shape-invariant potentials. We show that the isospectral deformations preserve their shape invariance properties. Hence, using the preserved shape invariance property of the deformed potentials, we obtain both discrete and continuous eigenspectrum of the deformed Rosen-Morse, Natanzon, Rosen-Morse with added Dirac delta term, and Natanzon with added Dirac delta term potentials, respectively. It is shown that deformation does not change their other pecurialities, such as the reflectionless property of the Rosen-Morse potential and the penetrationless property of the Natanzon one.

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“…(31). This has been done by several methods in the literature [35][36][37] extending fundamental ideas by Gelfand and Yaglom [34] and Forman [38]. The fact that a ratio of determinants appears is not a simple mathematical trick.…”

Section: Quantum Fluctuations Around the (Anti)kinkmentioning

confidence: 99%

Instantonic methods for quantum tunneling in finite size

Zoli¹

2009

Braz. J. Phys.

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The instantonic approach for a φ 4 model potential is reexamined in the asymptotic limit. The path integral of the system is derived in semiclassical approximation expanding the action around the classical background. It is shown that the singularity in the path integral, arising from the zero mode in the quantum fluctuation spectrum, can be tackled only assuming a finite (although large) system size. On the other hand the standard instantonic method assumes the (anti)kink as classical background. But the (anti)kink is the solution of the Euler-Lagrange equation for the infinite size system. This formal contradiction can be consistently overcome by the finite size instantonic theory based on the Jacobi elliptic functions formalism. In terms of the latter I derive in detail the classical background which solves the finite size Euler-Lagrange equation and obtain the general path integral in finite size. Both problem and solution offer an instructive example of fruitful interaction between mathematics and physics.

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Calculation of the determinant of shape invariant operators

Cited by 20 publications

References 8 publications

Tunneling inΛdecaying cosmologies and the cosmological constant problem

Tunneling inΛdecaying cosmologies and the cosmological constant problem

Isospectral deformation of some shape invariant potentials

Instantonic methods for quantum tunneling in finite size

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