Inversion of a tridiagonal jacobi matrix

Usmani, Riaz A.

doi:10.1016/0024-3795(94)90414-6

Cited by 149 publications

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“…. , 1 with the initial conditions φ n+1 = 1 and φ n = a n [16]. 13 The integral is convergent once we gauge-fix the SL(2, C) gauge freedom at each vertex, see [17] for details.…”

Section: (Almost)-analytic Machinerymentioning

confidence: 99%

On spinfoam models in large spin regime

Han

2013

Class. Quantum Grav.

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We study the semiclassical behavior of Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model, by taking into account the sum over spins in the large spin regime. We also employ the method of stationary phase analysis with parameters and the so called, almost-analytic machinery, in order to find the asymptotic behavior of the contributions from all possible large spin configurations in the spinfoam model. The spins contributing the sum are written as J f = λ j f where λ is a large parameter resulting in an asymptotic expansion via stationary phase approximation. The analysis shows that at least for the simplicial Lorentzian geometries (as spinfoam critical configurations), they contribute the leading order approximation of spinfoam amplitude only when their deficit angles satisfy γΘ f ≤ λ −1/2 mod 4πZ. Our analysis results in a curvature expansion of the semiclassical low energy effective action from the spinfoam model, where the UV modifications of Einstein gravity appear as subleading high-curvature corrections.

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“…. , 1 with the initial conditions φ n+1 = 1 and φ n = a n [16]. 13 The integral is convergent once we gauge-fix the SL(2, C) gauge freedom at each vertex, see [17] for details.…”

Section: (Almost)-analytic Machinerymentioning

confidence: 99%

On spinfoam models in large spin regime

Han

2013

Class. Quantum Grav.

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“…The particle densities in the hot and relaxed states are obtained from f h = −B −1 h g and f r = −A −1 τ −1 h f h , respectively. The escape probability η is calculated using the analytical solution of the tridiagonal matrix A as follows: 29,[36][37][38] …”

Section: Calculation Methodsmentioning

confidence: 99%

Theoretical study on the cooperative exciton dissociation process based on dimensional and hot charge-transfer state effects in an organic photocell

Shimazaki

Nakajima

2016

The Journal of Chemical Physics

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This paper discusses the exciton dissociation process at the donor-acceptor interface in organic photocells. In our previous study, we introduced a local temperature to handle the hot chargetransfer (CT) state and calculated the exciton dissociation probability based on the 1D organic semiconductor model [T. Shimazaki and T. Nakajima, Phys. Chem. Chem. Phys. 17, 12538 (2015)]. Although the hot CT state plays an essential role in exciton dissociations, the probabilities calculated are not high enough to efficiently separate bound electron-hole pairs. This paper focuses on the dimensional (entropy) effect together with the hot CT state effect and shows that cooperative behavior between both effects can improve the exciton dissociation process. In addition, we discuss cooperative effects with site-disorders and external-electric-fields. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

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“…For the non-interacting case studied here, H is a finite n × n symmetric tridiagonal matrix: H ij = a i for i = j, and H ij = b i for i = j ± 1. There is a simple and elegant formula to calculate the inverse of such matrix 42 : with φ n+1 = 1 and φ n = a n . Notice that θ n = det(H − Iz).…”

Section: Discussionmentioning

confidence: 99%

Designing a symmetry-protected molecular device

Büsser

Feiguin

2012

Phys. Rev. B

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Realizing a quantum transistor built of molecules or quantum dots has been one of the most ambitious challenges in nanotechnology. Even though remarkable progress has been made, being able to gate and control nanometer scale objects, as well to interconnect them to achieve scalability remains extremely difficult. Most experiments concern a single quantum dot or molecule, and they are made at ultra low temperature to avoid decoherence and tunneling. We propose to use canonical transformations to design quantum devices that are protected by symmetry, and therefore, may be operational at high temperatures. We illustrate the idea with examples of quantum transistor architectures that can be connected both in series and parallel.

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Inversion of a tridiagonal jacobi matrix

Cited by 149 publications

References 0 publications

On spinfoam models in large spin regime

On spinfoam models in large spin regime

Theoretical study on the cooperative exciton dissociation process based on dimensional and hot charge-transfer state effects in an organic photocell

Designing a symmetry-protected molecular device

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