On the Green function for a particle in a uniform electric field

Moyer, C. A.

doi:10.1088/0022-3719/6/9/005

Cited by 38 publications

(24 citation statements)

References 2 publications

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“…Multiplying both sides of (9) by 1 / (Z a 2 −Z 2 ) we integrate over (a, ∞) with respect to Z. Interchanging the order of integration and using (30) we obtain (28). Taking the Hilbert transform of (28) yields (29).…”

Section: Proofmentioning

confidence: 99%

Integrals containing products of Airy functions and planar photon propagation in a magnetic field

Schubert

Варламов²

2011

Math. Meth. Appl. Sci.

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Section: Proofmentioning

confidence: 99%

Integrals containing products of Airy functions and planar photon propagation in a magnetic field

Schubert

Варламов²

2011

Math. Meth. Appl. Sci.

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“…To deal with the transient current in open systems, a major approach is the embedding scheme (calculate a finite region in an extended environment with the help of self‐energy). For example, the open boundary condition derived from partitioned propagators is employed for the equation of motions (EOM) of the density matrix ; and the transparent boundary condition is employed for the wavefunction propagations . Another approach is to use finite leads with large lengths to mimic the open terminals and calculate the currents in a limited duration, as in Ref.…”

Section: Introductionmentioning

confidence: 99%

Time‐dependent quantum transport theory and its applications to graphene nanoribbons

Xie

Kwok

Zhang

et al. 2013

Physica Status Solidi (b)

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Time‐dependent quantum transport parameters for graphene nanoribbons (GNR) are calculated by the hierarchical equation of motion (HEOM) method based on the nonequilibrium Green's function (NEGF) theory [Xie et al., J. Chem. Phys. 137, 044113 (2012)]. In this paper, a new initial‐state calculation technique is introduced and accelerated by the contour integration for large systems. Some Lorentzian fitting schemes for the self‐energy matrices are developed to effectively reduce the number of Lorentzians and maintain good fitting results. With these two developments in HEOM, we have calculated the transient quantum transport parameters in GNR. We find a new type of surface state with delta‐function‐like density of states in many semi‐infinite armchair‐type GNR. For zigzag‐type GNR, a large overshooting current and slowly decaying transient charge are observed, which is due to the sharp lead spectra and the “even–odd” effect.

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“…When |z| is large, we employ Hankel's asymptotic series 27 for the Hankel functions in Eq. (23), in this way obtaining for any α > −1/2 and |arg(z)| < π:…”

Section: Application Class: the Spherical Wave Continuummentioning

confidence: 94%

“…Poles in the complex E-plane of the continued resolvent operator for H 0 + V (i.e., resonances) also have been studied for this model potential. [23][24][25][26] Again, one of these is characterized by a real part that approaches E b as F → 0 (plus an imaginary part that vanishes exponentially with F in this limit). In fact, the equation for the resonance energies is just Eq.…”

Section: B Example: Particle Bound To a Delta Well In A Uniform Fieldmentioning

confidence: 99%

A unified theory of quasibound states

Moyer

2014

AIP Advances

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We have developed a formalism that includes both quasibound states with real energies and quantum resonances within the same theoretical framework, and that admits a clean and unambiguous distinction between these states and the states of the embedding continuum. States described broadly as 'quasibound' are defined as having a connectedness (in the mathematical sense) to true bound states through the growth of some parameter. The approach taken here builds on our earlier work by clarifying several crucial points and extending the formalism to encompass a variety of continuous spectra, including those with degenerate energy levels. The result is a comprehensive framework for the study of quasibound states. The theory is illustrated by examining several cases pertinent to applications widely discussed in the literature.

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On the Green function for a particle in a uniform electric field

Cited by 38 publications

References 2 publications

Integrals containing products of Airy functions and planar photon propagation in a magnetic field

Integrals containing products of Airy functions and planar photon propagation in a magnetic field

Time‐dependent quantum transport theory and its applications to graphene nanoribbons

A unified theory of quasibound states

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