Asymptotic and numerical analysis of slowly varying two-dimensional quantum waveguides

Barrera-Figueroa, V.; Rabinovich, Vladimir; Loredo-Ramı́rez, Samantha Ana Cristina

doi:10.1088/1751-8121/ac4b14

Cited by 2 publications

(2 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(2.6) 1 We will use the notation I for the identity operator regardless of the space in which it acts.…”

Section: Spectrum Of System With the Straight Waveguidementioning

confidence: 99%

“…In [10], it has been shown that for a weak deformation the existence of the discrete spectrum points depends on the total area of deformation which is assumed to be positive if the deformation is localized on Σ \ Ω and negative if the deformation is situated on Ω \ Σ. It is also worth mentioning the paper [1], where the authors have considered two dimensional quantum waveguides modelled by confining potentials supported on slowly varying strips. The asymptotic and numerical analysis of the wave functions propagating in such waveguides has been proceeded and, for example, the leading asymptotic term of the wave functions has been determined by the adiabatic approach and the WKB approximation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum soft waveguides with resonances induced by broken symmetry

Kondej

2024

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We consider two-dimensional, non-relativistic quantum system with asymptotically straight soft waveguide. We show that the local deformation of the symmetric waveguide can lead to the emerging of the embedded eigenvalues living in the continuous spectrum. The main problem of this paper is devoted to the analysis of weak perturbation of the symmetric system. We show that the original embedded eigenvalues turn to the second sheet of the resolvent analytic continuation and constitute resonances. We describe the asymptotics of the real and imaginary components of the complex resonant pole depending on deformation. Finally, we generalize the problem to three dimensional system equipped with a soft layer.

show abstract

“…(2.6) 1 We will use the notation I for the identity operator regardless of the space in which it acts.…”

Section: Spectrum Of System With the Straight Waveguidementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum soft waveguides with resonances induced by broken symmetry

Kondej

2024

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

Fermi’s golden rule in tunneling models with quantum waveguides perturbed by Kato class measures

Kondej,

Ślipko

2024

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

In this paper we consider two dimensional quantum system with an infinite waveguide of the width $d$ and a transversally invariant profile. Furthermore, we assume that at a distant $\rho$ there is a perturbation defined by the Kato measure. We show that, under certain conditions, the resolvent of the Hamiltonian has the second sheet pole which reproduces the resonance at $z(\rho)$ with the asymptotics $z(\rho)=\mathcal E_{\beta ; n}+\mathcal O \Big(\frac{ \exp(-\sqrt{2 |\mathcal E_{\beta ;n}| } \rho )}{\rho }\Big)$ for $\rho$ large and with the resonant energy $\mathcal E_{\beta ;n}$. Moreover, we show that the imaginary component of $z(\rho)$ satisfies Fermi's golden rule which we explicitly derive.

show abstract

Asymptotic and numerical analysis of slowly varying two-dimensional quantum waveguides

Cited by 2 publications

References 59 publications

Quantum soft waveguides with resonances induced by broken symmetry

Quantum soft waveguides with resonances induced by broken symmetry

Fermi’s golden rule in tunneling models with quantum waveguides perturbed by Kato class measures

Contact Info

Product

Resources

About