Absolutely transparent multichannel systems. Unexpected peculiarities

Chabanov, V. M.; Zakhariev, B. N.

doi:10.1016/0370-2693(93)90773-b

Cited by 10 publications

(12 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…k and E (2) k ′ are the energy levels for two systems with the potentials V 1 (x) and V 2 (x), having the continuous spectra of values, ϕ (1) k (x) and ϕ…”

Section: Interdependences Between Spectral Characteristics Of Potentimentioning

confidence: 99%

See 1 more Smart Citation

SUSY-hierarchy of one-dimensional reflectionless potentials

Maydanyuk

2005

Annals of Physics

View full text Add to dashboard Cite

A class of one-dimensional reflectionless potentials is studied. It is found, that all possible types of the reflectionless potentials can be combined into one SUSYhierarchy with a constant potential. An approach for determination of a general form of the reflectionless potential on the basis of construction of such a hierarchy by the recurrent method is proposed. A general integral form of interdependence between superpotentials with neighboring numbers of this hierarchy, opening a possibility to find new reflectionless potentials, is found and has a simple analytical view. It is supposed that any possible type of the reflectionless potential can be expressed through finite number of elementary functions (unlike some presentations of the reflectionless potentials, which are constructed on the basis of soliton solutions or are shape invariant in one or many steps with involving scaling of parameters, and are expressed through series). An analysis of absolute transparency existence for the potential which has the inverse power dependence on space coordinate (and here tunneling is possible), i. e. which has the form V (x) = ±α/|x − x 0 | n (where α and x 0 are constants, n is natural number), is fulfilled. It is shown that such a potential can be reflectionless at n = 2 only. A SUSY-hierarchy of the inverse power reflectionless potentials is constructed. Isospectral expansions of this hierarchy is analyzed.

show abstract

“…k and E (2) k ′ are the energy levels for two systems with the potentials V 1 (x) and V 2 (x), having the continuous spectra of values, ϕ (1) k (x) and ϕ…”

Section: Interdependences Between Spectral Characteristics Of Potentimentioning

confidence: 99%

“…k ′ are the wave functions and the wave vectors, corresponding to the levels E (1) k and E (2) k ′ . From (9) we obtain:…”

Section: Interdependences Between Spectral Characteristics Of Potentimentioning

confidence: 99%

SUSY-hierarchy of one-dimensional reflectionless potentials

Maydanyuk

2005

Annals of Physics

View full text Add to dashboard Cite

show abstract

“…Such resonances have been studied for more general potentials, as for example symmetrical or asymmetrical doublebarrier structures in connection with resonant-tunneling, where they are denoted as unit resonances (see, e.g., [2] and references therein). Chabanov and Zakhariev [3] discovered that, at such a resonant energy, the potential scattering shows a surprising symmetry: Dividing V (x) into two distinct parts at some arbitrary point x defining a 'left' and a 'right' potential…”

mentioning

confidence: 99%

Barrier transmission for the nonlinear Schrödinger equation: surprises of nonlinear transport

Rapedius¹,

Korsch

2008

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

In this communication we report on a peculiar property of barrier transmission that systems governed by the nonlinear Schrödinger equation share with the linear one: For unit transmission the potential can be divided at an arbitrary point into two sub-potentials, a left and a right one, which have exactly the same transmission. This is a rare case of an exact property of a nonlinear wave function which will be of interest, e.g., for studies of coherent transport of Bose-Einstein condensates through mesoscopic waveguides.

show abstract

“…The isospectral transformation of a free motion system into the reflectionless one with a bound state gives [26] …”

Section: Transparencymentioning

confidence: 99%

“…In [26], the transparent interaction matrices in the case of different thresholds were derived and shown. For equal thresholds, the matrix elements of V αα (x) have a simple soliton-like form.…”

Section: Transparencymentioning

confidence: 99%

Toward the Quantum Design of Multichannel Systems The Inverse Problem Approach

Chabanov¹,

Zakhariev²,

Амирханов³

2000

Annals of Physics

View full text Add to dashboard Cite

The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of interaction matrices leading to the concentration of waves in a chosen partial channel and spatial localization are shown. The limiting instructive cases illustrating different phenomena which ooccur with the combination of 'incompatible' properties are considered. For example, the scattering solutions with different resonance widths at the same energy for the same interaction are revealed. Analogously, a 'paradoxical' coexistence of both strong reflection and absolute transparency is explained. The case of the violation of 'natural' asymptotic behavior of partial wave function is demonstrated : it has a greater damping decrement for the channel with a lower threshold. Peculiarities of the multichannel periodic structures, bound states embedded into continuum, resonance tunneling and degeneracy of states are described.

show abstract

Absolutely transparent multichannel systems. Unexpected peculiarities

Cited by 10 publications

References 3 publications

SUSY-hierarchy of one-dimensional reflectionless potentials

SUSY-hierarchy of one-dimensional reflectionless potentials

Barrier transmission for the nonlinear Schrödinger equation: surprises of nonlinear transport

Toward the Quantum Design of Multichannel Systems The Inverse Problem Approach

Contact Info

Product

Resources

About