Spectral Filtering in Quantum Y-Junction

Cheon, Taksu; Exner, Pavel; Turek, Ondřej

doi:10.1143/jpsj.78.124004

Cited by 13 publications

(17 citation statements)

References 11 publications

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“…The relation (4) together with the requirements (5) describe all possible vertex boundary conditions giving rise to a self-adjoint Hamiltonian. The requirements (5) can be partly included into the boundary conditions (4) by writing the matrices A, B in a special form. One of the ways was discovered by Harmer [10] and independently by Kostrykin and Schrader [11] who transformed (4) with (5) into "compact" boundary conditions…”

Section: Preliminariesmentioning

confidence: 99%

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Potential-controlled filtering in quantum star graphs

Turek¹,

Cheon²

2013

Annals of Physics

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We study the scattering in a quantum star graph with a F\"ul\"op--Tsutsui coupling in its vertex and with external potentials on the lines. We find certain special couplings for which the probability of the transmission between two given lines of the graph is strongly influenced by the potential applied on another line. On the basis of this phenomenon we design a tunable quantum band-pass spectral filter. The transmission from the input to the output line is governed by a potential added on the controlling line. The strength of the potential directly determines the passband position, which allows to control the filter in a macroscopic manner. Generalization of this concept to quantum devices with multiple controlling lines proves possible. It enables the construction of spectral filters with more controllable parameters or with more operation modes. In particular, we design a band-pass filter with independently adjustable multiple passbands. We also address the problem of the physical realization of F\"ul\"op--Tsutsui couplings and demonstrate that the couplings needed for the construction of the proposed quantum devices can be approximated by simple graphs carrying only $\delta$ potentials.Comment: 41 pages, 17 figure

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Section: Preliminariesmentioning

confidence: 99%

“…It is known that a line carrying the δ-interaction is usable as a high-pass filter, and similarly, a line carrying the δ -interaction works as a low-pass filter. More complex spectral filters have been developed as well, for instance a trident filter [4], or a Y-shaped branching filter, functionning as a high-pass/low-pass junction [5].…”

Section: Introductionmentioning

confidence: 99%

Potential-controlled filtering in quantum star graphs

Turek¹,

Cheon²

2013

Annals of Physics

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“…System of this type is fully reflecting, S(k) ∼ −I, at k → 0. Physically speaking, this can be identified as generalized δ-coupling, see also [10]. Prominent representatives of this family are:…”

Section: Scattering Of Type Ii: Generalized δ-Couplingmentioning

confidence: 99%

Quantum graph vertices with permutation-symmetric scattering probabilities

Turek

Cheon

2011

Physics Letters A

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Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix U. Observing that if U has at most two eigenvalues, then the scattering matrix S(k) of the vertex is a linear combination of the identity matrix and a fixed Hermitian unitary matrix, we construct vertex couplings with this property: For all momenta k, the transmission probability from the j-th edge to ℓ-th edge is independent of ( j, ℓ), and all the reflection probabilities are equal. We classify these couplings according to their scattering properties, which leads to the concept of generalized δ and δ ′ couplings.

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“…The intersection of degree 3 has a point interaction parametrized by U(3) [1,2,3,4]. Some features of transmission of a quantum particle in the system with a Y-junction were investigated in [5] and also in the context of a star graph [6,7]. However, the thorough investigation of the system has not yet been completed.…”

Section: Introductionmentioning

confidence: 99%

Quantum reflection and transmission in ring systems with double Y-junctions: occurrence of perfect reflection

Fujimoto¹,

Konno²,

Nagasawa³

et al. 2020

J. Phys. A: Math. Theor.

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We consider the scattering problems of a quantum particle in a system with a single Y-junction and in ring systems with double Yjunctions. We provide new formalism for such quantum mechanical problems. Based on a path integral approach, we find compact formulas for probability amplitudes in the ring systems. We also discuss quantum reflection and transmission in the ring systems under scale-invariant junction conditions. It is remarkable that perfect reflection can occur in an anti-symmetric ring system, in contrast with the one-dimensional quantum systems having singular nodes of degree 2.

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Spectral Filtering in Quantum Y-Junction

Cited by 13 publications

References 11 publications

Potential-controlled filtering in quantum star graphs

Potential-controlled filtering in quantum star graphs

Quantum graph vertices with permutation-symmetric scattering probabilities

Quantum reflection and transmission in ring systems with double Y-junctions: occurrence of perfect reflection

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