Time dependent quantum graph with loop

Eremin, D A; Grishanov, E.N.; Kostrov, O G; Nikiforov, D S; Popov, I. Yu.

doi:10.17586/2220-8054-2017-8-4-420-425

Cited by 5 publications

(2 citation statements)

References 13 publications

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“…Recently, great attention has been devoted to time-depending metric graphs, i.e. graphs having characteristics (e.g., edge lengths) varying in time [9][10][11][12][13][14][15][16]. This problem is in relation to time-dependent boundary conditions and time dependent potentials [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

A time-dependent metric graph with a fourth-order operator on the edges

Blinova

Gnedash

Popov

2021

Theor appl mech (Belgr)

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The metric graph model is suggested for description of elastic vibration in a network of rods under the assumption that the rod lengths vary in time. A single rod and star-like graph are considered. Influence of the length variation law on the vibration distribution is investigated. For high-frequency length variation one observes a fast transition to high-frequency amplitude distribution

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Section: Introductionmentioning

confidence: 99%

A time-dependent metric graph with a fourth-order operator on the edges

Blinova

Gnedash

Popov

2021

Theor appl mech (Belgr)

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“…Although this model is very interesting from a physical point of view (see, e.g., [16]), there are only a few works devoted to this problem. One can mention papers concerning the time-dependent boundary conditions [17] or time dependent point-like interactions [18], but consideration of time-dependent graphs began recently [19][20][21][22][23]. Wave dynamics for time-dependent quantum graphs in a magnetic field was not studied previously.…”

Section: Introductionmentioning

confidence: 99%

Wave dynamics on timedepending graph with Aharonov–Bohm ring

Eremin¹,

Grishanov²,

Nikiforov³

et al. 2018

Nanosystems: Phys. Chem. Math.

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Aharonov-Bohm ring (AB ring) is an element frequently used in nanosystems. The paper deals with wave dynamics on quantum graph consisting of AB ring coupled to a segment. It is assumed that the lengths of the edges vary in time. Variable replacement is made to come to the problem for stationary geometric graph. The obtained equation is solved using the expansion with respect to a complete system of eigenfunctions of the unperturbed self-adjoint operator for the stationary graph. The coefficients of the expansion are found as solutions of a system of differential equations numerically. The influence of the magnetic field is studied. The comparison with the case of stable geometric graph is made.

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