Wave dynamics on timedepending graph with Aharonov–Bohm ring

Abstract

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.

Metric graph version of the FitzHugh–Nagumo model

“…where L is the axon length (we assume that all axons have the same length, this assumption is not essential). These vertex coupling conditions differ from the conventional conditions for stationary and non-stationary metric graphs (see, e.g., [21,22]). Thus, the system describes three neurons: the first is the start, the second and the third are tied to each other (see.…”

On the metric graph model for flows in tubular nanostructures

“…The pressure is determined at the next stage (by taking into account the solvability condition ∂ 2 P 0 ∂r∂z = ∂P 0 ∂z∂r where the right hand side is obtained as a derivative with respect to r of the expression obtained from (18) and the left hand side -as a derivative in respect to z of the expression obtained from (17)). If we consider the first term of the asymptotic series for the velocity only, we obtain an interesting equation for v 0…”

“…The model has some relevant features. On the one hand, it allows one to obtain explicit solutions of the model problem; in addition, it permits good approximation in many particular physical problems (see, e.g., [16][17][18]). This is one reason for seeking of a new field of application for such an effective instrument.…”

Persistent current in a chain of two Holstein-Hubbard rings in the presence of Rashba spin-orbit interaction

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