Time-dependent quantum graph

Abstract

In this paper, we study quantum star graphs with time-dependent bond lengths. Quantum dynamics are treated by solving Schrodinger equation with time-dependent boundary conditions given on graphs. The time-dependence of the average kinetic energy is analyzed. The space-time evolution of a Gaussian wave packet is treated for an harmonically breathing star graph.

Photon generation in resonator with time dependent boundary conditions

“…Here, formalism of quantum graphs is widely used [20,26,27]. In this way, a number of spectral and transport problems were considered, particularly, with parameter-dependent or time-dependent characteristics (see, e.g., [21,22,[28][29][30]).…”

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

“…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].…”

Wave dynamics on timedepending graph with Aharonov–Bohm ring

“…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.…”