Parasupersymmetry in quantum graphs

Abstract

We study hidden parasupersymmetry structures in purely bosonic quantum mechanics on compact equilateral graphs. We consider a single free spinless particle on the graphs and show that the Huang-Su parasupersymmetry algebra is hidden behind degenerate spectra.

Path topology dependence of adiabatic time evolution

“…We have shown the path topology dependence of adiabatic time evolution in closed quantum systems through a topological argument, which is based on the recent study on the exotic quantum holonomy [17]. We finally note that examples of systems exhibit non-trivial adiabatic path topology dependence, according to the studies of exotic quantum holonomy in, for example, quantum graphs with generalized connection conditions [30][31][32][33], many-qubit systems [34], adiabatic quantum computation [14], and the Lieb-Liniger model [35].…”

Non-Abelian monopole in the parameter space of point-like interactions

“…We note that most of the materials presented in this section are already known and discussed in Ref. [5] (see also [7]). But some of the materials are new.…”

“…In order to make this note self-contained, we will reproduce all the relevant results. We also note that this section is mostly based on our previous work [7], with some minor changes to make things clearer.…”

Instantons and Berry's connections on quantum graph

“…(For reviews of quantum graph, see [1,2].) This system has been applied to various research areas such as scattering theory, nanotechnology on one dimensional graphs [3][4][5][6], quantum chaos [7][8][9], supersymmetric quantum mechanics [10][11][12], extra dimensional models [13][14][15] and so on, due to fascinating structures from boundary conditions. Therefore, the study of boundary conditions on the quantum graph will contribute to the further development of low and high energy physics.…”