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

Abstract

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.

Correspondence of topological classification between quantum graph extra dimension and topological matter

“…We mention that R should have the determinant det R = +1 since this matrix also belongs to the symplectic group. 6 We can write R as…”

“…This graph has been applied to the wide range of research areas, e.g. scattering theory on 1d graphs [3][4][5][6], quantum chaos [7][8][9], anyons [10][11][12], supersymmetric quantum mechanics [13][14][15], Berry's phases [16][17][18][19] and so on.…”

Instantons and Berry's connections on quantum graph

“…• The case of (N, K, l) = (6,4,4) In this case, there are two independent zero modes for f (i) 0 and the Berry's connection can be given as the SU(2) instantons with the topological charge Q = ±2. The vectors α q (q = 9, 10, 11, 12) are linearly independent with each other.…”

“…(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.…”

5d Dirac fermion on quantum graph

“…In 3 There are many studies in terms of star graphs, see e.g. [26][27][28][29]. In particular, several works have been carried out from the viewpoint of extra dimensions on star graphs which are realized by flux compactifications in string theory, see [30][31][32][33][34][35].…”