Figure 1

(a) The original $Y$ junction of Q1D channels considered in this paper, (b) the reformulated $Y$ junction of tight-binding channels, and (c) the effective $Y$ junction of 1D channels affiliated with the Griffith or our connection scheme.Reuse & Permissions

Figure 2

(Color online) The doubly connected 1D system and the related Q1D system we consider. (a) The 1D system is a ring (with arms labeled by 1 and 2) connected to two leads (labeled by 0 and 3). The coodinate system $x_i$ is defined for the line segment labeled by $i$ ($i=0$, 1, 2, and 3). The arrows denote the positive directions of the coordinates, the right $Y$ junction is defined at $x_1=x_2=x_3=0$, and the left $Y$ junction at $x_0=0$, $x_1=L_1$, and $x_2=L_2$. (b) The Q1D system is an annulus with two radially connected leads. Both the annulus and the leads have the same width.Reuse & Permissions

Figure 3

(Color online) The transmission probability $T$ is plotted versus the dimensionless longitudinal wave numbers ($2L∕{\lambda }_{\Vert }$ in the case of Q1D channels, and $2L∕\lambda$ in the case of 1D channels), for the case of $L_1=L_2\equiv L$. The Q1D results (solid lines), 1D results due to our scheme [dashed $(\nu =1.9)$ and dash-dotted $(\nu =1)$ lines], and 1D results due to the Griffith scheme (dotted lines) are shown. $T$ is plotted for the cases of broad and narrow Q1D channels, (a) $R∕w=3.5$ and (b) $R∕w=9.5$. Note that the Griffith result is independent of the channel widths. In the narrow channel case (b), the difference between the Q1D and $\nu =1.9$ results is indiscernible in the scale of this graph.Reuse & Permissions

Figure 4

(Color online) The transmission probability $T$ is plotted versus the dimensionless longitudinal wave numbers [$(L_1+L_2)∕{\lambda }_{\Vert }$ in the case of Q1D channels, and $(L_1+L_2)∕\lambda$ in the case of 1D channels], for the case of asymmetrical arm lengths. The Q1D results (solid lines), 1D results due to our scheme [dashed $(\nu =1.9)$ and dash-dotted $(\nu =1)$ lines], and 1D results due to the Griffith scheme (dotted lines) are shown. $T$ is plotted for the cases of broad and narrow Q1D channels, with small and appreciable differences in the arm lengths. $T$ is plotted for (a) $R∕w=3.5$, $L_2∕L_1=0.9$, (b) $R∕w=9.5$, $L_2∕L_1=0.9$, (c) $R∕w=3.5$, $L_2∕L_1=0.7$, and (d) $R∕w=9.5$, $L_2∕L_1=0.7$. Note that the Griffith result is independent of the channel widths. In the narrow channel cases [(b) and (d)], the differences between the Q1D and $\nu =1.9$ results are indiscernible in the scale of this graph.Reuse & Permissions