Particle escapes in an open quantum network via multiple leads

Abstract

Quantum escapes of a particle from an end of a one-dimensional finite region to $N$ number of semi-infinite leads are discussed by a scattering theoretical approach. Depending on a potential barrier amplitude at the junction, the probability $P(t)$ for a particle to remain in the finite region at time $t$ shows two different decay behaviors after a long time; one is proportional to $N^{2}/t^{3}$ and another is proportional to $1/(N^{2}t)$. In addition, the velocity $V(t)$ for a particle to leave from the finite region, defined from a probability current of the particle position, decays in power $\sim 1/t$ asymptotically in time, independently of the number $N$ of leads and the initial wave function, etc. For a finite time, the probability $P(t)$ decays exponentially in time with a smaller decay rate for more number $N$ of leads, and the velocity $V(t)$ shows a time-oscillation whose amplitude is larger for more number $N$ of leads. Particle escapes from the both ends of a finite region to multiple leads are also discussed by using a different boundary condition.Comment: 16 pages, 7 figure

Escape dynamics of many hard disks

“…Escape phenomena are characterized by various quantities, such as the survival probability [32][33][34][35][36][37][38][39] as the probability for a particle to remain in an initially confined area, the escape time [28,40,41] as the time period for a particle to stay in the initial area, and a velocity of a particle escaping from the initial area [38], etc. These quantities decay in time as a feature of escape phenomena in which materials continue leaking from the initial area.…”

Influence of boundary conditions on quantum escape

“…non-escape) probability. On the quantum mechanical side, there has been a surge of renewed interest in the escape properties of few-particle systems [2][3][4][5][6][7], in connection with recent advances in experimental control and manipulation of a small number of ultra-cold atoms [8,9]. In particular, particle-particle interactions and quantum statistics have been shown to significantly influence the escape.…”

Quantum particle escape from a time-dependent confining potential

“…It appears in many physical phenomena, such as the α decay of a nucleus [1,2], radiative decay of molecules [3], transition of states in chemical reactions [4], etc. Studies on quantum escapes have been done in one-dimensional systems with a stationary potential barrier [5][6][7], billiard systems with leads [8], kicked rotator models [9][10][11], network systems [12][13][14], and manyparticle systems [15][16][17], and so on.…”

“…In quantum escapes, the survival probability decays exponentially in time [7,13,18,20], by tunneling via a potential barrier, etc. Moreover, it also shows a power decay after a long time [6,8,14,21,22]. As decay properties of the survival probability, time scales of its exponential decay [9][10][11], and changes of the power of decay under different conditions [14,16,17,23], etc.…”

“…Moreover, it also shows a power decay after a long time [6,8,14,21,22]. As decay properties of the survival probability, time scales of its exponential decay [9][10][11], and changes of the power of decay under different conditions [14,16,17,23], etc. have been studied.…”