Hartman effect and nonlocality in quantum networks

Abstract

We study the phase time for various quantum mechanical networks having potential barriers in its arms to find the generic presence of Hartman effect. In such systems it is possible to control the 'super arrival' time in one of the arms by changing parameters on another, spatially separated from it. This is yet another quantum nonlocal effect. Negative time delays (time advancement) and 'ultra Hartman effect' with negative saturation times have been observed in some parameter regimes.

Controllable Hartman effect by vortex beam in a one dimensional photonic crystal doped by graphene quantum dots

“…This phenomenon, which implies the superluminal light propagation, is referred as a Hartman effect [6-8]. The Hartman effect was investigated in various proposals including spin waves [9], eld emission [10], graphene systems [11], quantum networks [12].…”

Particle escapes in an open quantum network via multiple leads

“…The quantum network system is also called the "quantum graph" and is constructed by connecting finite and infinite narrow wires like a network. It also has been widely used as a model to describe mesoscopic transport such as Aharonov-Bohm types of effects [29,30], resonance tunnellings [31,32], current splitters [33][34][35][36], chaos and diffusion [37,38], and so on. Steady electric currents in open quantum network systems are described by quantum scattering theory [39][40][41][42].…”

“…In this paper we discuss particle escapes in quantum mechanical networks as an example of open dynamical systems. The quantum network system is also called the "quantum graph," and is constructed by connecting finite and infinite narrow wires like a network, and have been widely used as models to describe mesoscopic transports like Aharonov-Bohm type of effects [27,28], resonance tunnellings [29,30], current splitters [31][32][33], chaos and diffusion [34,35], etc.…”

Phase Time for a Tunneling Particle

“…The paper is organized as follows. In section 2 we present phase times 29 for branched networks of quantum wires which can readily be realized in optical wave propagation experiments. This geometry allows us to check other nonlocality effect such as tuning of the saturation value of 'phase time' and consequently the superluminal speed in one branch by changing barrier strength or length in any other branch, spatially separated from the former.…”

“…In section 3 we study the Hartman effect on a quantum ring geometry i.e. beyond one dimension and in the presence of AB-flux 28,30 . Our results confirm 'Hartman effect' in quantum ring even in presence of AB-flux.…”