Transport in open quantum systems: comparing classical and quantum phase space dynamics

Abstract

Transport in open quantum systems is of great interest. We show that the discrete states of an open quantum system may be classified into three distinct groups, dependent upon the manner in which they influence transport when connected to an external environment. A first class of states is current-carrying states, which are naturally strongly connected to the environment. A second class of states is discrete, but stable and isolated, and thought to be the pointer states of decoherence theory. Finally, we identify backscattered states, which do not propagate through the system. KeywordsOpen quantum systems · Conductance · Pointer states · ResonancesThe study of open quantum systems is important to gaining an understanding of how quantum states evolve into their classical counterparts [1]. This is particularly true in nanoelectronics devices, where the decoherence and phasebreaking processes are important. Such systems are open quantum systems interacting with their environment, the latter of which may be a bath or even a measurement system. The manner in which the quantum properties are revealed by such classical measurements, as well as the manner in which these quantum properties evolve into intrinsic classical properties, has long been of interest. One interpretation, which explicitly includes the coupling of the device to its environment, is decoherence theory [2]. However, the interpretation of the decoherence process has varied widely, and is crucially dependent upon the nature of the states that can exist within the device itself.In this paper, we show that the discrete states of an isolated quantum system may be classified into three groups, dependent upon the manner in which they influence transport when the system is opened. We show first that there is a class of current-carrying states, which are strongly connected to the environment. A second class of states is found to be a discrete set of stable, and isolated, states which are thought to be the so-called pointer states of decoherence theory [3]. (We have previously shown a connection to these pointer states in transport through open quantum dots [4].) We show how some of the current-carrying states can connect to the pointer states via phase-space tunneling processes to produce Fano resonances in the transmission. Finally, we identify backscattered states, which do not propagate through the system. We illustrate this with examples taken from experiments on a prototypical open quantum system, namely an open quantum dot array [5,6], which has been modeled both classically and quantum mechanically [7]. Such an array also connects to systems arising from periodic structures such as carbon nanotubes or molecules.Usually, transport through an open system is treated via electrodes configured as large reservoirs. However, we adopt a different approach that allows us to identify the connection between the quantum states of the open and closed system. Rather than treating the reservoirs in their normal sense, we introduce complex potentials at the contact regi...

Magneto-conductance fingerprints of purely quantum states in the open quantum dot limit

“…In this way, the density of state map of the closed system will have the relevant information about the electronic transport of the open system until the QPC value of w l . These low energy results using semi-infinite contact leads, related to current-carrying states [47], are different from those observed at high energies or with macroscopic reservoirs as contacts. In the last case the quantum-classical coupling occurs through a selective set of states or pointer states [9].…”