Open quantum dots: II. Probing the classical to quantum transition

Abstract

Open quantum dots provide a natural system in which to study both classical and quantum features of transport. From the classical point of view these dots possess a mixed phase space which yields families of closed, regular orbits as well as an expansive sea of chaos. An important question concerns the manner in which these classical states evolve into the set of quantum states that populate the dot in the quantum limit. In the reverse direction, the manner in which the quantum states evolve to the classical world is governed strongly by Zurek's decoherence theory. This was discussed from the quantum perspective in an earlier review (Ferry et al 2011 Semicond. Sci. Technol. 26 043001). Here, we discuss the nature of the various classical states, how they are formed, how they progress to the quantum world, and the signatures that they create in magnetotransport and general conductance studies of these dots.

Fano resonances of microwave structures with embedded magneto-dipolar quantum dots

“…A spectrum of MDM quantization in a small ferrite-disk particle as a function of a bias magnetic field is very akin to a spectrum of charge quantization in a small metallic or semiconductor particle (quantum dots) as a function of a bias voltage shown in Refs. [38,39]. Following our previous discussions as well as discussions in Refs.…”

“…38,39 While a spectrum of MDM quantization in a small ferrite-disk particle is a function of a bias magnetic field, a spectrum of charge quantization in a small metallic or semiconductor particle (quantum dots) is a function of a bias voltage. 38,39 It is worth note also that the observed topologically distinctive energy eigenstates, appearing due to scattering of the cavity fields at the quasistatic-field MDM oscillations with the spin and orbital rotational motions, 21,34 are the Lorentz-violation excitations. The Lorentz violation is associated with rotations and boosts of localized field configurations in a fixed observer inertial frame.…”

“…Following our previous discussions as well as discussions in Refs. [38,39], we can say that both of them are artificial-atom spectra with energy eigenstates. When a MDM disk is embedded into a microwave structure, one has a dynamic system with mixed phase space.…”

Conductance stability in chaotic and integrable quantum dots with random impurities

“…Random disorders can also reduce the number of quantum pointer states. However, if a strong magnetic field is present, the nature of the classical dynamics and/or random disorders will have less pronounced effects on quantum transport [17,18,76]. One set of the quantum pointer states are associated with the stable orbits within the KAM islands in the classical phase space.…”

“…In particular, for mesoscopic systems in the ballistic transport regime, at low temperatures the conductance fluctuations tend to be independent of the sample size and impurities [1] and thus can serve as a probe of quantum chaos [5], a field aiming to uncover and understand the quantum manifestations of classical chaos [6]. For over two decades quantum dot systems have become a paradigm to study quantum chaotic scattering [7,8], and there has been a large body of literature on the effects of distinct types of classical dynamics on conductance fluctuations [9][10][11][12][13][14][15][16][17][18][19]. A basic result is that, for systems with integrable or mixed classical dynamics, the conductance curves typically contain a large number of Fano resonances [20][21][22][23][24], leading to sharp conductance fluctuations.…”