We report the observation of a metal-insulator transition at B 0 in a high mobility two dimensional hole gas in a GaAs-AlGaAs heterostructure. A clear critical point separates the insulating phase from the metallic phase, demonstrating the existence of a well defined minimum metallic conductivity s min 2e 2 ͞h. The s͑T͒ data either side of the transition can be "scaled" onto one curve with a single parameter T 0 . The application of a parallel magnetic field increases s min and broadens the transition. We argue that strong electron-electron interactions (r s Ӎ 10) suppress quantum interference corrections to the conductivity. [S0031-9007(98)05325-3] PACS numbers: 73.20.Dx, 71.30. + h, 73.20.Fz In the mid-1970s experiments on silicon inversion layers produced considerable evidence for the existence of a metal-insulator transition in 2D and a minimum metallic conductance, s min [1-3]. The decay constants of localized state wave functions were investigated, and it was shown that when the number of localized electrons exceeded 2 3 10 11 cm 22 the location of the mobility edge was determined by electron-electron interactions and increased with increasing carrier concentration. Subsequent theoretical work in 1979 suggested that all states in 2D were localized [4] and that phase incoherent scattering imposed a cutoff to a localized wave function giving a logarithmic correction to metallic conduction (weak localization) which was widely observed and used to obtain very detailed information on the various types of electronelectron scattering in all three dimensions [5,6]. However, in order to investigate the logarithmic correction at low, but accessible, temperatures it was necessary to use samples with low mobility so that the elastic scattering length l was small [7]. In view of the success of the theory it was then assumed that the earlier high mobility samples did not show a logarithmic correction because the phase coherence length l f was not greater than the elastic scattering length, but that if experiments could be performed at much lower temperatures (beyond the capability of cryogenics) then the logarithmic correction would be found.Recent experimental results have raised this issue again and indicate that states in 2D are not always localized with strong evidence for a metal-insulator transition in high mobility Si metal-oxide-semiconductor field-effect transistors (MOSFETs) [8]. It was found that the resistivity on both the metallic and insulating sides of the transition varied exponentially with decreasing temperature, and that a single scaling parameter could be used to collapse the data on both sides of the transition onto a single curve. While the exact nature of the transition is presently not understood, there have been several reports of similar scaling and duality between the resistivity (and conductivity) on opposite sides of the transition, both for electrons in Si MOSFETs [9,10] and for holes in SiGe quantum wells [11]. In all of these reports electron-electron interactions are known to be import...

The fractional quantum Hall effect 1 occurs in the conduction properties of a two-dimensional electron gas subjected to a strong perpendicular magnetic field. In this regime, the Hall conductance shows plateaux, or fractional states, at rational fractional multiples of e 2 /h, where e is the charge of an electron and h is Planck's constant. The explanation 1-3 of this behaviour invokes strong Coulomb interactions among the electrons that give rise to fractionally charged quasiparticles which can be regarded as noninteracting current carriers 1-5 . Previous studies 4,5 have demonstrated the existence of quasiparticles with one-third of an electron's charge, the same fraction as that of the respective fractional state. An outstanding ambiguity is therefore whether these studies measured the charge or the conductance. Here we report the observation of quasiparticles with a charge of e/5 in the 2/5 fractional state, from measurements of shot noise in a twodimensional electron gas 4 . Our results imply that charge can be measured independently of conductance in the fractional quantum Hall regime, generalizing previous observations of fractionally charged quasiparticles.In the fractional quantum Hall (FQH) regime, the first Landau level is partly populated, or 'fractionally filled'. Laughlin's explanation of the FQH effect 1-3 involved the emergence of new, fractionally charged, quasiparticles. Shot-noise measurements 4,5 have confirmed the existence of these quasiparticles in the FQH regime. Shot noise, resulting from the granular nature of the particles, is proportional to the charge of the current carriers, in this case quasiparticles 4,5 . In these experiments a quantum point contact (QPC) embedded in a two-dimensional electron gas (2DEG), serving as a potential constriction, was used as an electronic 'beam splitter'. Its purpose is to partly reflect back the incoming current and lead to partitioning of carriers and hence to shot noise. An applied magnetic field corresponding to fractional filling factors (in the bulk far from the QPC) of n B ¼ 1=3 in ref. 4 or 2/3 in ref. 5, was employed. Charge was deduced via the generalized equation for shot noise of non-interacting particles (the classical and simplified version is the Schottky formula: S ¼ 2qI B , with S the low-frequency spectral density of current fluctuations, I B the reflected current, and q the charge of the current-carrying particle). For small reflection by the QPC (small I B ) the quasiparticle's charge was found to be e/3 (ref. 4 and 5), as predicted theoretically 6-8 . The theories are based on the chiral Luttinger-liquid model and are applicable only for Laughlin fractional states, for example, 1/3, 1/5, and so on. For other, more general filling factors (such as n ¼ 2=5), however, such calculations become exceedingly complicated. Still, one can gain insight into the characteristics of the expected shot noise in such cases by considering the more intuitive composite fermion (CF) model 9,10 .Laughlin suggested that in the FQH regime the current is c...

Rational models of cognition typically consider the abstract computational problems posed by the environment, assuming that people are capable of optimally solving those problems. This differs from more traditional formal models of cognition, which focus on the psychological processes responsible for behavior. A basic challenge for rational models is thus explaining how optimal solutions can be approximated by psychological processes. We outline a general strategy for answering this question, namely to explore the psychological plausibility of approximation algorithms developed in computer science and statistics. In particular, we argue that Monte Carlo methods provide a source of rational process models that connect optimal solutions to psychological processes. We support this argument through a detailed example, applying this approach to Anderson's (1990, 1991) rational model of categorization (RMC), which involves a particularly challenging computational problem. Drawing on a connection between the RMC and ideas from nonparametric Bayesian statistics, we propose 2 alternative algorithms for approximate inference in this model. The algorithms we consider include Gibbs sampling, a procedure appropriate when all stimuli are presented simultaneously, and particle filters, which sequentially approximate the posterior distribution with a small number of samples that are updated as new data become available. Applying these algorithms to several existing datasets shows that a particle filter with a single particle provides a good description of human inferences

The charge of quasiparticles in a fractional quantum Hall (FQH) liquid, tunneling through a partly reflecting constriction with transmission t, was determined via shot noise measurements. In the ν = 1/3 FQH state, a charge smoothly evolving from e * = e/3 for t 1/3 ∼ = 1 to e * = e for t 1/3 ≪ 1 was determined, agreeing with chiral Luttinger liquid theory. In the ν = 2/5 FQH state the quasiparticle charge evolves smoothly from e * = e/5 at t 2/5 ∼ = 1 to a maximum charge less than e * = e/3 at t 2/5 ≪ 1. Thus it appears that quasiparticles with an approximate charge e/5 pass a barrier they see as almost opaque.PACS numbers: 73.20. Hm, 71.10.Pm, 73.50.Td The fractional quantum Hall (FQH) effect is a manifestation of the prominent and unique effects resulting from the Coulomb interactions between electrons in a two-dimensional electron gas (2DEG) under the influence of a strong magnetic field [1]. In this regime the lowest Landau level is partially populated. Laughlin's seminal explanation of the FQH effect [2] involved the emergence of intriguing fractionally charged quasiparticles. Recently, shot noise measurements confirmed the existence of such quasiparticles with charge e/3 and e/5 at filling factors ν = 1/3 [3] and ν = 2/5 [4], respectively. These experiments relied on the fact that shot noise, resulting from the granular nature of the quasiparticles, is proportional to their charge. Since current flowing in an ideal Hall state is noiseless [4] a quantum point contact (QPC) constriction was used to weakly reflect the incoming current, leading to partitioning of the incoming carriers and hence to shot noise. A charge e * was then deduced from the shot noise expression derived for non-interacting particles [5]. In this paper, we extend the range of QPC reflection to the strong back-scattering limit, where the apparent noise-producing quasiparticle charge is expected to be different. Specifically, an opaque barrier is expected to allow only the tunneling of electrons, as both sides of the barrier should be quantized in units of the electronic charge. How this charge evolves is an important question in the understanding of the behavior of quasiparticles, and here we explore the evolution of the charge of the e/3 and e/5 quasiparticles. We first briefly describe the expected dependence of shot noise on charge and transmission.At zero temperature (T = 0), the shot noise contribution of the p'th channel is [5,6]:where S is the low frequency (f << eV /h) spectral density of current fluctuations (S∆f = i 2 ), V the applied source-drain voltage, g p the conductance of the fully transmitted p'th channel in the QPC, and t p is its transmission coefficient. This reduces to the well known classical Poissonian expression for shot noise when t p ≪ 1 (the 'Schottky equation'), S T =0 = 2eI, with I = V g p t p the DC current in the QPC.The justification for the use of Eq. (1) comes from current theoretical studies of shot noise in the FQH regime, based on the chiral Luttinger liquid model. They are applicable only for Laug...

When faced with a decision between several options, people rarely fully consider every alternative. Instead, we direct our attention to the most promising candidates, focusing our limited cognitive resources on evaluating the options that we are most likely to choose. A growing body of empirical work has shown that attention plays an important role in human decision making, but it is still unclear how people choose with option to attend to at each moment in the decision making process. In this paper, we present an analysis of how a rational decision maker should allocate her attention. We cast attention allocation in decision making as a sequential sampling problem, in which the decision maker iteratively selects from which distribution to sample in order to update her beliefs about the values of the available alternatives. By approximating the optimal solution to this problem, we derive a model in which both the selection and integration of evidence are rational. This model predicts choices and reaction times, as well as sequences of visual fixations. Applying the model to a ternary-choice dataset, we find that its predictions align well with human data.