Singlet-triplet oscillations and far-infrared spectrum of four-minima quantum-dot molecule

We study ground states and far-infrared spectra (FIR) of two electrons in four-minima quantum-dot molecule in magnetic field by exact diagonalization. Ground states consist of altering singlet and triplet states, whose frequency, as a function of magnetic field, increases with increasing dot-dot separation. When the Zeeman energy is included, only the two first singlet states remain as ground states. In the FIR spectra, we observe discontinuities due to crossing ground states. Non-circular symmetry induces anticrossings, and also an additional mode above $\omega_+$ in the spin-triplet spectrum. In particular, we conclude that electron-electron interactions cause only minor changes to the FIR spectra and deviations from the Kohn modes result from the low-symmetry confinement potential.Comment: 4 pages, 3 figures, QD2004 conference paper, accepted in Physica

Vertex covering with monochromatic pieces of few colours

In 1995, Erd\H{o}s and Gy\'arf\'as proved that in every $2$-colouring of the edges of $K_n$, there is a vertex cover by $2\sqrt{n}$ monochromatic paths of the same colour, which is optimal up to a constant factor. The main goal of this paper is to study the natural multi-colour generalization of this problem: given two positive integers $r,s$, what is the smallest number $\text{pc}_{r,s}(K_n)$ such that in every colouring of the edges of $K_n$ with $r$ colours, there exists a vertex cover of $K_n$ by $\text{pc}_{r,s}(K_n)$ monochromatic paths using altogether at most $s$ different colours? For fixed integers $r>s$ and as $n\to\infty$, we prove that $\text{pc}_{r,s}(K_n) = \Theta(n^{1/\chi})$, where $\chi=\max{\{1,2+2s-r\}}$ is the chromatic number of the Kneser gr aph $\text{KG}(r,r-s)$. More generally, if one replaces $K_n$ by an arbitrary $n$-vertex graph with fixed independence number $\alpha$, then we have $\text{pc}_{r,s}(G) = O(n^{1/\chi})$, where this time around $\chi$ is the chromatic number of the Kneser hypergraph $\text{KG}^{(\alpha+1)}(r,r-s)$. This result is tight in the sense that there exist graphs with independence number $\alpha$ for which $\text{pc}_{r,s}(G) = \Omega(n^{1/\chi})$. This is in sharp contrast to the case $r=s$, where it follows from a result of S\'ark\"ozy (2012) that $\text{pc}_{r,r}(G)$ depends only on $r$ and $\alpha$, but not on the number of vertices. We obtain similar results for the situation where instead of using paths, one wants to cover a graph with bounded independence number by monochromatic cycles, or a complete graph by monochromatic $d$-regular graphs

Role of interactions in the far-infrared spectrum of a lateral quantum dot molecule

We study the effects of electron-electron correlations and confinement potential on the far-infrared spectrum of a lateral two-electron quantum dot molecule by exact diagonalization. The calculated spectra directly reflect the lowered symmetry of the external confinement potential. Surprisingly, we find interactions to drive the spectrum towards that of a high-symmetry parabolic quantum dot. We conclude that far-infrared spectroscopy is suitable for probing effective confinement of the electrons in a quantum dot system, even if interaction effects cannot be resolved in a direct fashion.Comment: 4 pages, 2 figure

The exclusionary approach to consciousness

The standard approach in the field of consciousness research involves identifying the neural correlates of consciousness (NCCs) by comparing neural activity between conscious and unconscious trials. However, this method has been met with criticism due to the lack of consensus on how to operationalize and measure consciousness. In this paper, I propose an alternative approach: the exclusionary approach. Rather than utilizing near-threshold conditions to contrast conscious and unconscious trials, this approach leverages the widely accepted notion that subjective reports are reliable under normal conditions. I propose that this can be done by assessing whether consciousness remains stable across trials while manipulating other factors such as reports, tasks, stimulation, or attention. We can use the resulting contrast to exclude certain kinds of neural activity as candidate NCCs. This method produces results that are less contentious, allowing for the establishment of hard criteria for theories of consciousness. Additionally, this approach does not require the development of new research paradigms, but can incorporate existing studies, particularly those aimed at identifying confounding factors in the standard approach. It is important to note, however, that the proposed exclusionary approach does not negate the value of the identification approach. Rather, they should be considered as complementary methods.Peer Reviewe

Shifting Cases: Advancing a New Artifact for Entrepreneurial Education

Entrepreneurship, as applied here, involves helping students develop an entrepreneurial mindset by working in a university-supported startup that lacks the artificiality of a simulation or the safety net of heavy financial subsidization. This article chronicles an organizational-wide change at a private Midwestern university and the development of a new “artifact”—the dynamic case study—to complement a new approach to business and entrepreneurial education. After reviewing the function of case studies in a teaching and research context, I consider this new kind of case study as a boundary object and means for making sense of early stage entrepreneurial activity