Electronic States and Transport Phenomena in Quantum Dot Systems

Electronic states and transport phenomena in semiconductor quantum dots are studied theoretically. Taking account of the electron-electron Coulomb interaction by the exact diagonalization method, the ground state and low-lying excited states are calculated as functions of magnetic field. Using the obtained many-body states, we discuss the temperature dependence of the conductance peaks in the Coulomb oscillation. In the Coulomb blockade region, elastic and inelastic cotunneling currents are evaluated under finite bias voltages. The cotunneling conductance is markedly enhanced by the Kondo effect. In coupled quantum dots, molecular orbitals and electronic correlation influence the transport properties.Comment: Review paper of our work, to appear in Proc. Int. Symp. on Formation, Physics and Device Application of Quantum Dot Structures (QDS 2000, Sapporo, Japan), Jpn. J. Appl. Phys. [11 pages, 6 figures

Sellars on Functionalism and Normativity

The term ‘functionalism’ is usually heard in connection with the philosophy of mind or cognition. The functionalism of Wilfrid Sellars, however, is in the first instance as response to the worries about the metaphysics not of mental states, but of meaning. Only late in his career did Sellars explore the possibility of extending his functionalism into an account of cognition. It has been suggested, though, that Sellars’ extension of his functionalist theory into subpersonal territory is not successful. In particular, there is a worry abroad that in order to be a functionalist about cognitive states, Sellars must succumb to a special form of the Myth of the Given. In this essay I will review and elucidate what I take to be the structure of Sellars’ functionalism, defending it from this worry. I will suggest a resolution of some apparent textual contradictions based in part on the chronology of Sellars’ writing, with the assumption that later writings express Sellars’ more nuanced views. Draft of 2009

The perturbation of the Seiberg-Witten equations revisited

We introduce a new class of perturbations of the Seiberg-Witten equations. Our perturbations offer flexibility in the way the Seiberg-Witten invariants are constructed and also shed a new light to LeBrun's curvature inequalities.Comment: typos correcte

The hamburger theorem

We generalize the ham sandwich theorem to $d+1$ measures in $\mathbb{R}^d$ as follows. Let $\mu_1,\mu_2, \dots, \mu_{d+1}$ be absolutely continuous finite Borel measures on $\mathbb{R}^d$. Let $\omega_i=\mu_i(\mathbb{R}^d)$ for $i\in [d+1]$, $\omega=\min\{\omega_i; i\in [d+1]\}$ and assume that $\sum_{j=1}^{d+1} \omega_j=1$. Assume that $\omega_i \le 1/d$ for every $i\in[d+1]$. Then there exists a hyperplane $h$ such that each open halfspace $H$ defined by $h$ satisfies $\mu_i(H) \le (\sum_{j=1}^{d+1} \mu_j(H))/d$ for every $i \in [d+1]$ and $\sum_{j=1}^{d+1} \mu_j(H) \ge \min(1/2, 1-d\omega) \ge 1/(d+1)$. As a consequence we obtain that every $(d+1)$-colored set of $nd$ points in $\mathbb{R}^d$ such that no color is used for more than $n$ points can be partitioned into $n$ disjoint rainbow $(d-1)$-dimensional simplices.Comment: 11 pages, 2 figures; a new proof of Theorem 8, extended concluding remark