Limited accuracy of conduction band effective mass equations for semiconductor quantum dots

Effective mass equations are the simplest models of carrier states in a semiconductor structures that reduce the complexity of a solid-state system to Schr\"odinger- or Pauli-like equations resempling those well known from quantum mechanics textbooks. Here we present a systematic derivation of a conduction-band effective mass equation for a self-assembled semiconductor quantum dot in a magnetic field from the 8-band kp theory. The derivation allows us to classify various forms of the effective mass equations in terms of a hierarchy of approximations. We assess the accuracy of the approximations in calculating selected spectral and spin-related characteristics. We indicate the importance of preserving the off-diagonal terms of the valence band Hamiltonian and argue that an effective mass theory cannot reach satisfactory accuracy without self-consistently including non-parabolicity corrections and renormalization of kp parameters. Quantitative comparison with the 8-band kp results supports the phenomenological Roth-Lax-Zwerdling formula for the g-factor in a nanostructure.Comment: Final versio

What is the meaning of the statistical hadronization model?

The statistical model of hadronization succeeds in reproducing particle abundances and transverse momentum spectra in high energy collisions of elementary particles as well as of heavy ions. Despite its apparent success, the interpretation of these results is controversial and the validity of the approach very often questioned. In this paper, we would like to summarize the whole issue by first outlining a basic formulation of the model and then comment on the main criticisms and different kinds of interpretations, with special emphasis on the so-called "phase space dominance". While the ultimate answer to the question why the statistical model works should certainly be pursued, we stress that it is a priority to confirm or disprove the fundamental scheme of the statistical model by performing some detailed tests on the rates of exclusive channels at lower energy.Comment: 14 pages, to be published in the Proceedings of the International workshop "Focus on multiplicity", Bari (Italy) June 17-19 200

Water alignment, dipolar interactions, and multiple proton occupancy during water-wire proton transport

A discrete multistate kinetic model for water-wire proton transport is constructed and analyzed using Monte-Carlo simulations. The model allows for each water molecule to be in one of three states: oxygen lone pairs pointing leftward, pointing rightward, or protonated (H$_{3}$O$^{+}$). Specific rules for transitions among these states are defined as protons hop across successive water oxygens. We then extend the model to include water-channel interactions that preferentially align the water dipoles, nearest-neighbor dipolar coupling interactions, and coulombic repulsion. Extensive Monte-Carlo simulations were performed and the observed qualitative physical behaviors discussed. We find the parameters that allow the model to exhibit superlinear and sublinear current-voltage relationships and show why alignment fields, whether generated by interactions with the pore interior or by membrane potentials {\it always} decrease the proton current. The simulations also reveal a ``lubrication'' mechanism that suppresses water dipole interactions when the channel is multiply occupied by protons. This effect can account for an observed sublinear-to-superlinear transition in the current-voltage relationship