States’ Rights, Southern Hypocrisy, and the Crisis of the Union

This article explores the arguments used by southern secessionists to explain why they left the Union. The article demonstrates that support for states\u27 rights was not the main reason for secession, and that on the contrary, most of the slave states left the Union because the free states were exercising their states\u27 rights in opposing slavery. The main reason for secession, as this essay shows, was the desire to protect slavery and to create a new nation, self-consciously based on slavery and white supremacy. This article began as part of an AALS legal history section program in 2010 and is part of a symposium based on the papers given at that session

Unfolding spinor wavefunctions and expectation values of general operators: Introducing the unfolding-density operator

We show that the spectral weights $W_{m\vec K}(\vec k)$ used for the unfolding of two-component spinor eigenstates $| {\psi_{m\vec K}^\mathrm{SC}} > = | \alpha > | {\psi_{m\vec{K}}^\mathrm{SC, \alpha}} > + | \beta > | {\psi_{m\vec{K}}^\mathrm{SC, \beta}} >$ can be decomposed as the sum of the partial spectral weights $W_{m\vec{K}}^{\mu}(\vec k)$ calculated for each component $\mu = \alpha, \beta$ independently, effortlessly turning a possibly complicated problem involving two coupled quantities into two independent problems of easy solution. Furthermore, we define the unfolding-density operator $\hat{\rho}_{\vec{K}}(\vec{k}_{i}; \, \varepsilon)$, which unfolds the primitive cell expectation values $\varphi^{pc}(\vec{k}; \varepsilon)$ of any arbitrary operator $\mathbf{\hat\varphi}$ according to $\varphi^{pc}(\vec{k}_{i}; \varepsilon) = \mathit{Tr}(\hat{\rho}_{\vec{K}}(\vec{k}_{i}; \, \varepsilon)\,\,\hat{\varphi})$. As a proof of concept, we apply the method to obtain the unfolded band structures, as well as the expectation values of the Pauli spin matrices, for prototypical physical systems described by two-component spinor eigenfunctions

Visualization and thermodynamic encoding of single-molecule partition functions

Ensemble averaging of molecular states is fundamental for the experimental determination of thermodynamic quantities. A special case occurs for single-molecule investigations under equilibrium conditions, for which free energy, entropy and enthalpy at finite-temperatures are challenging to determine with ensemble-averaging alone. Here, we provide a method to access single-molecule thermodynamics, by confining an individual molecule to a nanoscopic pore of a two-dimensional metal-organic nanomesh, where we directly record finite-temperature time-averaged statistical weights using temperature-controlled scanning tunneling microscopy. The obtained patterns represent a real space equilibrium probability distribution. We associate this distribution with a partition function projection to assess spatially resolved thermodynamic quantities, by means of computational modeling. The presented molecular dynamics based Boltzmann weighting model is able to reproduce experimentally observed molecular states with high accuracy. By an in-silico customized energy landscape we demonstrate that distinct probability distributions can be encrypted at different temperatures. Such modulation provides means to encode and decode information into position-temperature space or to realize nanoscopic thermal probes.Comment: 20 Pages Main text, 5 Figures. 10 Pages Annexed tex