One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures

In this review we provide a rigorous and self-contained presentation of one-body reduced density-matrix (1RDM) functional theory. We do so for the case of a finite basis set, where density-functional theory (DFT) implicitly becomes a 1RDM functional theory. To avoid non-uniqueness issues we consider the case of fermionic and bosonic systems at elevated temperature and variable particle number, i.e, a grand-canonical ensemble. For the fermionic case the Fock space is finite-dimensional due to the Pauli principle and we can provide a rigorous 1RDM functional theory relatively straightforwardly. For the bosonic case, where arbitrarily many particles can occupy a single state, the Fock space is infinite-dimensional and mathematical subtleties (not every hermitian Hamiltonian is self-adjoint, expectation values can become infinite, and not every self-adjoint Hamiltonian has a Gibbs state) make it necessary to impose restrictions on the allowed Hamiltonians and external non-local potentials. For simple conditions on the interaction of the bosons a rigorous 1RDM functional theory can be established, where we exploit the fact that due to the finite one-particle space all 1RDMs are finite-dimensional. We also discuss the problems arising from 1RDM functional theory as well as DFT formulated for an infinite-dimensional one-particle space.Comment: 55 pages, 7 figure

Politicians’ Motivation, Political Culture, and Electoral Competition

We study electoral competition among politicians who are heterogeneous both in competence and in how much they care about (what they perceive as) the public interest relative to the private rents from being in office. We show that politicians’ incentives to behave opportunistically increase with politicians’ pay and with polarization of policy preferences. Moreover, politicians may have stronger incentives to behave opportunistically if other politicians are more likely to behave opportunistically. A political culture may therefore be selfreinforcing and multiple equilibria may arise. Lastly, we show that the mere probability that politicians care about the public interest enables opportunistic politicians to damage the reputation of their competitors. Consequently, efficient policies may be reversed.politicians’ motivation, politicians’ pay, political culture, electoral competition, coalition governments, reputation bashing

Structural relaxation in the hydrogen-bonding liquids N-methylacetamide and water studied by optical Kerr-effect spectroscopy

Structural relaxation in the peptide model N-methylacetamide (NMA) is studied experimentally by ultrafast optical Kerr-effect spectroscopy over the normal-liquid temperature range and compared to the relaxation measured in water at room temperature. It is seen that in both hydrogen-bonding liquids, beta relaxation is present and in each case it is found that this can be described by the Cole-Cole function. For NMA in this temperature range, the alpha and beta relaxations are each found to have an Arrhenius temperature dependence with indistinguishable activation energies. It is known that the variations on the Debye function, including the Cole-Cole function, are unphysical, and we introduce two general modifications: one allows for the initial rise of the function, determined by the librational frequencies, and the second allows the function to be terminated in the alpha relaxation

Textural evolution and phase transformation in titania membranes: Part 1. -unsupported membranes

Textural evolution in sol–gel derived nanostructured unsupported titania membranes has been studied using differential scanning calorimetry (DSC), differential thermal analysis (DTA), thermal gravimetry (TG), X-ray diffraction (XRD) and N2 adsorption. The anatase-to-rutile phase transformation kinetics were studied using the Avrami model. The precursor gel had a surface area of ca. 165 m2 g–1, which after heat treatment at 600 °C for 8 h reduced to zero. Undoped titania-gel layers transformed to more than 95% rutile after calcination at 600 °C for 8 h. The causes of surface-area reduction and pore growth were anatase crystallite growth and the enhanced sintering of rutile during transformation. Lanthanum oxide was identified as a suitable dopant for shifting the transformation temperature to ca. 850 °C. Lanthanum oxide doped titania showed an improved stability of porous texture compared to that of the undoped titania membranes

Response calculations based on an independent particle system with the exact one-particle density matrix: polarizabilities

Recently, we have demonstrated that the problems finding a suitable adiabatic approximation in time-dependent one-body reduced density matrix functional theory can be remedied by introducing an additional degree of freedom to describe the system: the phase of the natural orbitals [Phys. Rev. Lett. 105, 013002 (2010), J. Chem. Phys. 133, 174119 (2010)]. In this article we will show in detail how the frequency-dependent response equations give the proper static limit ($\omega\to0$), including the perturbation in the chemical potential, which is required in static response theory to ensure the correct number of particles. Additionally we show results for the polarizability for H$_2$ and compare the performance of two different two-electron functionals: the phase-including L\"owdin-Shull functional and the density matrix form of the L\"owdin-Shull functional.Comment: 10 pages, 6 figure

Spectrum of slow and super-slow (picosecond to nanosecond) water dynamics around organic and biological solutes

Water dynamics in the solvation shell of solutes plays a very important role in the interaction of biomolecules and in chemical reaction dynamics. However, a selective spectroscopic study of the solvation shell is difficult because of the interference of the solute dynamics. Here we report on the observation of heavily slowed down water dynamics in the solvation shell of different solutes by measuring the low-frequency spectrum of solvation water, free from the contribution of the solute. A slowdown factor of ~50 is observed even for relatively low concentrations of the solute. We go on to show that the effect can be generalized to different solutes including proteins