Action functionals for strings in four dimensions

All possible action functionals on the space of surfaces in ${\bf R}^4$ that depend only on first and second derivatives of the functions, entering the equation of the surface, and satisfy the condition of invariance with respect to rigid motions are described.Comment: 9 pages, LaTeX, 7 figure

Complex Susceptibility of Liquid Water as a Two-Potential System of Reorienting Polar Molecules

The theory elaborated in ref. 1 and 2 is applied to the calculation of the liquid water wide-band (0 < ν/cm^(-1) < 1000) dielectric spectra. These comprise the Debye relaxation region at the centimetre/millimetre wavelengths and the two-humped absorption coefficient frequency dependence in the far infrared (FIR) region. It is supposed that a major part of H2O molecules, called [L]-particles or [L]-molecules, are bonded by relatively strong H-bonds; [L]-molecules perform librations of relatively small amplitude β (β is about 20°). The remaining molecules called R-molecules have more rotational / translational mobility. A new microscopic molecular confined rotator / doble well potential (CR DWP) model of liquid water is developed. The contributions of [L]-and [R]-molecules to the complex permittivity ε are found on the basis of the confined rotator (CR) and the double well potential (DWP) models, with rectangular and cos^2(θ) intermolecular potential profiles, respectively. It is shown that the CR/DWP model gives a good description of the Debye relaxation and a qualitative description of FIR the dielectric spectra of water

Theory of Model Kohn-Sham Potentials and its Applications

The purpose of Kohn-Sham density functional theory is to develop increasingly accurate approximations to the exchange-correlation functional or to the corresponding potential. When one chooses to approximate the potential, the resulting model must be integrable, that is, a functional derivative of some density functional. Non-integrable potentials produce unphysical results such as energies that are not translationally or rotationally invariant. The thesis introduces methods for constructing integrable model potentials, developing properly invariant energy functionals from model potentials, and designing model potentials that yield accurate electronic excitation energies. Integrable potentials can be constructed using powerful analytic integrability conditions derived in this work. Alternatively, integrable potentials can be developed using the knowledge about the analytic structure of functional derivatives. When these two approaches are applied to the model potential of van Leeuwen and Baerends (which is non-integrable), they produce an exchange potential that has a parent functional and yields accurate energies. It is also shown that model potentials can be used to develop new energy functionals by the line-integration technique. When a model potential is not a functional derivative, the line integral depends on the choice of the integration path. By integrating the model potential of van Leeuwen and Baerends along the path of magnitude-scaled density, an accurate and properly invariant exchange functional is developed. Finally, a simple method to improve exchange-correlation potentials obtained from standard density-functional approximations is proposed. This method is based on the observation that an approximate Kohn-Sham potential of a fractionally ionized system is a better representation of the exact potential than the approximate Kohn-Sham potential of the corresponding neutral system. Removing 1/2 of an electron leads to the greatest improvement of the highest occupied molecular orbital energy, which explains why the Slater transition state method works well for predicting ionization energies. Removing about 1/4 of an electron improves orbital energy gaps and, when used in time-dependent density functional calculations, reduces errors of Rydberg excitation energies by almost an order of magnitude

Dielectric Response and a Phenomenon of a Narrow Band Absorption for a Classical Rotor in a Double Well Potential

The theory of dielectric relaxation in a planar ensemble of polar molecules is presented for a model where dipoles rotate in an intermolecular conservative double well potential, having a profile U = U_0*sin^2(θ). The evolution of the wide band dielectric spectra is demonstrated when the potential depth U_0 is varied; an isotropic and anisotropic medium being taken as examples. The spectra comprise the Debye relaxation and the quasi-resonant Poley absorption region. The rigorous theory is compared with a simplified one which was called the hybrid quasi-elastic bond / extended diffusion model. This approximation is valid for a qualitative description and also for the quantitative one at the large field parameter p = (U_0/((k_B)T))^(1/2). For P >> 1 the spectrum comprises one narrow absorption band and one Debye relaxation region considerably shifted to low frequencies. It is show that in the long lifetime limit τ there exists a minimum absorption band Δν_0(p). The quantity Δν_0 becomes small if the parameter p >> 1.The dielectric relaxation in ice 1 is discussed with regards to this phenomenon

Low-temperature acoustic characteristics of the amorphous alloy Zr41.2Ti13.8Cu12.5Ni10Be22.5

The temperature dependences of the sound velocity v and attenuation alpha of high-frequency (50–160 MHz) sound in the bulk amorphous alloy Zr41.2Ti13.8Cu12.5Ni10Be22.5 are studied at helium temperatures in the normal and superconducting states. The alloy is characterized by a relatively small constant C determining the intensity of interaction between an elastic wave and two-level systems. The density of states of the latter systems is estimated. The peculiarities in the variation of v during the superconducting transition point to the possibility of a gapless superconductivity in a narrow temperature interval near Tc

Electron affinity of liquid water.

Understanding redox and photochemical reactions in aqueous environments requires a precise knowledge of the ionization potential and electron affinity of liquid water. The former has been measured, but not the latter. We predict the electron affinity of liquid water and of its surface from first principles, coupling path-integral molecular dynamics with ab initio potentials, and many-body perturbation theory. Our results for the surface (0.8 eV) agree well with recent pump-probe spectroscopy measurements on amorphous ice. Those for the bulk (0.1-0.3 eV) differ from several estimates adopted in the literature, which we critically revisit. We show that the ionization potential of the bulk and surface are almost identical; instead their electron affinities differ substantially, with the conduction band edge of the surface much deeper in energy than that of the bulk. We also discuss the significant impact of nuclear quantum effects on the fundamental gap and band edges of the liquid