BCS and generalized BCS superconductivity in relativistic quantum field theory. I. formulation

We investigate the BCS and generalized BCS theories in the relativistic quantum field theory. We select the gauge freedom as U(1), and introduce a BCS-type effective attractive interaction. After introducing the Gor'kov formalism and performing the group theoretical consideration of the mean fields, we solve the relativistic Gor'kov equation and obtain the Green's functions in analytical forms. We obtain various types of gap equations.Comment: 31 page

Electric field response of strongly correlated one-dimensional metals: a Bethe-Ansatz density functional theory study

We present a theoretical study on the response properties to an external electric field of strongly correlated one-dimensional metals. Our investigation is based on the recently developed Bethe-Ansatz local density approximation (BALDA) to the density functional theory formulation of the Hubbard model. This is capable of describing both Luttinger liquid and Mott-insulator correlations. The BALDA calculated values for the static linear polarizability are compared with those obtained by numerically accurate methods, such as exact (Lanczos) diagonalization and the density matrix renormalization group, over a broad range of parameters. In general BALDA linear polarizabilities are in good agreement with the exact results. The response of the exact exchange and correlation potential is found to point in the same direction of the perturbing potential. This is well reproduced by the BALDA approach, although the fine details depend on the specific parameterization for the local approximation. Finally we provide a numerical proof for the non-locality of the exact exchange and correlation functional.Comment: 8 pages and 8 figure

Entanglement entropy and entanglement witnesses in models of strongly interacting low-dimensional fermions

We calculate the entanglement entropy of strongly correlated low-dimensional fermions in metallic, superfluid and antiferromagnetic insulating phases. The entanglement entropy reflects the degrees of freedom available in each phase for storing and processing information, but is found not to be a state function in the thermodynamic sense. The role of critical points, smooth crossovers and Hilbert space restrictions in shaping the dependence of the entanglement entropy on the system parameters is illustrated for metallic, insulating and superfluid systems. The dependence of the spin susceptibility on entanglement in antiferromagnetic insulators is obtained quantitatively. The opening of spin gaps in antiferromagnetic insulators is associated with enhanced entanglement near quantum critical points.Comment: 5 pages, 5 figures, accepted by PR

Thermodynamics as an alternative foundation for zero-temperature density functional theory and spin density functional theory

Thermodynamics provides a transparent definition of the free energy of density functional theory (DFT), and of its derivatives - the potentials, at finite temperatures T. By taking the T to 0 limit, it is shown here that both DFT and spin-dependent DFT (for ground states) suffer from precisely the same benign ambiguities: (a) charge and spin quantization lead to "up to a constant" indeterminacies in the potential and the magnetic field respectively, and (b) the potential in empty subspaces is undetermined but irrelevant. Surprisingly, these simple facts were inaccessible within the standard formulation, leading to recent discussions of apparent difficulties within spin-DFT.Comment: RevTeX, to appear in Phys. Rev.

Surveying the solar system by measuring angles and times: from the solar density to the gravitational constant

A surprisingly large amount of information on our solar system can be gained from simple measurements of the apparent angular diameters of the sun and the moon. This information includes the average density of the sun, the distance between earth and moon, the radius of the moon, and the gravitational constant. In this note it is described how these and other quantities can be obtained by simple earthbound measurements of angles and times only, without using any explicit information on distances between celestial bodies. The pedagogical and historical aspects of these results are also discussed briefly.Comment: 12 pges, one figur

The generator coordinate method in time-dependent density-functional theory: memory made simple

The generator coordinate (GC) method is a variational approach to the quantum many-body problem in which interacting many-body wave functions are constructed as superpositions of (generally nonorthogonal) eigenstates of auxiliary Hamiltonians containing a deformation parameter. This paper presents a time-dependent extension of the GC method as a new approach to improve existing approximations of the exchange-correlation (XC) potential in time-dependent density-functional theory (TDDFT). The time-dependent GC method is shown to be a conceptually and computationally simple tool to build memory effects into any existing adiabatic XC potential. As an illustration, the method is applied to driven parametric oscillations of two interacting electrons in a harmonic potential (Hooke's atom). It is demonstrated that a proper choice of time-dependent generator coordinates in conjunction with the adiabatic local-density approximation reproduces the exact linear and nonlinear two-electron dynamics quite accurately, including features associated with double excitations that cannot be captured by TDDFT in the adiabatic approximation.Comment: 10 pages, 13 figure

A Note on the Hydrogen Bonding in Isomeric Aminopyridines in Relation to their Basicities

Physicians commonly advise patients to begin disease modifying therapies (DMT's) shortly after the establishment of a diagnosis of Multiple Sclerosis (MS) to prevent further relapses and disease progression. However, little is known about the meaning for patients going through the process of the diagnosis of MS and of making decisions on DMT's in early MS.To explore the patient perspective on using DMT's for MS. Methods: Ten participants with a recent (< 2 years) relapsing-remitting MS diagnosis were interviewed. Seven of them were using DMT's at the time of the interview. All interviews were transcribed and analyzed using a hermeneutical-phenomenological approach.The analysis revealed the following themes: (1) Constant confrontation with the disease, (2) Managing inevitable decline, (3) Hope of delaying the progression of the disease, and, (4) The importance of social support. The themes show that patients associate the recommendation to begin DMT's (especially injectable DMT's) with views about their bodies as well as their hopes about the future. Both considering and adhering to treatment are experienced by patients as not only matters of individual and rational deliberation, but also as activities that are lived within a web of relationships with relatives and friends.From the patient perspective, the use of DMT's is not a purely rational and individual experience. More attention to the use of DMT's as relational and lived phenomena will improve the understanding of the process of decision-making for DMT's in MS

Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field

We derive a closed analytical expression for the exchange energy of the three-dimensional interacting electron gas in strong magnetic fields, which goes beyond the quantum limit (L=0) by explicitly including the effect of the second, L=1, Landau level and arbitrary spin polarization. The inclusion of the L=1 level brings the fields to which the formula applies closer to the laboratory range, as compared to previous expressions, valid only for L=0 and complete spin polarization. We identify, and explain, two distinct regimes, separated by a critical density $n_c$. Below $n_c$, the per-particle exchange energy is lowered by the contribution of L=1, whereas above $n_c$ it is increased. As special cases of our general equation we recover various known, more limited, results for higher fields, and identify and correct a few inconsistencies in some of these earlier expressions.Comment: 7 pages, 2 figures, PRB accepte

Nonuniqueness and derivative discontinuities in density-functional theories for current-carrying and superconducting systems

Current-carrying and superconducting systems can be treated within density-functional theory if suitable additional density variables (the current density and the superconducting order parameter, respectively) are included in the density-functional formalism. Here we show that the corresponding conjugate potentials (vector and pair potentials, respectively) are {\it not} uniquely determined by the densities. The Hohenberg-Kohn theorem of these generalized density-functional theories is thus weaker than the original one. We give explicit examples and explore some consequences.Comment: revised version (typos corrected, some discussion added) to appear in Phys. Rev.

Density-functionals not based on the electron gas: Local-density approximation for a Luttinger liquid

By shifting the reference system for the local-density approximation (LDA) from the electron gas to other model systems one obtains a new class of density functionals, which by design account for the correlations present in the chosen reference system. This strategy is illustrated by constructing an explicit LDA for the one-dimensional Hubbard model. While the traditional {\it ab initio} LDA is based on a Fermi liquid (the electron gas), this one is based on a Luttinger liquid. First applications to inhomogeneous Hubbard models, including one containing a localized impurity, are reported.Comment: 4 pages, 4 figures (final version, contains additional applications and discussion; accepted by Phys. Rev. Lett.