Tulane University

About: Tulane University is a education organization based out in New Orleans, Louisiana, United States. It is known for research contribution in the topics: Population & Blood pressure. The organization has 24478 authors who have published 47205 publications receiving 1944993 citations. The organization is also known as: University of Louisiana.

Electron densities in search of Hamiltonians

Abstract: By utilizing the knowledge that a Hamiltonian is a unique functional of its ground-state density, the following fundamental connections between densities and Hamiltonians are revealed: Given that ${\ensuremath{\rho}}_{\ensuremath{\alpha}}, {\ensuremath{\rho}}_{\ensuremath{\beta}},\dots{},{\ensuremath{\rho}}_{\ensuremath{\omega}}$ are ground-level densities for interacting or noninteracting Hamiltonians ${H}_{1}, {H}_{2},\dots{},{H}_{M}$ ($M$ arbitrarily large) with local potentials ${v}_{1}$,${v}_{2}$,$\dots{}$,${v}_{M}$, but given that we do not know which $\ensuremath{\rho}$ belongs with which $H$, the correct mapping is possible and is obtained by minimizing $\ensuremath{\int}d\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}} [{v}_{1}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}){\ensuremath{\rho}}_{\ensuremath{\alpha}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})+{v}_{2}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}){\ensuremath{\rho}}_{\ensuremath{\beta}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})+\ensuremath{\cdots}{v}_{M}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}){\ensuremath{\rho}}_{\ensuremath{\omega}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})]$ with respect to optimum permutations of the $\ensuremath{\rho}$'s among the $v$'s. A tight rigorous bound connects a density to its interacting ground-state energy via the one-body potential of the interacting system and the Kohn-Sham effective one-body potential of the auxiliary noninteracting system. A modified Kohn-Sham effective potential is defined such that its sum of lowest orbital energies equals the true interacting ground-state energy. Moreover, of all those effective potentials which differ by additive constants and which yield the true interacting ground-state density, this modified effective potential is the most invariant with respect to changes in the one-body potential of the true Hamiltonian. With the exception of the occurrence of certain linear dependencies, $a$ density will not generally be associated with any ground-state wave function (is not wave function $v$ representable) if that density can be generated by a special linear combination of three or more densities that arise from a common set of degenerate ground-state wave functions. Applicability of the "constrained search" approach to density-functional theory is emphasized for non-$v$-representable as well as for $v$-representable densities. In fact, a particular constrained ensemble search is revealed which provides a general sufficient condition for non-$v$ representability by a wave function. The possible appearance of noninteger occupation numbers is discussed in connection with the existence of non-$v$ representability for some Kohn-Sham noninteracting systems.

The Regional Distribution of Somatostatin in the Rat Brain

Abstract: A sensitive and specific radioimmunoassay for somatostatin (SRIF) has been used to determine the regional distribution of SRIF in rat brain. The hypothalamus contained the highest concentration of SRIF. Lower, but significant amounts of SRIF were present outside of the hypothalamus. Within the hypothalamus, the concentration of SRIF was highest in the median eminence and arcuate nucleus although all of the hypothalamic nuclei contained some of this material. The implications of this distribution are discussed (Endocrinology96: 1456, 1975)