A density-matrix formulation of the hartree-fock-bogoliubov equations for space-dependent superconductivity

Temperature and velocity-dependent 1S0 pairing gaps, chemical potentials and entrainment matrix in dense homogeneous neutron–proton superfluid mixtures constituting the outer core of neutron stars, are determined fully self-consistently by solving numerically the time-dependent Hartree–Fock–Bogoliubov equations over the whole range of temperatures and flow velocities for which superfluidity can exist. Calculations have been made for npeμ in beta-equilibrium using the Brussels–Montreal functional BSk24. The accuracy of various approximations is assessed and the physical meaning of the different velocities and momentum densities appearing in the theory is clarified. Together with the unified equation of state published earlier, the present results provide consistent microscopic inputs for modeling superfluid neutron-star cores.

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Theory of Longitudinal Relaxation of an AX Spin System under Double Resonance. I. Density Matrix Formulation of Saturation Recovery

Journal of the Physical Society of Japan ◽

10.1143/jpsj.52.3943 ◽

1983 ◽

Vol 52 (11) ◽

pp. 3943-3952 ◽

Cited By ~ 3

Author(s):

Mitsumasa Ishiwata

Keyword(s):

Density Matrix ◽

Spin System ◽

Double Resonance ◽

Saturation Recovery ◽

Matrix Formulation ◽

Longitudinal Relaxation

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Is it Reasonable to Obtain Information on the Polarizability and Hyperpolarizability Only from the Electron Density?

Australian Journal of Chemistry ◽

10.1071/ch17624 ◽

2018 ◽

Vol 71 (4) ◽

pp. 295 ◽

Cited By ~ 1

Author(s):

Dylan Jayatilaka ◽

Kunal K. Jha ◽

Parthapratim Munshi

Keyword(s):

Density Matrix ◽

Electron Density ◽

Ground State ◽

Density Functional ◽

Particle Density ◽

Density Matrices ◽

Hartree Fock ◽

Electron Density Matrix ◽

Ground State Electron ◽

Side Result

Formulae for the static electronic polarizability and hyperpolarizability are derived in terms of moments of the ground-state electron density matrix by applying the Unsöld approximation and a generalization of the Fermi-Amaldi approximation. The latter formula for the hyperpolarizability appears to be new. The formulae manifestly transform correctly under rotations, and they are observed to be essentially cumulant expressions. Consequently, they are additive over different regions. The properties of the formula are discussed in relation to others that have been proposed in order to clarify inconsistencies. The formulae are then tested against coupled-perturbed Hartree-Fock results for a set of 40 donor-π-acceptor systems. For the polarizability, the correlation is reasonable; therefore, electron density matrix moments from theory or experiment may be used to predict polarizabilities. By constrast, the results for the hyperpolarizabilities are poor, not even within one or two orders of magnitude. The formula for the two- and three-particle density matrices obtained as a side result in this work may be interesting for density functional theories.

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