341,948 research outputs found
Ideal matrices. III.
In this paper ideal matrices with respect to ideals in the maximal order of an algebraic number field are connected with the different of the field and with group matrices in the case of normal fields whose maximal order has a normal basis
The 2-matrix of the spin-polarized electron gas: contraction sum rules and spectral resolutions
The spin-polarized homogeneous electron gas with densities
and for electrons with spin `up' () and spin `down'
(), respectively, is systematically analyzed with respect to its
lowest-order reduced densities and density matrices and their mutual relations.
The three 2-body reduced density matrices ,
, are 4-point functions for electron
pairs with spins , , and antiparallel,
respectively. From them, three functions ,
, , depending on only two variables,
are derived. These functions contain not only the pair densities but also the
1-body reduced density matrices. The contraction properties of the 2-body
reduced density matrices lead to three sum rules to be obeyed by the three key
functions , . These contraction sum rules contain corresponding
normalization sum rules as special cases. The momentum distributions
and , following from and
by Fourier transform, are correctly normalized through
. In addition to the non-negativity conditions
[these quantities are probabilities], it holds
and due to the Pauli principle and
due to the Coulomb repulsion. Recent parametrizations of the pair densities of
the spin-unpolarized homogeneous electron gas in terms of 2-body wave functions
(geminals) and corresponding occupancies are generalized (i) to the
spin-polarized case and (ii) to the 2-body reduced density matrix giving thus
its spectral resolutions.Comment: 32 pages, 4 figure
A PNJL model in 0+1 Dimensions
We formulate the Polyakov-Nambu-Jona-Lasinio (PNJL) model in 0+1 dimensions.
The thermodynamics captured by the partition function yields a bulk pressure,
as well as quark susceptibilities versus temperature that are similar to the
ones in 3+1 dimensions. Around the transition temperature the behavior in the
pressure and quark susceptibilities follows from the interplay between the
lowest Matsubara frequency and the Polyakov line. The reduction to the lowest
Matsubara frequency yields a matrix Model. In the presence of the Polyakov line
the UV part of the Dirac spectrum features oscillations when close to the
transition temperature.Comment: 18 pages, 13 figure
- …