General description of multiple-modulation effects and sideband production in magnetic resonance

1988 ◽  
Vol 66 (12) ◽  
pp. 3077-3082 ◽  
Author(s):  
Hirokazu Sakamoto ◽  
Takeji Takui ◽  
Koichi Itoh
Keyword(s):  
General Formula ◽  
Amplitude Modulation ◽  
Bloch Equation ◽  
Modulation Scheme ◽  
General Description ◽  
Matrix Formalism ◽  
Equivalent Result ◽  
Density Matrix Formalism ◽  
Field Modulation ◽  
Frequency Modulations

A theory is presented for the sideband structure produced by a general multiple-modulation scheme with arbitrary combination of p-tuple field modulation, q-tuple frequency modulation, and r-tuple amplitude modulation for integral p, q, and r. A general formula describing the multiple-modulation effects is analytically derived using a density matrix formalism under the assumption of negligible saturation; an equivalent result is obtained from the phenomenological Bloch equation. The general formula reveals that field and frequency modulations are equivalent for the sideband production, even in the presence of amplitude modulation. Two particular cases, viz., r-tuple amplitude modulation and double field modulation are dealt with to show the validity and applicability of the general formula.

Direct minimization of the energy functional in LCAO-MO density matrix formalism

1976 ◽  
Vol 41 (4) ◽  
pp. 311-319 ◽  
Author(s):  
Piercarlo Fantucci ◽  
Stefano Polezzo ◽  
Maria Paola Stabilini
Keyword(s):  
Density Matrix ◽  
Energy Functional ◽  
Matrix Formalism ◽  
Density Matrix Formalism ◽  
Direct Minimization ◽  
Lcao Mo

scholarly journals The Chandrasekhar Mass of A Gravitating Electron Crystal

1994 ◽  
Vol 147 ◽  
pp. 565-570
Author(s):  
D. Engelhardt ◽  
I. Bues
Keyword(s):  
Magnetic Field ◽  
Density Matrix ◽  
White Dwarf ◽  
Matrix Formalism ◽  
Plasma Zone ◽  
Isothermal Model ◽  
Fermi Function ◽  
Density Matrix Formalism ◽  
The Magnetic Field ◽  
Electron Crystal

AbstractThe internal structure of a white dwarf may be changed by a strong magnetic field. A local model of the electrons is constructed within a thermal density matrix formalism, essentially a Heisenberg magnetism model. This results in a matrix Fermi function which is used to construct an isothermal model of the electron crystal. The central density of the crystal is 108kg/m3 independent of the magnetic field within the plasma and therefore lower than the relativistic density, whereas this density is constant until the Fermi momentum x f = 0.3 * me * c. Chandrasekhar masses up to 1.44 * 1.4M0 are possible for polarizations of the plasma zone lower than 0.5, if the temperature is close to the Curie point, whereas the crystal itself destabilizes the white dwarf dependent on temperature.

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