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Boson-Fermion Algebraic Mapping in Second Quantization.
Entropy (Basel)
December 2024
Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica 1000000, Chile.
We present an algebraic method to derive the structure at the basis of the mapping of bosonic algebras of creation and annihilation operators into fermionic algebras, and vice versa, introducing a suitable identification between bosonic and fermionic generators. The algebraic structure thus obtained corresponds to a deformed Grassmann-type algebra, involving anticommuting Grassmann-type variables. The role played by the latter in implementing gauge invariance in second quantization within our procedure is then discussed.
View Article and Find Full Text PDFMapping spin contamination-free potential energy surfaces using restricted open-shell methods with Grassmannians.
Phys Chem Chem Phys
January 2024
Department of Chemistry, Virginia Commonwealth University, Richmond, VA, USA.
The Lagrange-based Grassmann interpolation (G-Int) method has been extended for open-shell systems using restricted open-shell (RO) methods. The performance of this method was assessed in constructing potential energy surfaces (PESs) for vanadium(II) oxide, benzyl radical, and methanesulfenyl chloride radical cation. The density matrices generated by G-Int when used as initial guesses for self-consistent field (SCF) calculations, exhibit superior performance compared to other traditional SCF initial guess schemes, such as SADMO, GWH, and CORE.
View Article and Find Full Text PDFZombie states for description of structure and dynamics of multi-electron systems.
J Chem Phys
May 2018
School of Chemistry, University of Leeds, Leeds LS2 9JT, United Kingdom.
Canonical Coherent States (CSs) of Harmonic Oscillator have been extensively used as a basis in a number of computational methods of quantum dynamics. However, generalising such techniques for fermionic systems is difficult because Fermionic Coherent States (FCSs) require complicated algebra of Grassmann numbers not well suited for numerical calculations. This paper introduces a coherent antisymmetrised superposition of "dead" and "alive" electronic states called here Zombie State (ZS), which can be used in a manner of FCSs but without Grassmann algebra.
View Article and Find Full Text PDFThe forgotten role of central volume in low frequency oscillations of heart rate variability.
PLoS One
February 2016
L. Sacco Hospital, Università degli Studi, Milan, Italy.
The hypothesis that central volume plays a key role in the source of low frequency (LF) oscillations of heart rate variability (HRV) was tested in a population of end stage renal disease patients undergoing conventional hemodialysis (HD) treatment, and thus subject to large fluid shifts and sympathetic activation. Fluid overload (FO) in 58 chronic HD patients was assessed by whole body bioimpedance measurements before the midweek HD session. Heart Rate Variability (HRV) was measured using 24-hour Holter electrocardiogram recordings starting before the same HD treatment.
View Article and Find Full Text PDFFermionic oscillator in a fermionic bath.
Phys Rev E Stat Nonlin Soft Matter Phys
July 2012
Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India.
The quantum dissipation of a fermionic oscillator in an environment of fermionic oscillators is considered. Since fermions anticommute, their eigenvalues are anticommuting numbers. Based on an expansion of the reduced density operator in terms of fermionic coherent states which make use of these anticommuting numbers or Grassmann variables, a Fokker-Planck equation for the associated quasiprobability distribution function is derived.
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