In this paper, we give the white noise calculus for the Fermion system and prove the Fock expansion for any continuous linear operators from the space of test functionals to the space of generalized functionals. As an application of the Fock expansion, we give a necessary and sufficient condition for implementability of Bogoliubov automorphisms on Z2-invariant subalgebra of canonical anti-commu...

The molecular geometry of complex of adenine with 8 water molecules was calculated with Hartree-Fock (HF). The standard 6-31G(d) basis set has been employed. The existence of C-H…O Hydrogen bonds between the water molecules and the hydrophobic part of nucleobase is stablished. We optimized structures and computed interaction energies of all complexes of adenine with water molecules step by step...

These notes are intended as a fairly self contained explanation of Fock space and various algebras that act on it, including a Clifford algebras, a Weyl algebra, and an affine Kac-Moody algebra. We also discuss how the various algebras are related, and in particular describe the celebrated boson-fermion correspondence. We finish by briefly discussing a deformation of Fock space, which is a repr...

We construct the quadratic analogue of the boson Fock functor. While in the first order (linear) case all contractions on the 1–particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. The encouraging fact is that it contains, as proper subgroups (i.e. the contractions), all the gauge transformation...

The K = 4 fractional superstring Fock space is constructed in terms of Z4 parafermions and free bosons. The bosonization of the Z4 parafermion theory and the generalized commutation relations satisfied by the modes of various parafermion fields are reviewed. In this preliminary analysis, we describe a Fock space which is simply a tensor product of Z4 parafermion and free boson Fock spaces. It i...

Quantum chaotic states over a noncommutative monoid, a unitalization of a noncommutative Ito algebra parametrizing a quantum stochastic Levy process, are described in terms of their infinitely divisible generating functionals over the simple monoid-valued fields on an atomless ‘space-time’ set. A canonical decomposition of the logarithmic conditionally posive-definite generating functional is c...

A measure of non-classicality of quantum states based on the volume of the negative part of the Wigner function is proposed. We analyse this quantity for Fock states, squeezed displaced Fock states and cat-like states defined as coherent superposition of two Gaussian wavepackets.

We extend the formalism of local exchange methods to calculate and investigate the electronic structure of metals. It is well-known that the Hatree-Fock method when applied to metals shows unphysical behaviour, however the accurate treatment of exchange via DFT’s exact exchange method (EXX) and using our local Fock exchange method (LFX) can be used to describe metallic band structures accurately.

Generalising the previous Fock case, we show that in an extremal universally invariant representation of the canonical commutation relations, a second quantised double product of infinitesimal rotations is a stochastic double product in the corresponding non-Fock quantum stochastic calculus. AMS Subject Classification 81S25.

Abstract: Based on Hartree-Fock theory with correlations, approximate solutions of the manybody Schrödinger equation are examined for their use for calculations of nuclear reaction rates for charged Bose nuclei confined in a harmonic trap. It is shown that the nuclear reaction rate calculated with the Hartree-Fock mean field solution makes a significant contribution even in the presence of two-...