312,833 research outputs found
The atomic orbitals of the topological atom
The effective atomic orbitals have been realized in the framework of Bader’s atoms in molecules theory for a general wavefunction. This formalism can be used to retrieve from any type of calculation a
proper set of orthonormalized numerical atomic orbitals, with occupation numbers that sum up to the
respective Quantum Theory of Atoms in Molecules (QTAIM) atomic populations. Experience shows
that only a limited number of effective atomic orbitals exhibit significant occupation numbers. These
correspond to atomic hybrids that closely resemble the core and valence shells of the atom. The
occupation numbers of the remaining effective orbitals are almost negligible, except for atoms with
hypervalent character. In addition, the molecular orbitals of a calculation can be exactly expressed
as a linear combination of this orthonormalized set of numerical atomic orbitals, and the Mulliken
population analysis carried out on this basis set exactly reproduces the original QTAIM atomic populations of the atoms. Approximate expansion of the molecular orbitals over a much reduced set of
orthogonal atomic basis functions can also be accomplished to a very good accuracy with a singular
value decomposition procedure
Atomistic subsemirings of the lattice of subspaces of an algebra
Let A be an associative algebra with identity over a field k. An atomistic
subsemiring R of the lattice of subspaces of A, endowed with the natural
product, is a subsemiring which is a closed atomistic sublattice. When R has no
zero divisors, the set of atoms of R is endowed with a multivalued product. We
introduce an equivalence relation on the set of atoms such that the quotient
set with the induced product is a monoid, called the condensation monoid. Under
suitable hypotheses on R, we show that this monoid is a group and the class of
k1_A is the set of atoms of a subalgebra of A called the focal subalgebra. This
construction can be iterated to obtain higher condensation groups and focal
subalgebras. We apply these results to G-algebras for G a group; in particular,
we use them to define new invariants for finite-dimensional irreducible
projective representations.Comment: 14 page
Direct evaporative cooling of 39K atoms to Bose-Einstein condensation
We report the realization of Bose-Einstein condensates of 39K atoms without
the aid of an additional atomic coolant. Our route to Bose-Einstein
condensation comprises Sub Doppler laser cooling of large atomic clouds with
more than 10^10 atoms and evaporative cooling in optical dipole traps where the
collisional cross section can be increased using magnetic Feshbach resonances.
Large condensates with almost 10^6 atoms can be produced in less than 15
seconds. Our achievements eliminate the need for sympathetic cooling with Rb
atoms which was the usual route implemented till date due to the unfavourable
collisional property of 39K. Our findings simplify the experimental set-up for
producing Bose-Einstein condensates of 39K atoms with tunable interactions,
which have a wide variety of promising applications including
atom-interferometry to studies on the interplay of disorder and interactions in
quantum gases.Comment: 7 pages, 6 figure
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