123 research outputs found
Quantum cohomology of minuscule homogeneous spaces II : Hidden symmetries
We prove that the quantum cohomology ring of any minuscule or cominuscule
homogeneous space, once localized at the quantum parameter, has a non trivial
involution mapping Schubert classes to multiples of Schubert classes. This can
be stated as a strange duality property for the Gromov-Witten invariants, which
turn out to be very symmetric.Comment: 17 page
Phonon-phonon interactions in transition metals
In this paper the phonon self energy produced by anharmonicity is calculated
using second order many body perturbation theory for all bcc, fcc and hcp
transition metals. The symmetry properties of the phonon interactions are used
to obtain an expression for the self energy as a sum over irreducible triplets,
very similar to integration in the irreducible part of the Brillouin zone for
one particle properties. The results obtained for transition metals shows that
the lifetime is on the order of 10^10 s. Moreover the Peierls approximation for
the imaginary part of the self energy is shown to be reasonable for bcc and fcc
metals. For hcp metals we show that the Raman active mode decays into a pair of
acoustic phonons, their wave vector being located on a surface defined by
conservation laws.Comment: 14 pages, 3 figure
Discovery of low thermal conductivity compounds with first-principles anharmonic lattice dynamics calculations and Bayesian optimization
Compounds of low lattice thermal conductivity (LTC) are essential for seeking
thermoelectric materials with high conversion efficiency. Some strategies have
been used to decrease LTC. However, such trials have yielded successes only
within a limited exploration space. Here we report the virtual screening of a
library containing 54,779 compounds. Our strategy is to search the library
through Bayesian optimization using for the initial data the LTC obtained from
first-principles anharmonic lattice dynamics calculations for a set of 101
compounds. We discovered 221 materials with very low LTC. Two of them have even
an electronic band gap < 1 eV, what makes them exceptional candidates for
thermoelectric applications. In addition to those newly discovered
thermoelectric materials, the present strategy is believed to be powerful for
many other applications in which chemistry of materials are required to be
optimized.Comment: 6 pages, 4 figure
Implementation strategies in phonopy and phono3py
Scientific simulation codes are public property sustained by the community.
Modern technology allows anyone to join scientific software projects, from
anywhere, remotely via the internet.
The phonopy and phono3py codes are widely used open source phonon calculation
codes. This review describes a collection of computational methods and
techniques as implemented in these codes and shows their implementation
strategies as a whole, aiming to be useful for the community. Some of the
techniques presented here are not limited to phonon calculations and may
therefore be useful in other area of condensed matter physics
On the equivariant cohomology of Hilbert schemes of points in the plane
Let be the affine plane regarded as a toric variety with an action of the 2-dimensional torus . We study the equivariant Chow ring of the punctual Hilbert scheme with equivariant coefficients inverted. We compute base change formulas in between the natural bases introduced by Nakajima, Ellingsrud and Str{\o}mme, and the classical basis associated with the fixed points. We compute the equivariant commutation relations between creation/annihilation operators. We express the class of the small diagonal in in terms of the equivariant Chern classes of the tautological bundle. We prove that the nested Hilbert scheme parametrizing nested punctual subschemes of degree and is irreducible
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