19 research outputs found
Role of oxygen vacancy defect states in the n-type conduction of β-Ga[sub 2]O[sub 3]
Based on semiempirical quantum-chemical calculations, the electronic band structure of β-Ga2O3 is presented and the formation and properties of oxygen vacancies are analyzed. The equilibrium geometries and formation energies of neutral and doubly ionized vacancies were calculated. Using the calculated donor level positions of the vacancies, the high temperature n-type conduction is explained. The vacancy concentration is obtained by fitting to the experimental resistivity and electron mobility
The complete conformal spectrum of a invariant network model and logarithmic corrections
We investigate the low temperature asymptotics and the finite size spectrum
of a class of Temperley-Lieb models. As reference system we use the spin-1/2
Heisenberg chain with anisotropy parameter and twisted boundary
conditions. Special emphasis is placed on the study of logarithmic corrections
appearing in the case of in the bulk susceptibility data and in
the low-energy spectrum yielding the conformal dimensions. For the
invariant 3-state representation of the Temperley-Lieb algebra with
we give the complete set of scaling dimensions which show huge
degeneracies.Comment: 18 pages, 5 figure
The Complexity of Approximating complex-valued Ising and Tutte partition functions
We study the complexity of approximately evaluating the Ising and Tutte
partition functions with complex parameters. Our results are partly motivated
by the study of the quantum complexity classes BQP and IQP. Recent results show
how to encode quantum computations as evaluations of classical partition
functions. These results rely on interesting and deep results about quantum
computation in order to obtain hardness results about the difficulty of
(classically) evaluating the partition functions for certain fixed parameters.
The motivation for this paper is to study more comprehensively the complexity
of (classically) approximating the Ising and Tutte partition functions with
complex parameters. Partition functions are combinatorial in nature and
quantifying their approximation complexity does not require a detailed
understanding of quantum computation. Using combinatorial arguments, we give
the first full classification of the complexity of multiplicatively
approximating the norm and additively approximating the argument of the Ising
partition function for complex edge interactions (as well as of approximating
the partition function according to a natural complex metric). We also study
the norm approximation problem in the presence of external fields, for which we
give a complete dichotomy when the parameters are roots of unity. Previous
results were known just for a few such points, and we strengthen these results
from BQP-hardness to #P-hardness. Moreover, we show that computing the sign of
the Tutte polynomial is #P-hard at certain points related to the simulation of
BQP. Using our classifications, we then revisit the connections to quantum
computation, drawing conclusions that are a little different from (and
incomparable to) ones in the quantum literature, but along similar lines