241 research outputs found
Correlation functions for time-dependent calculation of linear-response functions
We emphasize the importance of choosing an appropriate correlation function
to reduce numerical errors in calculating the linear-response function as a
Fourier transformation of a time-dependent correlation function. As an example
we take dielectric functions of silicon crystal calculated with a
time-dependent method proposed by Iitaka et al. [Phys. Rev. E 56, 1222 (1997)].Comment: to be published in Phys.Rev.E 01 Dec 1997, 2 pages, 4 figures, more
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Calculating response functions in time domain with non-orthonormal basis sets
We extend the recently proposed order-N algorithms (cond-mat/9703224) for
calculating linear- and nonlinear-response functions in time domain to the
systems described by nonorthonormal basis sets.Comment: 4 pages, no figure
Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices
A theoretical analysis is given of the equation of motion method, due to
Alben et al., to compute the eigenvalue distribution (density of states) of
very large matrices. The salient feature of this method is that for matrices of
the kind encountered in quantum physics the memory and CPU requirements of this
method scale linearly with the dimension of the matrix. We derive a rigorous
estimate of the statistical error, supporting earlier observations that the
computational efficiency of this approach increases with matrix size. We use
this method and an imaginary-time version of it to compute the energy and the
specific heat of three different, exactly solvable, spin-1/2 models and compare
with the exact results to study the dependence of the statistical errors on
sample and matrix size.Comment: 24 pages, 24 figure
Temperature dependence of ESR intensity for the nanoscale molecular magnet V15
The electron spin resonance (ESR) of nanoscale molecular magnet is studied. Since the Hamiltonian of has a large
Hilbert space and numerical calculations of the ESR signal evaluating the Kubo
formula with exact diagonalization method is difficult, we implement the
formula with the help of the random vector technique and the Chebyshev
polynominal expansion, which we name the double Chebyshev expansion method. We
calculate the temperature dependence of the ESR intensity of and
compare it with the data obtained in experiment. As another complementary
approach, we also implement the Kubo formula with the subspace iteration method
taking only important low-lying states into account. We study the ESR
absorption curve below by means of both methods. We find that side
peaks appear due to the Dzyaloshinsky-Moriya interaction and these peaks grows
as temperature decreases.Comment: 9 pages, 4 figures. To appear in J. Phys. Soc. Jpn. Supp
Algorithm for Linear Response Functions at Finite Temperatures: Application to ESR spectrum of s=1/2 Antiferromagnet Cu benzoate
We introduce an efficient and numerically stable method for calculating
linear response functions of quantum systems at finite
temperatures. The method is a combination of numerical solution of the
time-dependent Schroedinger equation, random vector representation of trace,
and Chebyshev polynomial expansion of Boltzmann operator. This method should be
very useful for a wide range of strongly correlated quantum systems at finite
temperatures. We present an application to the ESR spectrum of s=1/2
antiferromagnet Cu benzoate.Comment: 4 pages, 4 figure
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Failure of Conventional Density Functionals for the Prediction of Molecular Crystal Polymorphism: A Quantum Monte Carlo Study
We have applied the diffusion Monte Carlo method, for the first time, to an organic molecular crystal (para-diiodobenzene) in order to determine the relative stability of its two well-known polymorphs. The DMC result predicts that the α phase is more stable than the β phase at zero temperature, in agreement with experiment. In comparison, we evaluated four commonly used local, semilocal, and hybrid density functionals, including an empirical correction to include the effects of dispersion. We conclude that while density functional theory may provide the most practical method for estimating the effects of electron correlation, conventional functionals which do not accurately describe noncovalent interactions may not be considered reliable for determining highly accurate energies in such systems.Chemistry and Chemical Biolog
Equivalent birational embeddings II: divisors
Two divisors in are said to be Cremona equivalent if there is a
Cremona modification sending one to the other. We produce infinitely many non
equivalent divisorial embeddings of any variety of dimension at most 14. Then
we study the special case of plane curves and rational hypersurfaces. For the
latter we characterise surfaces Cremona equivalent to a plane.Comment: v2 Exposition improved, thanks to referee, unconditional
characterization of surfaces Cremona equivalent to a plan
Time-dependent properties of proton decay from crossing single-particle metastable states in deformed nuclei
A dynamical study of the decay of a metastable state by quantum tunneling
through an anisotropic, non separable, two-dimensional potential barrier is
performed by the numerical solution of the time-dependent Schrodinger equation.
Initial quasi- stationary proton states are chosen in the framework of a
deformed Woods-Saxon single-particle model. The decay of two sets of states
corresponding to true and quasi levels-crossing is studied and the evolution of
their decay properties as a function of nuclear deformation is calculated
around the crossing point. The results show that the investigation of the
proton decay from metastable states in deformed nuclei can unambiguously
distinguish between the two types of crossing and determine the structure of
the nuclear states involved.Comment: 15 pages, 9 figures, submitted to Phys. Rev.
Fast algorithm for calculating two-photon absorption spectra
We report a numerical calculation of the two-photon absorption coefficient of
electrons in a binding potential using the real-time real-space higher-order
difference method. By introducing random vector averaging for the intermediate
state, the task of evaluating the two-dimensional time integral is reduced to
calculating two one-dimensional integrals. This allows the reduction of the
computation load down to the same order as that for the linear response
function. The relative advantage of the method compared to the straightforward
multi-dimensional time integration is greater for the calculation of non-linear
response functions of higher order at higher energy resolution.Comment: 4 pages, 2 figures. It will be published in Phys. Rev. E on 1, March,
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