260 research outputs found
Fast and stable method for simulating quantum electron dynamics
A fast and stable method is formulated to compute the time evolution of a
wavefunction by numerically solving the time-dependent Schr{\"o}dinger
equation. This method is a real space/real time evolution method implemented by
several computational techniques such as Suzuki's exponential product, Cayley's
form, the finite differential method and an operator named adhesive operator.
This method conserves the norm of the wavefunction, manages periodic conditions
and adaptive mesh refinement technique, and is suitable for vector- and
parallel-type supercomputers. Applying this method to some simple electron
dynamics, we confirmed the efficiency and accuracy of the method for simulating
fast time-dependent quantum phenomena.Comment: 10 pages, 35 eps figure
Finite-size Effects in a Two-Dimensional Electron Gas with Rashba Spin-Orbit Interaction
Within the Kubo formalism, we estimate the spin-Hall conductivity in a
two-dimensional electron gas with Rashba spin-orbit interaction and study its
variation as a function of disorder strength and system size. The numerical
algorithm employed in the calculation is based on the direct numerical
integration of the time-dependent Schrodinger equation in a spin-dependent
variant of the particle source method. We find that the spin-precession length,
L_s controlled by the strength of the Rashba coupling, establishes the critical
lengthscale that marks the significant reduction of the spin-Hall conductivity
in bulk systems. In contrast, the electron mean free path, inversely
proportional to the strength of disorder, appears to have only a minor effect.Comment: 5 pages, 3 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
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
Solid helium at high pressure: A path-integral Monte Carlo simulation
Solid helium (3He and 4He) in the hcp and fcc phases has been studied by
path-integral Monte Carlo. Simulations were carried out in the
isothermal-isobaric (NPT) ensemble at pressures up to 52 GPa. This allows one
to study the temperature and pressure dependences of isotopic effects on the
crystal volume and vibrational energy in a wide parameter range. The obtained
equation of state at room temperature agrees with available experimental data.
The kinetic energy, E_k, of solid helium is found to be larger than the
vibrational potential energy, E_p. The ratio E_k/E_p amounts to about 1.4 at
low pressures, and decreases as the applied pressure is raised, converging to
1, as in a harmonic solid. Results of these simulations have been compared with
those yielded by previous path integral simulations in the NVT ensemble. The
validity range of earlier approximations is discussed.Comment: 7 pages, 5 figure
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
Direct perturbation theory on the shift of Electron Spin Resonance
We formulate a direct and systematic perturbation theory on the shift of the
main paramagnetic peak in Electron Spin Resonance, and derive a general
expression up to second order. It is applied to one-dimensional XXZ and
transverse Ising models in the high field limit, to obtain explicit results
including the polarization dependence for arbitrary temperature.Comment: 5 pages (no figures) in REVTE
Quantum Dynamics of Spin Wave Propagation Through Domain Walls
Through numerical solution of the time-dependent Schrodinger equation, we
demonstrate that magnetic chains with uniaxial anisotropy support stable
structures, separating ferromagnetic domains of opposite magnetization. These
structures, domain walls in a quantum system, are shown to remain stable if
they interact with a spin wave. We find that a domain wall transmits the
longitudinal component of the spin excitations only. Our results suggests that
continuous, classical spin models described by LLG equation cannot be used to
describe spin wave-domain wall interaction in microscopic magnetic systems
Origin of the Canonical Ensemble: Thermalization with Decoherence
We solve the time-dependent Schrodinger equation for the combination of a
spin system interacting with a spin bath environment. In particular, we focus
on the time development of the reduced density matrix of the spin system. Under
normal circumstances we show that the environment drives the reduced density
matrix to a fully decoherent state, and furthermore the diagonal elements of
the reduced density matrix approach those expected for the system in the
canonical ensemble. We show one exception to the normal case is if the spin
system cannot exchange energy with the spin bath. Our demonstration does not
rely on time-averaging of observables nor does it assume that the coupling
between system and bath is weak. Our findings show that the canonical ensemble
is a state that may result from pure quantum dynamics, suggesting that quantum
mechanics may be regarded as the foundation of quantum statistical mechanics.Comment: 12 pages, 4 figures, accepted for publication by J. Phys. Soc. Jp
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