2,586 research outputs found
Matrix Product States Algorithms and Continuous Systems
A generic method to investigate many-body continuous-variable systems is
pedagogically presented. It is based on the notion of matrix product states
(so-called MPS) and the algorithms thereof. The method is quite versatile and
can be applied to a wide variety of situations. As a first test, we show how it
provides reliable results in the computation of fundamental properties of a
chain of quantum harmonic oscillators achieving off-critical and critical
relative errors of the order of 10^(-8) and 10^(-4) respectively. Next, we use
it to study the ground state properties of the quantum rotor model in one
spatial dimension, a model that can be mapped to the Mott insulator limit of
the 1-dimensional Bose-Hubbard model. At the quantum critical point, the
central charge associated to the underlying conformal field theory can be
computed with good accuracy by measuring the finite-size corrections of the
ground state energy. Examples of MPS-computations both in the finite-size
regime and in the thermodynamic limit are given. The precision of our results
are found to be comparable to those previously encountered in the MPS studies
of, for instance, quantum spin chains. Finally, we present a spin-off
application: an iterative technique to efficiently get numerical solutions of
partial differential equations of many variables. We illustrate this technique
by solving Poisson-like equations with precisions of the order of 10^(-7).Comment: 22 pages, 14 figures, final versio
Electrical polarization of nuclear spins in a breakdown regime of quantum Hall effect
We have developed a method for electrical polarization of nuclear spins in
quantum Hall systems. In a breakdown regime of odd-integer quantum Hall effect
(QHE), excitation of electrons to the upper Landau subband with opposite spin
polarity dynamically polarizes nuclear spins through the hyperfine interaction.
The polarized nuclear spins in turn accelerate the QHE breakdown, leading to
hysteretic voltage-current characteristics of the quantum Hall conductor.Comment: 3 pages, 4 figures, submitted to Appl. Phys. Let
Hydrodynamic interactions of spherical particles in Poiseuille flow between two parallel walls
We study hydrodynamic interactions of spherical particles in incident
Poiseuille flow in a channel with infinite planar walls. The particles are
suspended in a Newtonian fluid, and creeping-flow conditions are assumed.
Numerical results, obtained using our highly accurate Cartesian-representation
algorithm [Physica A xxx, {\bf xx}, 2005], are presented for a single sphere,
two spheres, and arrays of many spheres. We consider the motion of freely
suspended particles as well as the forces and torques acting on particles
adsorbed at a wall. We find that the pair hydrodynamic interactions in this
wall-bounded system have a complex dependence on the lateral interparticle
distance due to the combined effects of the dissipation in the gap between the
particle surfaces and the backflow associated with the presence of the walls.
For immobile particle pairs we have examined the crossover between several
far-field asymptotic regimes corresponding to different relations between the
particle separation and the distances of the particles from the walls. We have
also shown that the cumulative effect of the far-field flow substantially
influences the force distribution in arrays of immobile spheres. Therefore, the
far-field contributions must be included in any reliable algorithm for
evaluating many-particle hydrodynamic interactions in the parallel-wall
geometry.Comment: submitted to Physics of Fluid
Planar Elongation Flow Analysis of Non-Newtonian Fluids Using a Disk-Shaped Bob
Planar elongation viscosity is a material property involved in extensional deformation, which plays a significant role in many processes such as film-casting and coating. As for the elongation behavior of a polymeric film, some commercial measurement methods are available. However, these measurement methods cannot be applied to liquids with lower viscosities. A method of measuring planar elongation viscosity, especially for low viscosity liquids, has been proposed, which generates a planar elongation flow by pushing a bullet-shaped bob into a cup filled with the sample liquid. The pushing force, which can be measured by a conventional rheometer, reflects the responses of shear, planar extensional deformation, and buoyancy. However, measurements using a bulletshaped bob may be strongly affected by the shear flow between the bob and the cup. Therefore, an alternative measurement using a flat disk-shaped bob is proposed, in order to significantly reduce the influence of shear flow. However, such improvements cannot be estimated numerically. In this study, we performed numerical simulations of viscoelastic fluids for both measurement methods to clarify the shear flow effects
The development of air shower in the iron absorber
The iron open-sandwich experiments to observe one dimensional development of individual air showers were carried out at Akeno Observatory. One dimensional energy flow, incident energy and production height of shower is estimated using the data of size and age obtained from the above experiment and simple calculation
Density matrix renormalization group in a two-dimensional Hamiltonian lattice model
Density matrix renormalization group (DMRG) is applied to a (1+1)-dimensional
model. Spontaneous breakdown of discrete symmetry is
studied numerically using vacuum wavefunctions. We obtain the critical coupling
and the critical exponent
, which are consistent with the Monte Carlo and the
exact results, respectively. The results are based on extrapolation to the
continuum limit with lattice sizes , and 1000. We show that the
lattice size L=500 is sufficiently close to the the limit .Comment: 16 pages, 10 figures, minor corrections, accepted for publication in
JHE
Fitting Voronoi Diagrams to Planar Tesselations
Given a tesselation of the plane, defined by a planar straight-line graph
, we want to find a minimal set of points in the plane, such that the
Voronoi diagram associated with "fits" \ . This is the Generalized
Inverse Voronoi Problem (GIVP), defined in \cite{Trin07} and rediscovered
recently in \cite{Baner12}. Here we give an algorithm that solves this problem
with a number of points that is linear in the size of , assuming that the
smallest angle in is constant.Comment: 14 pages, 8 figures, 1 table. Presented at IWOCA 2013 (Int. Workshop
on Combinatorial Algorithms), Rouen, France, July 201
Variational Calculation of the Effective Action
An indication of spontaneous symmetry breaking is found in the
two-dimensional model, where attention is paid to the
functional form of an effective action. An effective energy, which is an
effective action for a static field, is obtained as a functional of the
classical field from the ground state of the hamiltonian interacting
with a constant external field. The energy and wavefunction of the ground state
are calculated in terms of DLCQ (Discretized Light-Cone Quantization) under
antiperiodic boundary conditions. A field configuration that is physically
meaningful is found as a solution of the quantum mechanical Euler-Lagrange
equation in the limit. It is shown that there exists a nonzero field
configuration in the broken phase of symmetry because of a boundary
effect.Comment: 26 pages, REVTeX, 7 postscript figures, typos corrected and two
references adde
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