3,778 research outputs found
Riesz transforms associated to Schr\"odinger operators with negative potentials
The goal of this paper is to study the Riesz transforms \na A^{-1/2} where
is the Schr\"odinger operator -\D-V, V\ge 0, under different conditions
on the potential . We prove that if is strongly subcritical, \na
A^{-1/2} is bounded on , , for all where
is the dual exponent of where $2<\frac{2N}{N-2
Efficient calculation of imaginary time displaced correlation functions in the projector auxiliary field quantum Monte-Carlo algorithm
The calculation of imaginary time displaced correlation functions with the
auxiliary field projector quantum Monte-Carlo algorithm provides valuable
insight (such as spin and charge gaps) in the model under consideration. One of
the authors and M. Imada [F.F. Assaad and M. Imada, J. Phys. Soc. Jpn. 65 189
(1996).] have proposed a numerically stable method to compute those quantities.
Although precise this method is expensive in CPU time. Here, we present an
alternative approach which is an order of magnitude quicker, just as precise,
and very simple to implement. The method is based on the observation that for a
given auxiliary field the equal time Green function matrix, , is a
projector: .Comment: 4 papes, 1 figure in eps forma
Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions
We show that the two recently proposed methods to compute Renyi entanglement
entropies in the realm of determinant quantum Monte Carlo methods for fermions
are in principle equivalent, but differ in sampling strategies. The analogy
allows to formulate a numerically stable calculation of the entanglement
spectrum at strong coupling. We demonstrate the approach by studying static and
dynamical properties of the entanglement hamiltonian across the interaction
driven quantum phase transition between a topological insulator and quantum
antiferromagnet in the Kane-Mele Hubbard model. The formulation is not limited
to fermion systems and can readily be adapted to world-line based simulations
of bosonic systems.Comment: 8 pages, 5 figure
Coupled analysis of material flow and die deflection in direct aluminum extrusion
The design of extrusion dies depends on the experience of the designer. After the die has\ud
been manufactured, it is tested during an extrusion trial and machined several times until it works\ud
properly. The die is designed by a trial and error method which is an expensive process in terms\ud
of time and the amount of scrap. In order to decrease the time and the amount of scrap, research is\ud
going on to replace the trial pressing with finite element simulations. The goal of these simulations\ud
is to predict the material flow through the die. In these simulations, it is required to calculate the\ud
material flow and the tool deformation simultaneously. Solving the system of equations concerning\ud
the material flow and the tool deformation becomes more difficult with increasing the complexity\ud
of the die. For example the total number of degrees of freedom can reach a value of 500,000 for\ud
a flat die. Therefore, actions must be taken to solve the material flow and the tool deformation\ud
simultaneously and faster. This paper describes the calculation of a flat die deformation used in the\ud
production of a U-shape profile with a coupled method. In this calculation an Arbitrary Lagrangian\ud
Eulerian and Updated Lagrangian formulation are applied for the aluminum and the tool finite\ud
element models respectively. In addition, for decreasing the total number of degrees of freedom,\ud
the stiffness matrix of the tool is condensed to the contact nodes between the aluminum and the tool\ud
finite element models. Finally, the numerical results are compared with experiment results in terms\ud
of extrusion force and the angular deflection of the tongue
The influence of magnetic steps on bulk superconductivity
We study the distribution of bulk superconductivity in presence of an applied
magnetic field, supposed to be a step function, modeled by the Ginzburg-Landau
theory. Our results are valid for the minimizers of the two-dimensional
Ginzburg-Landau functional with a large Ginzburg-Landau parameter and with an
applied magnetic field of intensity comparable with the Ginzburg-Landau
parameter
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