133,757 research outputs found
Refined Solutions of Time Inhomogeneous Optimal Stopping Games via Dirichlet Form
The properties of value functions of time inhomogeneous optimal stopping
problem and zero-sum game (Dynkin game) are studied through time dependent
Dirichlet form. Under the absolute continuity condition on the transition
function of the underlying diffusion process and some other assumptions, the
refined solutions without exceptional starting points are proved to exist, and
the value functions of the optimal stopping and zero-sum game, which are finely
and cofinely continuous, are characterized as the solutions of some variational
inequalities, respectively
Ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model on the triangular lattice: A variational study based on entangled-plaquette states
We study, on the basis of the general entangled-plaquette variational ansatz,
the ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model
on the triangular lattice. Our numerical estimates are in good agreement with
available exact results and comparable, for large system sizes, to those
computed via the best alternative numerical approaches, or by means of
variational schemes based on specific (i.e., incorporating problem dependent
terms) trial wave functions. The extrapolation to the thermodynamic limit of
our results for lattices comprising up to N=324 spins yields an upper bound of
the ground-state energy per site (in units of the exchange coupling) of
[ for the XX model], while the estimated
infinite-lattice order parameter is (i.e., approximately 64% of the
classical value).Comment: 8 pages, 3 tables, 2 figure
Ab initio quantum Monte Carlo calculations of spin superexchange in cuprates: the benchmarking case of CaCuO
In view of the continuous theoretical efforts aimed at an accurate
microscopic description of the strongly correlated transition metal oxides and
related materials, we show that with continuum quantum Monte Carlo (QMC)
calculations it is possible to obtain the value of the spin superexchange
coupling constant of a copper oxide in a quantitatively excellent agreement
with experiment. The variational nature of the QMC total energy allows us to
identify the best trial wave function out of the available pool of wave
functions, which makes the approach essentially free from adjustable parameters
and thus truly ab initio. The present results on magnetic interactions suggest
that QMC is capable of accurately describing ground state properties of
strongly correlated materials.Comment: Published in Physical Review
LASSO reloaded: a variational analysis perspective with applications to compressed sensing
This paper provides a variational analysis of the unconstrained formulation
of the LASSO problem, ubiquitous in statistical learning, signal processing,
and inverse problems. In particular, we establish smoothness results for the
optimal value as well as Lipschitz properties of the optimal solution as
functions of the right-hand side (or measurement vector) and the regularization
parameter. Moreover, we show how to apply the proposed variational analysis to
study the sensitivity of the optimal solution to the tuning parameter in the
context of compressed sensing with subgaussian measurements. Our theoretical
findings are validated by numerical experiments
Variational Monte-Carlo investigation of SU() Heisenberg chains
Motivated by recent experimental progress in the context of ultra-cold
multi-color fermionic atoms in optical lattices, we have investigated the
properties of the SU() Heisenberg chain with totally antisymmetric
irreducible representations, the effective model of Mott phases with
particles per site. These models have been studied for arbitrary and
with non-abelian bosonization [I. Affleck, Nuclear Physics B 265, 409 (1986);
305, 582 (1988)], leading to predictions about the nature of the ground state
(gapped or critical) in most but not all cases. Using exact diagonalization and
variational Monte-Carlo based on Gutzwiller projected fermionic wave functions,
we have been able to verify these predictions for a representative number of
cases with and , and we have shown that the opening of
a gap is associated to a spontaneous dimerization or trimerization depending on
the value of m and N. We have also investigated the marginal cases where
abelian bosonization did not lead to any prediction. In these cases,
variational Monte-Carlo predicts that the ground state is critical with
exponents consistent with conformal field theory.Comment: 9 pages, 10 figures, 3 table
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