670 research outputs found
The Mayer series of the Lennard-Jones gas: improved bounds for the convergence radius
We provide a lower bound for the convergence radius of the Mayer series of
the Lennard-Jones gas which strongly improves on the classical bound obtained
by Penrose and Ruelle 1963. To obtain this result we use an alternative
estimate recently proposed by Morais et al. (J. Stat. Phys. 2014) for a
restricted class of stable and tempered pair potentials (namely those which can
be written as the sum of a non-negative potential plus an absolutely integrable
and stable potential) combined with a method developed by Locatelli and Schoen
(J. Glob. Optim. 2002) for establishing a lower bound for the minimal
interatomic distance between particles interacting via a Morse potential in a
cluster of minimum-energy configurations
Truncation of long-range percolation model with square non-summable interactions
We consider some problems related to the truncation question in long-range
percolation. It is given probabilities that certain long-range oriented bonds
are open; assuming that this probabilities are not summable, we ask if the
probability of percolation is positive when we truncate the graph, disallowing
bonds of range above a possibly large but finite threshold. This question is
still open if the set of vertices is . We give some conditions in which
the answer is affirmative. One of these results generalize the previous result
in [Alves, Hil\'ario, de Lima, Valesin, Journ. Stat. Phys. {\bf 122}, 972
(2017)]
Quantum state tomography of photons polarization and path degrees of freedom
Quantum state tomography (QST), the process through which the density matrix
of a quantum system is characterized from measurements of specific observables,
is a fundamental pillar in the fields of quantum information and computation.
We propose a simple QST method to reconstruct the density matrix of two qubits
encoded in the polarization and path degrees of freedom of a single photon,
which can be realized with a single linear-optical setup. We demonstrate that
the density matrix can be fully described in terms of the one-point Stokes
parameters related to the two possibles paths of the photon, together with a
quantum version of the two-point Stokes parameters introduced here.Comment: 5 pages, 2 figure
Long-range contact process and percolation on a random lattice
We study the phase transition phenomena for long-range oriented percolation
and contact process. We studied a contact process in which the range of each
vertex are independent, updated dynamically and given by some distribution .
We also study an analogous oriented percolation model on the hyper-cubic
lattice, here there is a special direction where long-range oriented bonds are
allowed; the range of all vertices are given by an i.i.d. sequence of random
variables with common distribution . For both models, we prove some results
about the existence of a phase transition in terms of the distribution
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