478 research outputs found
Random Sequential Adsorption on Fractals
Irreversible adsorption of spheres on flat collectors having dimension
is studied. Molecules are adsorbed on Sierpinski's Triangle and Carpet like
fractals (), and on General Cantor Set (). Adsorption process is
modeled numerically using Random Sequential Adsorption (RSA) algorithm. The
paper concentrates on measurement of fundamental properties of coverages, i.e.
maximal random coverage ratio and density autocorrelation function, as well as
RSA kinetics. Obtained results allow to improve phenomenological relation
between maximal random coverage ratio and collector dimension. Moreover,
simulations show that, in general, most of known dimensional properties of
adsorbed monolayers are valid for non-integer dimensions.Comment: 12 pages, 8 figure
Entanglement monotones
In the context of quantifying entanglement we study those functions of a
multipartite state which do not increase under the set of local
transformations. A mathematical characterization of these monotone magnitudes
is presented. They are then related to optimal strategies of conversion of
shared states. More detailed results are presented for pure states of bipartite
systems. It is show that more than one measure are required simultaneously in
order to quantify completely the non-local resources contained in a bipartite
pure state, while examining how this fact does not hold in the so-called
asymptotic limit. Finally, monotonicity under local transformations is proposed
as the only natural requirement for measures of entanglement.Comment: Revtex, 13 pages, no figures. Previous title: "On the
characterization of entanglement". Major changes in notation and structure.
Some new results, comments and references have been adde
Random packing of spheres in Menger sponge
Random packing of spheres inside fractal collectors of dimension 2 < d < 3 is
studied numerically using Random Sequential Adsorption (RSA) algorithm. The
paper focuses mainly on the measurement of random packing saturation limit.
Additionally, scaling properties of density autocorrelations in the obtained
packing are analyzed. The RSA kinetics coefficients are also measured. Obtained
results allow to test phenomenological relation between random packing
saturation density and collector dimension. Additionally, performed simulations
together with previously obtained results confirm that, in general, the known
dimensional relations are obeyed by systems having non-integer dimension, at
least for d < 3.Comment: 13 pages, 6 figure
Entanglement entropy and entanglement spectrum of the Kitaev model
In this paper, we obtain an exact formula for the entanglement entropy of the
ground state and all excited states of the Kitaev model. Remarkably, the
entanglement entropy can be expressed in a simple separable form S=S_G+S_F,
with S_F the entanglement entropy of a free Majorana fermion system and S_G
that of a Z_2 gauge field. The Z_2 gauge field part contributes to the
universal "topological entanglement entropy" of the ground state while the
fermion part is responsible for the non-local entanglement carried by the Z_2
vortices (visons) in the non-Abelian phase. Our result also enables the
calculation of the entire entanglement spectrum and the more general Renyi
entropy of the Kitaev model. Based on our results we propose a new quantity to
characterize topologically ordered states--the capacity of entanglement, which
can distinguish the states with and without topologically protected gapless
entanglement spectrum.Comment: 4.0 pages + supplementary material, published version in Phys. Rev.
Let
Contradictory uncertainty relations
We show within a very simple framework that different measures of
fluctuations lead to uncertainty relations resulting in contradictory
conclusions. More specifically we focus on Tsallis and Renyi entropic
uncertainty relations and we get that the minimum uncertainty states of some
uncertainty relations are the maximum uncertainty states of closely related
uncertainty relations, and vice versa.Comment: 4 pages, 10 figure
Thermodynamic interpretation of the uniformity of the phase space probability measure
Uniformity of the probability measure of phase space is considered in the
framework of classical equilibrium thermodynamics. For the canonical and the
grand canonical ensembles, relations are given between the phase space
uniformities and thermodynamic potentials, their fluctuations and correlations.
For the binary system in the vicinity of the critical point the uniformity is
interpreted in terms of temperature dependent rates of phases of well defined
uniformities. Examples of a liquid-gas system and the mass spectrum of nuclear
fragments are presented.Comment: 11 pages, 2 figure
Fascinating Night
https://digitalcommons.library.umaine.edu/mmb-vp/1428/thumbnail.jp
Multiple-copy entanglement transformation and entanglement catalysis
We prove that any multiple-copy entanglement transformation [S.
Bandyopadhyay, V. Roychowdhury, and U. Sen, Phys. Rev. A \textbf{65}, 052315
(2002)] can be implemented by a suitable entanglement-assisted local
transformation [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. \textbf{83},
3566 (1999)]. Furthermore, we show that the combination of multiple-copy
entanglement transformation and the entanglement-assisted one is still
equivalent to the pure entanglement-assisted one. The mathematical structure of
multiple-copy entanglement transformations then is carefully investigated. Many
interesting properties of multiple-copy entanglement transformations are
presented, which exactly coincide with those satisfied by the
entanglement-assisted ones. Most interestingly, we show that an arbitrarily
large number of copies of state should be considered in multiple-copy
entanglement transformations.Comment: 11 pages, RevTex 4. Main results unchanged. Journal versio
Moments of Wigner function and Renyi entropies at freeze-out
Relation between Renyi entropies and moments of the Wigner function,
representing the quantum mechanical description of the M-particle
semi-inclusive distribution at freeze-out, is investigated. It is shown that in
the limit of infinite volume of the system, the classical and quantum
descriptions are equivalent. Finite volume corrections are derived and shown to
be small for systems encountered in relativistic heavy ion collisions.Comment: 15 pages, one figur
Random sequential adsorption of shrinking or spreading particles
We present a model of one-dimensional irreversible adsorption in which
particles once adsorbed immediately shrink to a smaller size or expand to a
larger size. Exact solutions for the fill factor and the particle number
variance as a function of the size change are obtained. Results are compared
with approximate analytical solutions.Comment: 9 pages, 8 figure
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