28 research outputs found
PageRank model of opinion formation on Ulam networks
We consider a PageRank model of opinion formation on Ulam networks, generated
by the intermittency map and the typical Chirikov map. The Ulam networks
generated by these maps have certain similarities with such scale-free networks
as the World Wide Web (WWW), showing an algebraic decay of the PageRank
probability. We find that the opinion formation process on Ulam networks have
certain similarities but also distinct features comparing to the WWW. We
attribute these distinctions to internal differences in network structure of
the Ulam and WWW networks. We also analyze the process of opinion formation in
the frame of generalized Sznajd model which protects opinion of small
communities.Comment: 7 pages, 6 figures. Updated version for publicatio
Superstable cycles for antiferromagnetic Q-state Potts and three-site interaction Ising models on recursive lattices
We consider the superstable cycles of the Q-state Potts (QSP) and the
three-site interaction antiferromagnetic Ising (TSAI) models on recursive
lattices. The rational mappings describing the models' statistical properties
are obtained via the recurrence relation technique. We provide analytical
solutions for the superstable cycles of the second order for both models. A
particular attention is devoted to the period three window. Here we present an
exact result for the third order superstable orbit for the QSP and a numerical
solution for the TSAI model. Additionally, we point out a non-trivial
connection between bifurcations and superstability: in some regions of
parameters a superstable cycle is not followed by a doubling bifurcation.
Furthermore, we use symbolic dynamics to understand the changes taking place at
points of superstability and to distinguish areas between two consecutive
superstable orbits.Comment: 12 pages, 5 figures. Updated version for publicatio
Arnold Tongues and Feigenbaum Exponents of the Rational Mapping for Q-state Potts Model on Recursive Lattice: Q<2
We considered Q-state Potts model on Bethe lattice in presence of external
magnetic field for Q<2 by means of recursion relation technique. This allows to
study the phase transition mechanism in terms of the obtained one dimensional
rational mapping. The convergence of Feigenabaum and
exponents for the aforementioned mapping is investigated for the period
doubling and three cyclic window. We regarded the Lyapunov exponent as an order
parameter for the characterization of the model and discussed its dependence on
temperature and magnetic field. Arnold tongues analogs with winding numbers
w=1/2, w=2/4 and w=1/3 (in the three cyclic window) are constructed for Q<2.
The critical temperatures of the model are discussed and their dependence on Q
is investigated. We also proposed an approximate method for constructing Arnold
tongues via Feigenbaum exponent.Comment: 15 pages, 12 figure
A quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices
We construct a quantum-inspired classical algorithm for computing the
permanent of Hermitian positive semidefinite matrices, by exploiting a
connection between these mathematical structures and the boson sampling model.
Specifically, the permanent of a Hermitian positive semidefinite matrix can be
expressed in terms of the expected value of a random variable, which stands for
a specific photon-counting probability when measuring a linear-optically
evolved random multimode coherent state. Our algorithm then approximates the
matrix permanent from the corresponding sample mean and is shown to run in
polynomial time for various sets of Hermitian positive semidefinite matrices,
achieving a precision that improves over known techniques. This work
illustrates how quantum optics may benefit algorithms development.Comment: 9 pages, 1 figure. Updated version for publicatio
Direct dialling of Haar random unitary matrices
Random unitary matrices find a number of applications in quantum information
science, and are central to the recently defined boson sampling algorithm for
photons in linear optics. We describe an operationally simple method to
directly implement Haar random unitary matrices in optical circuits, with no
requirement for prior or explicit matrix calculations. Our physically-motivated
and compact representation directly maps independent probability density
functions for parameters in Haar random unitary matrices, to optical circuit
components. We go on to extend the results to the case of random unitaries for
qubits
Magnetic Properties and Thermal Entanglement on a Triangulated Kagome Lattice
The magnetic and entanglement thermal (equilibrium) properties in spin-1/2
Ising-Heisenberg model on a triangulated Kagome lattice are analyzed by means
of variational mean-field like treatment based on Gibbs-Bogoliubov inequality.
Because of the separable character of Ising-type exchange interactions between
the Heisenberg trimers the calculation of quantum entanglement in a
self-consistent field can be performed for each of the trimers individually.
The concurrence in terms of three qubit isotropic Heisenberg model in effective
Ising field is non-zero even in the absence of a magnetic field. The magnetic
and entanglement properties exhibit common (plateau and peak) features
observable via (antferromagnetic) coupling constant and external magnetic
field. The critical temperature for the phase transition and threshold
temperature for concurrence coincide in the case of antiferromagnetic coupling
between qubits. The existence of entangled and disentangled phases in saturated
and frustrated phases is established.Comment: 21 pages, 13 figure
Thermal Entanglement of a Spin-1/2 Ising-Heisenberg Model on a Symmetrical Diamond Chain
The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a
symmetrical diamond chain were analyzed. Due to the separable nature of the
Ising-type exchange interactions between neighboring Heisenberg dimers,
calculation of the entanglement can be performed exactly for each individual
dimer. Pairwise thermal entanglement was studied in terms of the isotropic
Ising-Heisenberg model, and analytical expressions for the concurrence (as a
measure of bipartite entanglement) were obtained. The effects of external
magnetic field and next-nearest neighbor interaction between nodal
Ising sites were considered. The ground-state structure and entanglement
properties of the system were studied in a wide range of the coupling constant
values. Various regimes with different values of the ground-state entanglement
were revealed, depending on the relation between competing interaction
strengths. Finally, some novel effects, such as the two-peak behavior of
concurrence versus temperature and coexistence of phases with different values
of magnetic entanglement were observed
Thermal Entanglement and Critical Behavior of Magnetic Properties on a Triangulated Kagomé Lattice
The equilibrium magnetic and entanglement properties in a spin-1/2 Ising-Heisenberg model on a triangulated Kagomé lattice are analyzed by means of the effective field for the Gibbs-Bogoliubov inequality. The calculation is reduced to decoupled individual (clusters) trimers due to the separable character of the Ising-type exchange interactions between the Heisenberg trimers. The concurrence in terms of the three qubit isotropic Heisenberg model in the effective Ising field in the absence of a magnetic field is non-zero. The magnetic and entanglement properties exhibit common (plateau, peak) features driven by a magnetic field and (antiferromagnetic) exchange interaction. The (quantum) entangled and non-entangled phases can be exploited as a useful tool for signalling the quantum phase transitions and crossovers at finite temperatures. The critical temperature of order-disorder coincides with the threshold temperature of thermal entanglement
Stimulated Raman Adiabatic Passage via bright state in Lambda medium of unequal oscillator strengths
We consider the population transfer process in a Lambda-type atomic medium of
unequal oscillator strengths by stimulated Raman adiabatic passage via
bright-state (b-STIRAP) taking into account propagation effects. Using both
analytic and numerical methods we show that the population transfer efficiency
is sensitive to the ratio q_p/q_s of the transition oscillator strengths. We
find that the case q_p>q_s is more detrimental for population transfer process
as compared to the case where . For this case it is possible to
increase medium dimensions while permitting efficient population transfer. A
criterion determining the interaction adiabaticity in the course of propagation
process is found. We also show that the mixing parameter characterizing the
population transfer propagates superluminally