582 research outputs found
Advertising, consensus, and ageing in multilayer Sznajd model
In the Sznajd consensus model on the square lattice, two people who agree in
their opinions convince their neighbours of this opinion. We generalize it to
many layers representing many age levels, and check if still a consensus among
all layers is possible. Advertising sometimes but not always produces a
consensus on the advertised opinion.Comment: 6 pages including 4 figures, for Int. J. Mod. Phys.
Diffusing opinions in bounded confidence processes
We study the effects of diffusing opinions on the Deffuant et al. model for
continuous opinion dynamics. Individuals are given the opportunity to change
their opinion, with a given probability, to a randomly selected opinion inside
an interval centered around the present opinion. We show that diffusion induces
an order-disorder transition. In the disordered state the opinion distribution
tends to be uniform, while for the ordered state a set of well defined opinion
clusters are formed, although with some opinion spread inside them. If the
diffusion jumps are not large, clusters coalesce, so that weak diffusion favors
opinion consensus. A master equation for the process described above is
presented. We find that the master equation and the Monte-Carlo simulations do
not always agree due to finite-size induced fluctuations. Using a linear
stability analysis we can derive approximate conditions for the transition
between opinion clusters and the disordered state. The linear stability
analysis is compared with Monte Carlo simulations. Novel interesting phenomena
are analyzed
Treating some solid state problems with the Dirac equation
The ambiguity involved in the definition of effective-mass Hamiltonians for
nonrelativistic models is resolved using the Dirac equation. The multistep
approximation is extended for relativistic cases allowing the treatment of
arbitrary potential and effective-mass profiles without ordering problems. On
the other hand, if the Schrodinger equation is supposed to be used, our
relativistic approach demonstrate that both results are coincidents if the
BenDaniel and Duke prescription for the kinetic-energy operator is implemented.
Applications for semiconductor heterostructures are discussed.Comment: 06 pages, 5 figure
Exact solution of Schrodinger equation for modified Kratzer's molecular potential with the position-dependent mass
Exact solutions of Schrodinger equation are obtained for the modified Kratzer
and the corrected Morse potentials with the position-dependent effective mass.
The bound state energy eigenvalues and the corresponding eigenfunctions are
calculated for any angular momentum for target potentials. Various forms of
point canonical transformations are applied. PACS numbers: 03.65.-w; 03.65.Ge;
12.39.Fd Keywords: Morse potential, Kratzer potential, Position-dependent mass,
Point canonical transformation, Effective mass Schr\"{o}dinger equation.Comment: 9 page
Local Manipulation of Nuclear Spin in a Semiconductor Quantum Well
The shaping of nuclear spin polarization profiles and the induction of
nuclear resonances are demonstrated within a parabolic quantum well using an
externally applied gate voltage. Voltage control of the electron and hole wave
functions results in nanometer-scale sheets of polarized nuclei positioned
along the growth direction of the well. RF voltages across the gates induce
resonant spin transitions of selected isotopes. This depolarizing effect
depends strongly on the separation of electrons and holes, suggesting that a
highly localized mechanism accounts for the observed behavior.Comment: 18 pages, 4 figure
Effect of weak magnetic field on polariton-electron scattering in semiconductor microcavities
We theoretically calculate the polariton linewidth associated with the
polariton-electron scattering in a microcavity in presence of a magnetic field
perpendicular to the microcavity plane. It is shown that the polariton
linewidth oscillates as a function of the magnetic field magnitude and the
polariton-electron scattering rate can be not only decreased but also increased
by the magnetic field. The possible applications of such an effect are
discussed.Comment: LaTex, 6 pages, 3 figure
A squeeze-like operator approach to position-dependent mass in quantum mechanics
We provide a squeeze-like transformation that allows one to remove a position
dependent mass from the Hamiltonian. Methods to solve the Schr\"{o}dinger
equation may then be applied to find the respective eigenvalues and
eigenfunctions. As an example, we consider a position-dependent-mass that leads
to the integrable Morse potential and therefore to well-known solutions
Conductance distributions of 1D-disordered wires at finite temperature and bias voltage
We calculate the distribution of the conductance G in a one-dimensional
disordered wire at finite temperature T and bias voltage V in a
independent-electron picture and assuming full coherent transport. At high
enough temperature and bias voltage, where several resonances of the system
contribute to the conductance, the distribution P(G(T,V)) can be represented
with good accuracy by autoconvolutions of the distribution of the conductance
at zero temperature and zero bias voltage. The number of convolutions depends
on T and V. In the regime of very low T and V, where only one resonance is
relevant to G(T,V), the conductance distribution is analyzed by a resonant
tunneling conductance model. Strong effects of finite T and V on the
conductance distribution are observed and well described by our theoretical
analysis, as we verify by performing a number of numerical simulations of a
one-dimensional disordered wire at different temperatures, voltages, and
lengths of the wire. Analytical estimates for the first moments of P(G(T,V)) at
high temperature and bias voltage are also provided.Comment: 9 pages, 7 figures, Submitted to PR
Strongly Correlated Two-Electron Transport in a Quantum Waveguide Having a Single Anderson Impurity
The strongly correlated two-electron transport in one-dimensional channel
coupled with an Anderson-type impurity is solved exactly via a Bethe ansatz
approach. We show that the transport properties are fundamentally different for
spin singlet and triplet states, thus the impurity acts as a novel filter that
operates based on the total spin angular momentum of the electron pairs, but
not individual spins. The filter provides a deterministic generation of
electron entanglement in spin, as well as energy and momentum space.Comment: 12 pages, 3 figure
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