29,515 research outputs found
One-dimensional relativistic dissipative system with constant force and its quantization
For a relativistic particle under a constant force and a linear velocity
dissipation force, a constant of motion is found. Problems are shown for
getting the Hamiltoninan of this system. Thus, the quantization of this system
is carried out through the constant of motion and using the quantization of the
velocity variable. The dissipative relativistic quantum bouncer is outlined
within this quantization approach.Comment: 11 pages, no figure
On algebraic classification of quasi-exactly solvable matrix models
We suggest a generalization of the Lie algebraic approach for constructing
quasi-exactly solvable one-dimensional Schroedinger equations which is due to
Shifman and Turbiner in order to include into consideration matrix models. This
generalization is based on representations of Lie algebras by first-order
matrix differential operators. We have classified inequivalent representations
of the Lie algebras of the dimension up to three by first-order matrix
differential operators in one variable. Next we describe invariant
finite-dimensional subspaces of the representation spaces of the one-,
two-dimensional Lie algebras and of the algebra sl(2,R). These results enable
constructing multi-parameter families of first- and second-order quasi-exactly
solvable models. In particular, we have obtained two classes of quasi-exactly
solvable matrix Schroedinger equations.Comment: LaTeX-file, 16 pages, submitted to J.Phys.A: Math.Ge
Adsorption of Self-Assembled Rigid Rods on Two-Dimensional Lattices
Monte Carlo (MC) simulations have been carried out to study the adsorption on
square and triangular lattices of particles with two bonding sites that, by
decreasing temperature or increasing density, polymerize reversibly into chains
with a discrete number of allowed directions and, at the same time, undergo a
continuous isotropic-nematic (IN) transition. The process has been monitored by
following the behavior of the adsorption isotherms for different values of
lateral interaction energy/temperature. The numerical data were compared with
mean-field analytical predictions and exact functions for noninteracting and 1D
systems. The obtained results revealed the existence of three adsorption
regimes in temperature. (1) At high temperatures, above the critical one
characterizing the IN transition at full coverage Tc(\theta=1), the particles
are distributed at random on the surface and the adlayer behaves as a
noninteracting 2D system. (2) At very low temperatures, the asymmetric monomers
adsorb forming chains over almost the entire range of coverage, and the
adsorption process behaves as a 1D problem. (3) In the intermediate regime, the
system exhibits a mixed regime and the filling of the lattice proceeds
according to two different processes. In the first stage, the monomers adsorb
isotropically on the lattice until the IN transition occurs in the system and,
from this point, particles adsorb forming chains so that the adlayer behaves as
a 1D fluid. The two adsorption processes are present in the adsorption
isotherms, and a marked singularity can be observed that separates both
regimes. Thus, the adsorption isotherms appear as sensitive quantities with
respect to the IN phase transition, allowing us (i) to reproduce the phase
diagram of the system for square lattices and (ii) to obtain an accurate
determination of the phase diagram for triangular lattices.Comment: Langmuir, 201
One pion production in neutrino-nucleon scattering and the different parametrizations of the weak vertex
The weak vertex provides an important contribution to the one
pion production in neutrino-nucleon and neutrino-nucleus scattering for
invariant masses below 1.4 GeV. Beyond its interest as a tool in neutrino
detection and their background analyses, one pion production in
neutrino-nucleon scattering is useful to test predictions based on the quark
model and other internal symmetries of strong interactions. Here we try to
establish a connection between two commonly used parametrizations of the weak
vertex and form factors (FF) and we study their effects on the
determination of the axial coupling , the common normalization of the
axial FF, which is predicted to hold 1.2 by using the PCAC hypothesis.
Predictions for the total cross sections within
the two approaches, which include the resonant and other
background contributions in a coherent way, are compared to experimental data.Comment: Submitted to Physics Letters
Velocity quantization approach of the one-dimensional dissipative harmonic oscillator
Given a constant of motion for the one-dimensional harmonic oscillator with
linear dissipation in the velocity, the problem to get the Hamiltonian for this
system is pointed out, and the quantization up to second order in the
perturbation approach is used to determine the modification on the eigenvalues
when dissipation is taken into consideration. This quantization is realized
using the constant of motion instead of the Hamiltonian.Comment: 10 pages, 2 figure
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