198 research outputs found
Klein-Gordon and Dirac particles in non-constant scalar-curvature background
The Klein-Gordon and Dirac equations are considered in a semi-infinite lab
() in the presence of background metrics and with . These metrics have non-constant scalar-curvatures. Various aspects of the
solutions are studied. For the first metric with , it is shown
that the spectrums are discrete, with the ground state energy for spin-0 particles. For , the spectrums are
found to be continuous. For the second metric with , each
particle, depends on its transverse-momentum, can have continuous or discrete
spectrum. For Klein-Gordon particles, this threshold transverse-momentum is
, while for Dirac particles it is . There is no solution for
case. Some geometrical properties of these metrics are also
discussed.Comment: 14 pages, LaTeX, to be published in Int. Jour. Mod. Phys.
Exactly solvable reaction diffusion models on a Cayley tree
The most general reaction-diffusion model on a Cayley tree with
nearest-neighbor interactions is introduced, which can be solved exactly
through the empty-interval method. The stationary solutions of such models, as
well as their dynamics, are discussed. Concerning the dynamics, the spectrum of
the evolution Hamiltonian is found and shown to be discrete, hence there is a
finite relaxation time in the evolution of the system towards its stationary
state.Comment: 9 pages, 2 figure
A new class of integrable diffusion-reaction processes
We consider a process in which there are two types of particles, A and B, on
an infinite one-dimensional lattice. The particles hop to their adjacent sites,
like the totally asymmetric exclusion process (ASEP), and have also the
following interactions: A+B -> B+B and B+A -> B+B, all occur with equal rate.
We study this process by imposing four boundary conditions on ASEP master
equation. It is shown that this model is integrable, in the sense that its
N-particle S-matrix is factorized into a product of two-particle S-matrices
and, more importantly, the two-particle S-matrix satisfy quantum Yang-Baxter
equation. Using coordinate Bethe-ansatz, the N-particle wavefunctions and the
two-particle conditional probabilities are found exactly.
Further, by imposing four reasonable physical conditions on two-species
diffusion-reaction processes (where the most important ones are the equality of
the reaction rates and the conservation of the number of particles in each
reaction), we show that among the 4096 types of the interactions which have
these properties and can be modeled by a master equation and an appropriate set
of boundary conditions, there are only 28 independent interactions which are
integrable. We find all these interactions and also their corresponding wave
functions. Some of these may be new solutions of quantum Yang-Baxter equation.Comment: LaTex,16 pages, some typos are corrected, will be appeared in Phys.
Rev. E (2000
Laughlin states on the Poincare half-plane and its quantum group symmetry
We find the Laughlin states of the electrons on the Poincare half-plane in
different representations. In each case we show that there exist a quantum
group symmetry such that the Laughlin states are a representation of
it. We calculate the corresponding filling factor by using the plasma analogy
of the FQHE.Comment: 9 pages,Late
Quantum Hall Effect Wave Functions as Cyclic Representations of U_q(sl(2))
Quantum Hall effect wave functions corresponding to the filling factors
1/2p+1, 2/2p+1, ..., 2p/2p+1, 1, are shown to form a basis of irreducible
cyclic representation of the quantum algebra U_q(sl(2)) at q^{2p+1}=1. Thus,
the wave functions \Psi_{P/Q} possessing filling factors P/Q<1 where Q is odd
and P, Q are relatively prime integers are classified in terms of U_q(sl(2)).Comment: Version to appear in Jour. Phys.
Neutrino oscillation in a space-time with torsion
Using the Einstein-Cartan-Dirac theory, we study the effect of torsion on
neutrino oscillation. We see that torsion cannot induce neutrino oscillation,
but affects it whenever oscillation exists for other reasons. We show that the
torsion effect on neutrino oscillation is as important as the neutrino mass
effect, whenever the ratio of neutrino number density to neutrino energy is
cm /eV, or the number density of the matter is cm.Comment: 7 pages, LaTex,Some typos corrected Journal: Int. J. Mod. Phys. A
(1999) (will be appeared
Torsion Phenomenology at the LHC
We explore the potential of the CERN Large Hadron Collider (LHC) to test the
dynamical torsion parameters. The form of the torsion action can be established
from the requirements of consistency of effective quantum field theory. The
most phenomenologically relevant part of the torsion tensor is dual to a
massive axial vector field. This axial vector has geometric nature, that means
it does not belong to any representation of the gauge group of the SM extension
or GUT theory. At the same time, torsion should interact with all fermions,
that opens the way for the phenomenological applications.
We demonstrate that LHC collider can establish unique constraints on the
interactions between fermions and torsion field considerably exceeding present
experimental lower bounds on the torsion couplings and its mass. It is also
shown how possible non-universal nature of torsion couplings due to the
renormalization group running between the Planck and TeV energy scales can be
tested via the combined analysis of Drell-Yan and production
processes
Exact solution of a one-parameter family of asymmetric exclusion processes
We define a family of asymmetric processes for particles on a one-dimensional
lattice, depending on a continuous parameter ,
interpolating between the completely asymmetric processes [1] (for ) and the n=1 drop-push models [2] (for ). For arbitrary \la,
the model describes an exclusion process, in which a particle pushes its right
neighbouring particles to the right, with rates depending on the number of
these particles. Using the Bethe ansatz, we obtain the exact solution of the
master equation .Comment: 14 pages, LaTe
p-species integrable reaction-diffusion processes
We consider a process in which there are p-species of particles, i.e.
A_1,A_2,...,A_p, on an infinite one-dimensional lattice. Each particle
can diffuse to its right neighboring site with rate , if this site is not
already occupied. Also they have the exchange interaction A_j+A_i --> A_i+A_j
with rate We study the range of parameters (interactions) for which
the model is integrable. The wavefunctions of this multi--parameter family of
integrable models are found. We also extend the 2--species model to the case in
which the particles are able to diffuse to their right or left neighboring
sites.Comment: 16 pages, LaTe
Thermodynamic Properties of a Quantum Group Boson Gas
An approach is proposed enabling to effectively describe the behaviour of a
bosonic system. The approach uses the quantum group formalism. In
effect, considering a bosonic Hamiltonian in terms of the
generators, it is shown that its thermodynamic properties are connected to
deformation parameters and . For instance, the average number of
particles and the pressure have been computed. If is fixed to be the same
value for , our approach coincides perfectly with some results developed
recently in this subject. The ordinary results, of the present system, can be
found when we take the limit .Comment: 13 pages, Late
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