211 research outputs found
A Canonical Approach to the Quantization of the Damped Harmonic Oscillator
We provide a new canonical approach for studying the quantum mechanical
damped harmonic oscillator based on the doubling of degrees of freedom
approach. Explicit expressions for Lagrangians of the elementary modes of the
problem, characterising both forward and backward time propagations are given.
A Hamiltonian analysis, showing the equivalence with the Lagrangian approach,
is also done. Based on this Hamiltonian analysis, the quantization of the model
is discussed.Comment: Revtex, 6 pages, considerably expanded with modified title and refs.;
To appear in J.Phys.
Caldirola-Kanai Oscillator in Classical Formulation of Quantum Mechanics
The quadrature distribution for the quantum damped oscillator is introduced
in the framework of the formulation of quantum mechanics based on the
tomography scheme. The probability distribution for the coherent and Fock
states of the damped oscillator is expressed explicitly in terms of Gaussian
and Hermite polynomials, correspondingly.Comment: LaTeX, 5 pages, 1 Postscript figure, Contribution to the VIII
International Conference on Symmetry Methods in Physics, Dubna 1997, to be
published in the Proceedings of the Conferenc
Hamiltonian formalism in Friedmann cosmology and its quantization
We propose a Hamiltonian formalism for a generalized
Friedmann-Roberson-Walker cosmology model in the presence of both a variable
equation of state (EOS) parameter and a variable cosmological constant
, where is the scale factor. This Hamiltonian system containing
1 degree of freedom and without constraint, gives Friedmann equations as the
equation of motion, which describes a mechanical system with a variable mass
object moving in a potential field. After an appropriate transformation of the
scale factor, this system can be further simplified to an object with constant
mass moving in an effective potential field. In this framework, the
cold dark matter model as the current standard model of cosmology corresponds
to a harmonic oscillator. We further generalize this formalism to take into
account the bulk viscosity and other cases. The Hamiltonian can be quantized
straightforwardly, but this is different from the approach of the
Wheeler-DeWitt equation in quantum cosmology.Comment: 7 pages, no figure; v2: matches the version accepted by PR
Ion energy distribution functions in a supersonic plasma jet
Starting from experimental measurements of ion energy distribution functions (IEDFs) in a low pressure supersonic plasma jet, we propose a model to simulate them numerically from first principles calculations. Experimentally we acquired IEDFs with a quadrupole mass spectrometer (QMS) collecting the argon ions produced from a inductively coupled plasma (ICP) and driven into a supersonic free gas expansion. From the discussion of these results and the physics of our system we developed a simulation code. Integrating the equations of motion the code evolves the trajectory of a single ion across the jet. Ar+- Ar collisions are modelled with a 12-4 Lennard-Jones potential which considers induced dipole interactions. IEDFs were simulated at different positions along the jet and compared with the experimental data showing good agreement. We have also implemented a charge transfer mechanism in which the ion releases its charge to a neutral atom which can take place at sufficiently close distances and is a function of the impact energy
Generalization of Dirac Non-Linear Electrodynamics, and Spinning Charged Particles
In this note we generalized the Dirac non-linear electrodynamics, by
introducing two potentials (namely, the vector potential A and the
pseudo-vector potential gamma^5 B of the electromagnetic theory with charges
and magnetic monopoles) and by imposing the pseudoscalar part of the product
omega.omega* to be zero, with omega = A + gamma^5 B. We show that the field
equations of such a theory possess a soliton-like solution which can represent
a priori a "charged particle", since it is endowed with a Coulomb field plus
the field of a magnetic dipole. The rest energy of the soliton is finite, and
the angular momentum stored in its electromagnetic field can be identified
--for suitable choices of the parameters-- with the spin of the charged
particle. Thus this approach seems to yield a classical model for the charged
(spinning) particle, which does not meet the problems met by earlier attempts
in the same direction.Comment: standard LaTeX file; 16 pages; it is a corrected version of a paper
appeared in Found. Phys. (issue in honour of A.O.Barut) 23 (1993) 46
Squeezed States of the Generalized Minimum Uncertainty State for the Caldirola-Kanai Hamiltonian
We show that the ground state of the well-known pseudo-stationary states for
the Caldirola-Kanai Hamiltonian is a generalized minimum uncertainty state,
which has the minimum allowed uncertainty , where is a constant depending on the damping
factor and natural frequency. The most general symmetric Gaussian states are
obtained as the one-parameter squeezed states of the pseudo-stationary ground
state. It is further shown that the coherent states of the pseudo-stationary
ground state constitute another class of the generalized minimum uncertainty
states.Comment: RevTex4, 9 pages, no fingure; to be published in Journal of Physics
Mesoscopic circuits with charge discreteness:quantum transmission lines
We propose a quantum Hamiltonian for a transmission line with charge
discreteness. The periodic line is composed of an inductance and a capacitance
per cell. In every cell the charge operator satisfies a nonlinear equation of
motion because of the discreteness of the charge. In the basis of one-energy
per site, the spectrum can be calculated explicitly. We consider briefly the
incorporation of electrical resistance in the line.Comment: 11 pages. 0 figures. Will be published in Phys.Rev.
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
Unitary relations in time-dependent harmonic oscillators
For a harmonic oscillator with time-dependent (positive) mass and frequency,
an unitary operator is shown to transform the quantum states of the system to
those of a harmonic oscillator system of unit mass and time-dependent
frequency, as well as operators. For a driven harmonic oscillator, it is also
shown that, there are unitary transformations which give the driven system from
the system of same mass and frequency without driving force. The transformation
for a driven oscillator depends on the solution of classical equation of motion
of the driven system. These transformations, thus, give a simple way of finding
exact wave functions of a driven harmonic oscillator system, provided the
quantum states of the corresponding system of unit mass are given.Comment: Submitted to J. Phys.
Novel approach to the study of quantum effects in the early universe
We develop a theoretical frame for the study of classical and quantum
gravitational waves based on the properties of a nonlinear ordinary
differential equation for a function of the conformal time
, called the auxiliary field equation. At the classical level,
can be expressed by means of two independent solutions of the
''master equation'' to which the perturbed Einstein equations for the
gravitational waves can be reduced. At the quantum level, all the significant
physical quantities can be formulated using Bogolubov transformations and the
operator quadratic Hamiltonian corresponding to the classical version of a
damped parametrically excited oscillator where the varying mass is replaced by
the square cosmological scale factor . A quantum approach to the
generation of gravitational waves is proposed on the grounds of the previous
dependent Hamiltonian. An estimate in terms of and
of the destruction of quantum coherence due to the gravitational
evolution and an exact expression for the phase of a gravitational wave
corresponding to any value of are also obtained. We conclude by
discussing a few applications to quasi-de Sitter and standard de Sitter
scenarios.Comment: 20 pages, to appear on PRD. Already published background material has
been either settled up in a more compact form or eliminate
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