312 research outputs found
Minimal coupling method and the dissipative scalar field theory
Quantum field theory of a damped vibrating string as the simplest dissipative
scalar field investigated by its coupling with an infinit number of
Klein-Gordon fields as the environment by introducing a minimal coupling
method. Heisenberg equation containing a dissipative term proportional to
velocity obtained for a special choice of coupling function and quantum
dynamics for such a dissipative system investigated. Some kinematical relations
calculated by tracing out the environment degrees of freedom. The rate of
energy flowing between the system and it's environment obtained.Comment: 15 pages, no figur
Deriving Spin within a discrete-time theory
We prove that the classical theory with a discrete time (chronon) is a
particular case of a more general theory in which spinning particles are
associated with generalized Lagrangians containing time-derivatives of any
order (a theory that has been called "Non-Newtonian Mechanics"). As a
consequence, we get, for instance, a classical kinematical derivation of
Hamiltonian and spin vector for the mentioned chronon theory (e.g., in
Caldirola et al.'s formulation).Comment: 10 pages; LaTeX fil
On the Classical Theory of the Electron
A classical theory of the electron, proposed by one of us several years ago and based on finite-difference equations, is discussed by considering the three possible following cases: radiating electron, absorbing electron and nonradiating, nonabsorbing electron. In particular the so-called transmission laws necessary to determine, in conjunction with the dynamical equations, the motion of a charged particle corresponding to given initial values of position and velocity are critically reconsidered. The general characteristics of the one-dimensional motion in the non-relativistic approximation are discussed in detail. It is found that in the case of the radiating electron the particle position tends asimptotically to the point of stable equilibrium. The present theory is, therefore, free from the unphysical phenomenon of runaway solutions. These general results are illustrated by studying the motion of a particle under the action of a restoring elastic force and under the action of purely time-dependent forces
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.
Comments on discrete time in quantum mechanics
The possibility that time can be regarded as a discrete parameter is
re-examined. We study the dynamics of the free particle and find in some cases
superluminal propagation
Scattering and delay time for 1D asymmetric potentials: the step-linear and the step-exponential cases
We analyze the quantum-mechanical behavior of a system described by a
one-dimensional asymmetric potential constituted by a step plus (i) a linear
barrier or (ii) an exponential barrier. We solve the energy eigenvalue equation
by means of the integral representation method, classifying the independent
solutions as equivalence classes of homotopic paths in the complex plane.
We discuss the structure of the bound states as function of the height U_0 of
the step and we study the propagation of a sharp-peaked wave packet reflected
by the barrier. For both the linear and the exponential barrier we provide an
explicit formula for the delay time \tau(E) as a function of the peak energy E.
We display the resonant behavior of \tau(E) at energies close to U_0. By
analyzing the asymptotic behavior for large energies of the eigenfunctions of
the continuous spectrum we also show that, as expected, \tau(E) approaches the
classical value for E -> \infty, thus diverging for the step-linear case and
vanishing for the step-exponential one.Comment: 14 pages, 10 figure
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
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
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
Some Heuristic Semiclassical Derivations of the Planck Length, the Hawking Effect and the Unruh Effect
The formulae for Planck length, Hawking temperature and Unruh-Davies
temperature are derived by using only laws of classical physics together with
the Heisenberg principle. Besides, it is shown how the Hawking relation can be
deduced from the Unruh relation by means of the principle of equivalence; the
deep link between Hawking effect and Unruh effect is in this way clarified.Comment: LaTex file, 6 pages, no figure
- …