920 research outputs found
Cornelius Lanczos's derivation of the usual action integral of classical electrodynamics
The usual action integral of classical electrodynamics is derived starting
from Lanczos's electrodynamics -- a pure field theory in which charged
particles are identified with singularities of the homogeneous Maxwell's
equations interpreted as a generalization of the Cauchy-Riemann regularity
conditions from complex to biquaternion functions of four complex variables. It
is shown that contrary to the usual theory based on the inhomogeneous Maxwell's
equations, in which charged particles are identified with the sources, there is
no divergence in the self-interaction so that the mass is finite, and that the
only approximation made in the derivation are the usual conditions required for
the internal consistency of classical electrodynamics. Moreover, it is found
that the radius of the boundary surface enclosing a singularity interpreted as
an electron is on the same order as that of the hypothetical "bag" confining
the quarks in a hadron, so that Lanczos's electrodynamics is engaging the
reconsideration of many fundamental concepts related to the nature of
elementary particles.Comment: 16 pages. Final version to be published in "Foundations of Physics
Driven classical diffusion with strong correlated disorder
We analyze one-dimensional motion of an overdamped classical particle in the
presence of external disorder potential and an arbitrary driving force F. In
thermodynamical limit the effective force-dependent mobility mu(F) is
self-averaging, although the required system size may be exponentially large
for strong disorder. We calculate the mobility mu(F) exactly, generalizing the
known results in linear response (weak driving force) and the perturbation
theory in powers of the disorder amplitude. For a strong disorder potential
with power-law correlations we identify a non-linear regime with a prominent
power-law dependence of the logarithm of mu(F) on the driving force.Comment: 4 pages, 2 figures include
Approach to equilibrium in adiabatically evolving potentials
For a potential function (in one dimension) which evolves from a specified
initial form to a different asymptotically, we study the
evolution, in an overdamped dynamics, of an initial probability density to its
final equilibeium.There can be unexpected effects that can arise from the time
dependence. We choose a time variation of the form
. For a , which is
double welled and a which is simple harmonic, we show that, in
particular, if the evolution is adiabatic, the results in a decrease in the
Kramers time characteristics of . Thus the time dependence makes
diffusion over a barrier more efficient. There can also be interesting
resonance effects when and are two harmonic potentials
displaced with respect to each other that arise from the coincidence of the
intrinsic time scale characterising the potential variation and the Kramers
time.Comment: This paper contains 5 page
Escape from a zero current state in a one dimensional array of Josephson junctions
A long one dimensional array of small Josephson junctions exhibits Coulomb
blockade of Cooper pair tunneling. This zero current state exists up to a
switching voltage, Vsw, where there is a sudden onset of current. In this paper
we present histograms showing how Vsw changes with temperature for a long array
and calculations of the corresponding escape rates. Our analysis of the problem
is based on the existence of a voltage dependent energy barrier and we do not
make any assumptions about its shape. The data divides up into two temperature
regimes, the higher of which can be explained with Kramers thermal escape
model. At low temperatures the escape becomes independent of temperature.Comment: 4 pages 5 figure
Unitary transformation for the system of a particle in a linear potential
A unitary operator which relates the system of a particle in a linear
potential with time-dependent parameters to that of a free particle, has been
given. This operator, closely related to the one which is responsible for the
existence of coherent states for a harmonic oscillator, is used to find a
general wave packet described by an Airy function. The kernel (propagator) and
a complete set of Hermite-Gaussian type wave functions are also given.Comment: Europhysics Letters (in press
Relativistically extended Blanchard recurrence relation for hydrogenic matrix elements
General recurrence relations for arbitrary non-diagonal, radial hydrogenic
matrix elements are derived in Dirac relativistic quantum mechanics. Our
approach is based on a generalization of the second hypervirial method
previously employed in the non-relativistic Schr\"odinger case. A relativistic
version of the Pasternack-Sternheimer relation is thence obtained in the
diagonal (i.e. total angular momentum and parity the same) case, from such
relation an expression for the relativistic virial theorem is deduced. To
contribute to the utility of the relations, explicit expressions for the radial
matrix elements of functions of the form and
---where is a Dirac matrix--- are presented.Comment: 21 pages, to be published in J. Phys. B: At. Mol. Opt. Phys. in Apri
Chiral discrimination in optical trapping and manipulation
When circularly polarized light interacts with chiral molecules or nanoscale particles powerful symmetry principles determine the possibility of achieving chiral discrimination, and the detailed form of electrodynamic mechanisms dictate the types of interaction that can be involved. The optical trapping of molecules and nanoscale particles can be described in terms of a forward-Rayleigh scattering mechanism, with trapping forces being dependent on the positioning within the commonly non-uniform intensity beam profile. In such a scheme, nanoparticles are commonly attracted to local potential energy minima, ordinarily towards the centre of the beam. For achiral particles the pertinent material response property usually entails an electronic polarizability involving transition electric dipole moments. However, in the case of chiral molecules, additional effects arise through the engagement of magnetic counterpart transition dipoles. It emerges that, when circularly polarized light is used for the trapping, a discriminatory response can be identified between left- and right-handed polarizations. Developing a quantum framework to accurately describe this phenomenon, with a tensor formulation to correctly represent the relevant molecular properties, the theory leads to exact analytical expressions for the associated energy landscape contributions. Specific results are identified for liquids and solutions, both for isotropic media and also where partial alignment arises due to a static electric field. The paper concludes with a pragmatic analysis of the scope for achieving enantiomer separation by such methods
Exact time evolution and master equations for the damped harmonic oscillator
Using the exact path integral solution for the damped harmonic oscillator it
is shown that in general there does not exist an exact dissipative Liouville
operator describing the dynamics of the oscillator for arbitrary initial bath
preparations. Exact non-stationary Liouville operators can be found only for
particular preparations. Three physically meaningful examples are examined. An
exact new master equation is derived for thermal initial conditions. Second,
the Liouville operator governing the time-evolution of equilibrium correlations
is obtained. Third, factorizing initial conditions are studied. Additionally,
one can show that there are approximate Liouville operators independent of the
initial preparation describing the long time dynamics under appropriate
conditions. The general form of these approximate master equations is derived
and the coefficients are determined for special cases of the bath spectral
density including the Ohmic, Drude and weak coupling cases. The connection with
earlier work is discussed.Comment: to be published in Phys. Rev.
Relativistic Kramers-Pasternack Recurrence Relations
Recently we have evaluated the matrix elements ,O={1,\beta, i\mathbf{\alpha n}\beta} _{3}F_{2}(1) $ for all suitable powers and established two sets of
Pasternack-type matrix identities for these integrals. The corresponding
Kramers--Pasternack three-term vector recurrence relations are derived here.Comment: 12 pages, no figures Will appear as it is in Journal of Physics B:
Atomic, Molecular and Optical Physics, Special Issue on Hight Presicion
Atomic Physic
Rectification of Fluctuations in an Underdamped Ratchet
We investigate analytically the motion of underdamped particles subject to a
deterministic periodic potential and a periodic temperature. Despite the fact
that an underamped particle experiences the temperature oscillation many times
in its escape out of a well and in its motion along the potential, a net
directed current linear in the friction constant is found. If both the
potential and the temperature modulation are sinusoidal with a phase lag
, this current is proportional to .Comment: 4 pages REVTEX, 2 figures include
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