711 research outputs found
Generalizing the autonomous Kepler Ermakov system in a Riemannian space
We generalize the two dimensional autonomous Hamiltonian Kepler Ermakov
dynamical system to three dimensions using the sl(2,R) invariance of Noether
symmetries and determine all three dimensional autonomous Hamiltonian Kepler
Ermakov dynamical systems which are Liouville integrable via Noether
symmetries. Subsequently we generalize the autonomous Kepler Ermakov system in
a Riemannian space which admits a gradient homothetic vector by the
requirements (a) that it admits a first integral (the Riemannian Ermakov
invariant) and (b) it has sl(2,R) invariance. We consider both the
non-Hamiltonian and the Hamiltonian systems. In each case we compute the
Riemannian Ermakov invariant and the equations defining the dynamical system.
We apply the results in General Relativity and determine the autonomous
Hamiltonian Riemannian Kepler Ermakov system in the spatially flat Friedman
Robertson Walker spacetime. We consider a locally rotational symmetric (LRS)
spacetime of class A and discuss two cosmological models. The first
cosmological model consists of a scalar field with exponential potential and a
perfect fluid with a stiff equation of state. The second cosmological model is
the f(R) modified gravity model of {\Lambda}_{bc}CDM. It is shown that in both
applications the gravitational field equations reduce to those of the
generalized autonomous Riemannian Kepler Ermakov dynamical system which is
Liouville integrable via Noether integrals.Comment: Reference [25] update, 21 page
Time-Dependent Invariants for Dirac Equation and Newton-Wigner Position Operator
For Dirac equation, operator-invariants containing explicit time-dependence
in parallel to known time-dependent invariants of nonrelativistic Schr\"odinger
equation are introduced and discussed. As an example, a free Dirac particle is
considered and new invariants are constructed for it. The integral of motion,
which is initial Newton-Wigner position operator, is obtained explicitly for a
free Dirac particle. For such particle with kick modeled by delta-function of
time, the time-depending integral, which has physical meaning of initial
momentum, is found.Comment: LATEX,21 pages,submitted to Physica Script
Fast atomic transport without vibrational heating
We use the dynamical invariants associated with the Hamiltonian of an atom in
a one dimensional moving trap to inverse engineer the trap motion and perform
fast atomic transport without final vibrational heating. The atom is driven
non-adiabatically through a shortcut to the result of adiabatic, slow trap
motion. For harmonic potentials this only requires designing appropriate trap
trajectories, whereas perfect transport in anharmonic traps may be achieved by
applying an extra field to compensate the forces in the rest frame of the trap.
The results can be extended to atom stopping or launching. The limitations due
to geometrical constraints, energies and accelerations involved are analyzed,
as well as the relation to previous approaches (based on classical trajectories
or "fast-forward" and "bang-bang" methods) which can be integrated in the
invariant-based framework.Comment: 10 pages, 5 figure
Symmetry, singularities and integrability in complex dynamics III: approximate symmetries and invariants
The different natures of approximate symmetries and their corresponding first
integrals/invariants are delineated in the contexts of both Lie symmetries of
ordinary differential equations and Noether symmetries of the Action Integral.
Particular note is taken of the effect of taking higher orders of the
perturbation parameter. Approximate symmetries of approximate first
integrals/invariants and the problems of calculating them using the Lie method
are considered
Resonant enhancement of the jump rate in a double-well potential
We study the overdamped dynamics of a Brownian particle in the double-well
potential under the influence of an external periodic (AC) force with zero
mean. We obtain a dependence of the jump rate on the frequency of the external
force. The dependence shows a maximum at a certain driving frequency. We
explain the phenomenon as a switching between different time scales of the
system: interwell relaxation time (the mean residence time) and the intrawell
relaxation time. Dependence of the resonant peak on the system parameters,
namely the amplitude of the driving force A and the noise strength
(temperature) D has been explored. We observe that the effect is well
pronounced when A/D > 1 and if A/D 1 the enhancement of the jump rate can be of
the order of magnitude with respect to the Kramers rate.Comment: Published in J. Phys. A: Math. Gen. 37 (2004) 6043-6051; 6 figure
Vacuum energy and spectral function sum rules
We reformulate the problem of the cancellation of the ultraviolet
divergencies of the vacuum energy, particularly important at the cosmological
level, in terms of a saturation of spectral function sum rules which leads to a
set of conditions on the spectrum of the fundamental theory. We specialize the
approach to both Minkowski and de Sitter space-times and investigate some
examples.Comment: 11 pages, revtex4, no figures, version to be published on PR
Finished plasma strengthening and restoration of fuel equipment details
© 2018 Institute of Physics Publishing. All rights reserved. The results of the investigation of the physical and mechanical properties of diamond-like coatings of the DLCPateks type (a-C: H / a-SiOCN) obtained on friction surfaces by transporting the atomic and molecular flux of vapor particles of liquid chemical compounds by a plasma jet of an arc plasma torch of atmospheric pressure are presented. The layer formed on the working surfaces is a non-metallic amorphous multilayer coating with a low coefficient of friction, increased microhardness, chemical inertness, hydrophilicity, high heat resistance and dielectric characteristics. To minimize the possible defectiveness of the main material, it is proposed to apply thin-film coatings to them at the final stage of manufacturing fuel equipment parts
The Equivalence Postulate of Quantum Mechanics
The Equivalence Principle (EP), stating that all physical systems are
connected by a coordinate transformation to the free one with vanishing energy,
univocally leads to the Quantum Stationary HJ Equation (QSHJE). Trajectories
depend on the Planck length through hidden variables which arise as initial
conditions. The formulation has manifest p-q duality, a consequence of the
involutive nature of the Legendre transform and of its recently observed
relation with second-order linear differential equations. This reflects in an
intrinsic psi^D-psi duality between linearly independent solutions of the
Schroedinger equation. Unlike Bohm's theory, there is a non-trivial action even
for bound states. No use of any axiomatic interpretation of the wave-function
is made. Tunnelling is a direct consequence of the quantum potential which
differs from the usual one and plays the role of particle's self-energy. The
QSHJE is defined only if the ratio psi^D/psi is a local self-homeomorphism of
the extended real line. This is an important feature as the L^2 condition,
which in the usual formulation is a consequence of the axiomatic interpretation
of the wave-function, directly follows as a basic theorem which only uses the
geometrical gluing conditions of psi^D/psi at q=\pm\infty as implied by the EP.
As a result, the EP itself implies a dynamical equation that does not require
any further assumption and reproduces both tunnelling and energy quantization.
Several features of the formulation show how the Copenhagen interpretation
hides the underlying nature of QM. Finally, the non-stationary higher
dimensional quantum HJ equation and the relativistic extension are derived.Comment: 1+3+140 pages, LaTeX. Invariance of the wave-function under the
action of SL(2,R) subgroups acting on the reduced action explicitly reveals
that the wave-function describes only equivalence classes of Planck length
deterministic physics. New derivation of the Schwarzian derivative from the
cocycle condition. "Legendre brackets" introduced to further make "Legendre
duality" manifest. Introduction now contains examples and provides a short
pedagogical review. Clarifications, conclusions, ackn. and references adde
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