10,368 research outputs found
Energy Levels of "Hydrogen Atom" in Discrete Time Dynamics
We analyze dynamical consequences of a conjecture that there exists a
fundamental (indivisible) quant of time. In particular we study the problem of
discrete energy levels of hydrogen atom. We are able to reconstruct potential
which in discrete time formalism leads to energy levels of unperturbed hydrogen
atom. We also consider linear energy levels of quantum harmonic oscillator and
show how they are produced in the discrete time formalism. More generally, we
show that in discrete time formalism finite motion in central potential leads
to discrete energy spectrum, the property which is common for quantum
mechanical theory. Thus deterministic (but discrete time!) dynamics is
compatible with discrete energy levels.Comment: accepted for publication in Open Systems & Information Dynamic
Statistical properties of energy levels of chaotic systems: Wigner or non-Wigner
For systems whose classical dynamics is chaotic, it is generally believed
that the local statistical properties of the quantum energy levels are well
described by Random Matrix Theory. We present here two counterexamples - the
hydrogen atom in a magnetic field and the quartic oscillator - which display
nearest neighbor statistics strongly different from the usual Wigner
distribution. We interpret the results with a simple model using a set of
regular states coupled to a set of chaotic states modeled by a random matrix.Comment: 10 pages, Revtex 3.0 + 4 .ps figures tar-compressed using uufiles
package, use csh to unpack (on Unix machine), to be published in Phys. Rev.
Let
Semi-classical analysis of real atomic spectra beyond Gutzwiller's approximation
Real atomic systems, like the hydrogen atom in a magnetic field or the helium
atom, whose classical dynamics are chaotic, generally present both discrete and
continuous symmetries. In this letter, we explain how these properties must be
taken into account in order to obtain the proper (i.e. symmetry projected)
expansion of semiclassical expressions like the Gutzwiller trace
formula. In the case of the hydrogen atom in a magnetic field, we shed light on
the excellent agreement between present theory and exact quantum results.Comment: 4 pages, 1 figure, final versio
Population control of 2s-2p transitions in hydrogen
We consider the time evolution of the occupation probabilities for the 2s-2p
transition in a hydrogen atom interacting with an external field, V(t). A
two-state model and a dipole approximation are used. In the case of degenerate
energy levels an analytical solution of the time-dependent Shroedinger equation
for the probability amplitudes exists. The form of the solution allows one to
choose the ratio of the field amplitude to its frequency that leads to temporal
trapping of electrons in specific states. The analytic solution is valid when
the separation of the energy levels is small compared to the energy of the
interacting radiation.Comment: 6 pages, 3 figure
Strong Analytic Controllability for Hydrogen Control Systems
The realization and representation of so(4,2) associated with the hydrogen
atom Hamiltonian are derived. By choosing operators from the realization of
so(4,2) as interacting Hamiltonians, a hydrogen atom control system is
constructed, and it is proved that this control system is strongly analytically
controllable based on a time-dependent strong analytic controllability theorem.Comment: 6 pages; corrected typo; added equations in section III for
representation states of so(4,2). accepted by CDC 200
Hydrogen atom in crossed electric and magnetic fields: Phase space topology and torus quantization via periodic orbits
A hierarchical ordering is demonstrated for the periodic orbits in a strongly
coupled multidimensional Hamiltonian system, namely the hydrogen atom in
crossed electric and magnetic fields. It mirrors the hierarchy of broken
resonant tori and thereby allows one to characterize the periodic orbits by a
set of winding numbers. With this knowledge, we construct the action variables
as functions of the frequency ratios and carry out a semiclassical torus
quantization. The semiclassical energy levels thus obtained agree well with
exact quantum calculations
A discrete time-dependent method for metastable atoms in intense fields
The full-dimensional time-dependent Schrodinger equation for the electronic
dynamics of single-electron systems in intense external fields is solved
directly using a discrete method.
Our approach combines the finite-difference and Lagrange mesh methods. The
method is applied to calculate the quasienergies and ionization probabilities
of atomic and molecular systems in intense static and dynamic electric fields.
The gauge invariance and accuracy of the method is established. Applications to
multiphoton ionization of positronium and hydrogen atoms and molecules are
presented. At very high intensity above saturation threshold, we extend the
method using a scaling technique to estimate the quasienergies of metastable
states of the hydrogen molecular ion. The results are in good agreement with
recent experiments.Comment: 10 pages, 9 figure, 4 table
The phase space geometry underlying roaming reaction dynamics
Recent studies have found an unusual way of dissociation in formaldehyde. It
can be characterized by a hydrogen atom that separates from the molecule, but
instead of dissociating immediately it roams around the molecule for a
considerable amount of time and extracts another hydrogen atom from the
molecule prior to dissociation. This phenomenon has been coined roaming and has
since been reported in the dissociation of a number of other molecules. In this
paper we investigate roaming in Chesnavich's CH model. During
dissociation the free hydrogen must pass through three phase space bottleneck
for the classical motion, that can be shown to exist due to unstable periodic
orbits. None of these orbits is associated with saddle points of the potential
energy surface and hence related to transition states in the usual sense. We
explain how the intricate phase space geometry influences the shape and
intersections of invariant manifolds that form separatrices, and establish the
impact of these phase space structures on residence times and rotation numbers.
Ultimately we use this knowledge to attribute the roaming phenomenon to
particular heteroclinic intersections
Classical approach in quantum physics
The application of a classical approach to various quantum problems - the
secular perturbation approach to quantization of a hydrogen atom in external
fields and a helium atom, the adiabatic switching method for calculation of a
semiclassical spectrum of hydrogen atom in crossed electric and magnetic
fields, a spontaneous decay of excited states of a hydrogen atom, Gutzwiller's
approach to Stark problem, long-lived excited states of a helium atom recently
discovered with the help of Poincar section, inelastic
transitions in slow and fast electron-atom and ion-atom collisions - is
reviewed. Further, a classical representation in quantum theory is discussed.
In this representation the quantum states are treating as an ensemble of
classical states. This approach opens the way to an accurate description of the
initial and final states in classical trajectory Monte Carlo (CTMC) method and
a purely classical explanation of tunneling phenomenon. The general aspects of
the structure of the semiclassical series such as renormgroup symmetry,
criterion of accuracy and so on are reviewed as well. In conclusion, the
relation between quantum theory, classical physics and measurement is
discussed.Comment: This review paper was rejected from J.Phys.A with referee's comment
"The author has made many worthwhile contributions to semiclassical physics,
but this article does not meet the standard for a topical review"
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