20 research outputs found
Diffraction of ultra-cold fermions by quantized light fields: Standing versus traveling waves
We study the diffraction of quantum degenerate fermionic atoms off of
quantized light fields in an optical cavity. We compare the case of a linear
cavity with standing wave modes to that of a ring cavity with two
counter-propagating traveling wave modes. It is found that the dynamics of the
atoms strongly depends on the quantization procedure for the cavity field. For
standing waves, no correlations develop between the cavity field and the atoms.
Consequently, standing wave Fock states yield the same results as a classical
standing wave field while coherent states give rise to a collapse and revivals
in the scattering of the atoms. In contrast, for traveling waves the scattering
results in quantum entanglement of the radiation field and the atoms. This
leads to a collapse and revival of the scattering probability even for Fock
states. The Pauli Exclusion Principle manifests itself as an additional
dephasing of the scattering probability
Testing the Dirac equation
The dynamical equations which are basic for the description of the dynamics
of quantum felds in arbitrary space--time geometries, can be derived from the
requirements of a unique deterministic evolution of the quantum fields, the
superposition principle, a finite propagation speed, and probability
conservation. We suggest and describe observations and experiments which are
able to test the unique deterministic evolution and analyze given experimental
data from which restrictions of anomalous terms violating this basic principle
can be concluded. One important point is, that such anomalous terms are
predicted from loop gravity as well as from string theories. Most accurate data
can be obtained from future astrophysical observations. Also, laboratory tests
like spectroscopy give constraints on the anomalous terms.Comment: 11 pages. to appear in: C. L\"ammerzahl, C.W.F. Everitt, and F.W.
Hehl (eds.): Gyros, Clocks, Interferometers...: Testing Relativistic Gravity
in Space, Lecture Notes in Physics 562, Springer 200
Note on the Existence of Hydrogen Atoms in Higher Dimensional Euclidean Spaces
The question of whether hydrogen atoms can exist or not in spaces with a
number of dimensions greater than 3 is revisited, considering higher
dimensional Euclidean spaces. Previous results which lead to different answers
to this question are briefly reviewed. The scenario where not only the
kinematical term of Schr\"odinger equation is generalized to a D-dimensional
space but also the electric charge conservation law (expressed here by the
Poisson law) should actually remains valid is assumed. In this case, the
potential energy in the Schr\"odinger equation goes like 1/r^{D-2}. The lowest
quantum mechanical bound states and the corresponding wave functions are
determined by applying the Numerov numerical method to solve Schr\"odinger's
eigenvalue equation. States for different angular momentum quantum number (l =
0; 1) and dimensionality (5 \leq D \leq 10) are considered. One is lead to the
result that hydrogen atoms in higher dimensions could actually exist. For the
same range of the dimensionality D, the energy eigenvalues and wave functions
are determined for l = 1. The most probable distance between the electron and
the nucleus are then computed as a function of D showing the possibility of
tiny bound states.Comment: 19 pages, 6 figure
Quantum three-body system in D dimensions
The independent eigenstates of the total orbital angular momentum operators
for a three-body system in an arbitrary D-dimensional space are presented by
the method of group theory. The Schr\"{o}dinger equation is reduced to the
generalized radial equations satisfied by the generalized radial functions with
a given total orbital angular momentum denoted by a Young diagram
for the SO(D) group. Only three internal variables are
involved in the functions and equations. The number of both the functions and
the equations for the given angular momentum is finite and equal to
.Comment: 16 pages, no figure, RevTex, Accepted by J. Math. Phy