131 research outputs found
Infinite matrices may violate the associative law
The momentum operator for a particle in a box is represented by an infinite
order Hermitian matrix . Its square is well defined (and diagonal),
but its cube is ill defined, because . Truncating these
matrices to a finite order restores the associative law, but leads to other
curious results.Comment: final version in J. Phys. A28 (1995) 1765-177
Critical Behaviour of 3D Systems with Long-Range Correlated Quenched Defects
A field-theoretic description of the critical behaviour of systems with
quenched defects obeying a power law correlations for
large separations is given. Directly for three-dimensional systems
and different values of correlation parameter a
renormalization analysis of scaling function in the two-loop approximation is
carried out, and the fixed points corresponding to stability of the various
types of critical behaviour are identified. The obtained results essentially
differ from results evaluated by double - expansion. The
critical exponents in the two-loop approximation are calculated with the use of
the Pade-Borel summation technique.Comment: Submitted to J. Phys. A, Letter to Editor 9 pages, 4 figure
Dissipative light field as a way to create strongly localized structures for atom lithography
Generally, the conditions for deep sub-Doppler laser cooling do not match the
conditions for the strong atomic localization that takes a place in deeper
optical potential and, in consequence, leads to larger temperature. Moreover,
for a given detuning in a deep optical potential the secular approximation
which is usually used for quantum description of laser cooling becomes no more
valid. Here we perform an analysis of atomic localization in optical potential
based on a full quantum approach for atomic density matrix. We also show that
the laser cooling in a deep far-off detuned optical potential, created by a
light field with a polarization gradient, can be used as an alternative method
for forming high contrast spatially localized structures of atoms for the
purposes of atom lithography and atomic nanofabrication. Finally, we perform an
analysis of the possible limits for the width and the contrast of localized
atomic structures that can in principle be reached by this type of the light
mask.Comment: 4 figure
Evaporative Deposition Patterns Revisited: Spatial Dimensions of the Deposit
A model accounting for finite spatial dimensions of the deposit patterns in
the evaporating sessile drops of colloidal solution on a plane substrate is
proposed. The model is based on the assumption that the solute particles occupy
finite volume and hence these dimensions are of the steric origin. Within this
model, the geometrical characteristics of the deposition patterns are found as
functions of the initial concentration of the solute, the initial geometry of
the drop, and the time elapsed from the beginning of the drying process. The
model is solved analytically for small initial concentrations of the solute and
numerically for arbitrary initial concentrations of the solute. The agreement
between our theoretical results and the experimental data is demonstrated, and
it is shown that the observed dependence of the deposit dimensions on the
experimental parameters can indeed be attributed to the finite dimensions of
the solute particles. These results are universal and do not depend on any free
or fitting parameters; they are important for understanding the evaporative
deposition and may be useful for creating controlled deposition patterns.Comment: 34 pages, 14 figures, LaTeX; submitted to Physical Review
Calculations of the dynamical critical exponent using the asymptotic series summation method
We consider how the Pad'e-Borel, Pad'e-Borel-Leroy, and conformal mapping
summation methods for asymptotic series can be used to calculate the dynamical
critical exponent for homogeneous and disordered Ising-like systems.Comment: 21 RevTeX pages, 2 figure
Deep macroscopic pure-optical potential for laser cooling and trapping of neutral atoms without using a magneto-optical trap
We show the possibility of implementing a deep dissipative optical lattice
for neutral atoms with a macroscopic period. The depth of the lattice can reach
magnitudes comparable to the depth of the magneto-optical traps (MOT), while
the presence of dissipative friction forces allows for trapping and cooling of
atoms. The area of localization of trapped atoms reaches sub-millimeter size,
and the number of atoms is comparable to the number trapped in MOT. As an
example, we study lithium atoms for which the macroscopic period of the lattice
cm. Such deep optical lattices with a macroscopic period open up
possibility for developing effective methods for cooling and trapping neutral
atoms without use of magnetic field as an alternative to MOT. This is important
for developing compact systems based on cold atoms
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