4,412 research outputs found
Search for Anderson localization of light by cold atoms in a static electric field
We explore the potential of a static electric field to induce Anderson
localization of light in a large three-dimensional (3D) cloud of randomly
distributed, immobile atoms with a degenerate ground state (total angular
momentum ) and a three-fold degenerate excited state (). We
study both the spatial structure of quasimodes of the atomic cloud and the
scaling of the Thouless number with the size of the cloud. Our results indicate
that unlike the static magnetic field, the electric field does not induce
Anderson localization of light by atoms. We explain this conclusion by the
incomplete removal of degeneracy of the excited atomic state by the field and
the relatively strong residual dipole-dipole coupling between atoms which is
weaker than in the absence of external fields but stronger than in the presence
of a static magnetic field. A joint analysis of these results together with our
previous results concerning Anderson localization of scalar waves and light
suggests the existence of a critical strength of dipole-dipole interactions
that should not be surpassed for Anderson localization to be possible in 3D.Comment: Misprints corrected in Table
Ioffe-Regel criterion of Anderson localization in the model of resonant point scatterers
We establish a phase diagram of a model in which scalar waves are scattered
by resonant point scatterers pinned at random positions in the free
three-dimensional (3D) space. A transition to Anderson localization takes place
in a narrow frequency band near the resonance frequency provided that the
number density of scatterers exceeds a critical value , where is the wave number in the free space. The
localization condition can be rewritten as ,
where is the on-resonance mean free path in the independent-scattering
approximation. At mobility edges, the decay of the average amplitude of a
monochromatic plane wave is not purely exponential and the growth of its phase
is nonlinear with the propagation distance. This makes it impossible to define
the mean free path and the effective wave number in a usual way. If
the latter are defined as an effective decay length of the intensity and an
effective growth rate of the phase of the average wave field, the Ioffe-Regel
parameter at the mobility edges can be calculated and takes values
from 0.3 to 1.2 depending on . Thus, the Ioffe-Regel criterion of
localization is valid only
qualitatively and cannot be used as a quantitative condition of Anderson
localization in 3D.Comment: Revised and extended version. 9 pages, 6 figure
Transport of light through a dense ensemble of cold atoms in a static electric field
We demonstrate that the transport of coherent quasiresonant light through a
dense cloud of immobile two-level atoms subjected to a static external electric
field can be described by a simple diffusion process up to atomic number
densities of the order of at least atoms per wavelength cubed. Transport
mean free paths well below the wavelength of light in the free space can be
reached without inducing any sign of Anderson localization of light or of any
other mechanism of breakdown of diffusion.Comment: Revised text. 9 pages, 3 figure
Magnetic-field-driven localization of light in a cold-atom gas
We discover a transition from extended to localized quasi-modes for light in
a gas of immobile two-level atoms in a magnetic field. The transition takes
place either upon increasing the number density of atoms in a strong field or
upon increasing the field at a high enough density. It has many characteristic
features of a disorder-driven (Anderson) transition but is strongly influenced
by near-field interactions between atoms and the anisotropy of the atomic
medium induced by the magnetic field.Comment: 5+8 pages, 4+8 figures, supplemental material adde
Universal fluctuations in subdiffusive transport
Subdiffusive transport in tilted washboard potentials is studied within the
fractional Fokker-Planck equation approach, using the associated continuous
time random walk (CTRW) framework. The scaled subvelocity is shown to obey a
universal law, assuming the form of a stationary Levy-stable distribution. The
latter is defined by the index of subdiffusion alpha and the mean subvelocity
only, but interestingly depends neither on the bias strength nor on the
specific form of the potential. These scaled, universal subvelocity
fluctuations emerge due to the weak ergodicity breaking and are vanishing in
the limit of normal diffusion. The results of the analytical heuristic theory
are corroborated by Monte Carlo simulations of the underlying CTRW
Fluctuations, Higher Order Anharmonicities, and Landau Expansion for Barium Titanate
Correct phenomenological description of ferroelectric phase transitions in
barium titanate requires accounting for eighth-order terms in the free energy
expansion, in addition to the conventional sixth-order contributions. Another
unusual feature of BaTiO_3 crystal is that the coefficients B_1 and B_2 of the
terms P_x^4 and P_x^2*P_y^2 in the Landau expansion depend on the temperature.
It is shown that the temperature dependence of B_1 and B_2 may be caused by
thermal fluctuations of the polarization, provided the fourth-order
anharmonicity is anomalously small, i. e. the nonlinearity of P^4 type and
higher-order ones play comparable roles. Non-singular (non-critical)
fluctuation contributions to B_1 and B_2 are calculated in the first
approximation in sixth-order and eighth-order anharmonic constants. Both
contributions increase with the temperature, which is in agreement with
available experimental data. Moreover, the theory makes it possible to
estimate, without any additional assumptions, the ratio of fluctuation
(temperature dependent) contributions to coefficients B_1 and B_2. Theoretical
value of B_1/B_2 appears to be close to that given by experiments.Comment: 5 pages, 1 figur
Brownian yet non-Gaussian diffusion in heterogeneous media: from superstatistics to homogenization
We discuss the situations under which Brownian yet non-Gaussian (BnG)
diffusion can be observed in the model of a particle's motion in a random
landscape of diffusion coefficients slowly varying in space. Our conclusion is
that such behavior is extremely unlikely in the situations when the particles,
introduced into the system at random at , are observed from the
preparation of the system on. However, it indeed may arise in the case when the
diffusion (as described in Ito interpretation) is observed under equilibrated
conditions. This paradigmatic situation can be translated into the model of the
diffusion coefficient fluctuating in time along a trajectory, i.e. into a kind
of the "diffusing diffusivity" model.Comment: 12 pages; 10 figure
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