181 research outputs found
Pairing of bosons in the condensed state of the boson-fermion model
A two component model of negative U centers coupled with the Fermi sea of
itinerant fermions is discussed in connection with high-temperature
superconductivity of cuprates, and superfluidity of atomic fermions. We examine
the phase transition and the condensed state of this boson-fermion model (BFM)
beyond the ordinary mean-field approximation in two and three dimensions. No
pairing of fermions and no condensation are found in two-dimensions for any
symmetry of the order parameter. The expansion in the strength of the order
parameter near the transition yields no linear homogeneous term in the
Ginzburg-Landau-Gor'kov equation and a zero upper critical field in
any-dimensional BFM, which indicates that previous mean-field discussions of
the model are flawed. Normal and anomalous Green's functions are obtained
diagrammatically and analytically in the condensed state of a simplest version
of 3D BFM. A pairing of bosons analogous to the Cooper pairing of fermions is
found. There are three coupled condensates in the model, described by the
off-diagonal single-particle boson, pair-fermion and pair-boson fields. These
results negate the common wisdom that the boson-fermion model is adequately
described by the BCS theory at weak coupling.Comment: 7 pages, 4 figure
The connected components of the space of Alexandrov surfaces
Denote by the set of all compact Alexandrov surfaces
with curvature bounded below by without boundary, endowed with the
topology induced by the Gromov-Hausdorff metric. We determine the connected
components of and of its closure
Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime
In view of some recent works on the role of vertex corrections in the
electron-phonon system we readress an important question of the validity of the
Migdal-Eliashberg theory.
Based on the solution of the Holstein model and inverse coupling constant
expansion, we argue that the standard Feynman-Dyson perturbation theory by
Migdal and Eliashberg with or without vertex corrections cannot be applied if
the electron-phonon coupling constant is larger than 1 for any ratio
of the phonon and Fermi energies.
In the extreme adiabatic limit of the Holstein model electrons collapse into
self-trapped small polarons or bipolarons due to spontaneous
translational-symmetry breaking when is between 0.5 and 1.3
(depending on the lattice dimensionality). With the increasing phonon frequency
the region of the applicability of the theory shrinks to lower values of the
coupling constant.Comment: 4 pages, 1 figur
Theory of double resonance magnetometers based on atomic alignment
We present a theoretical study of the spectra produced by
optical-radio-frequency double resonance devices, in which resonant linearly
polarized light is used in the optical pumping and detection processes. We
extend previous work by presenting algebraic results which are valid for atomic
states with arbitrary angular momenta, arbitrary rf intensities, and arbitrary
geometries. The only restriction made is the assumption of low light intensity.
The results are discussed in view of their use in optical magnetometers
Detection of radio frequency magnetic fields using nonlinear magneto-optical rotation
We describe a room-temperature alkali-metal atomic magnetometer for detection
of small, high frequency magnetic fields. The magnetometer operates by
detecting optical rotation due to the precession of an aligned ground state in
the presence of a small oscillating magnetic field. The resonance frequency of
the magnetometer can be adjusted to any desired value by tuning the bias
magnetic field. We demonstrate a sensitivity of in a 3.5 cm diameter, paraffin coated cell. Based
on detection at the photon shot-noise limit, we project a sensitivity of
.Comment: 6 pages, 6 figure
Profiles of inflated surfaces
We study the shape of inflated surfaces introduced in \cite{B1} and
\cite{P1}. More precisely, we analyze profiles of surfaces obtained by
inflating a convex polyhedron, or more generally an almost everywhere flat
surface, with a symmetry plane. We show that such profiles are in a
one-parameter family of curves which we describe explicitly as the solutions of
a certain differential equation.Comment: 13 pages, 2 figure
Dynamic effects in nonlinear magneto-optics of atoms and molecules
A brief review is given of topics relating to dynamical processes arising in
nonlinear interactions between light and resonant systems (atoms or molecules)
in the presence of a magnetic field.Comment: 15 pages, 11 figure
The Necessary and Sufficient Conditions for Representing Lipschitz Bivariate Functions as a Difference of Two Convex Functions
In the article the necessary and sufficient conditions for a representation
of Lipschitz function of two variables as a difference of two convex functions
are formulated. An algorithm of this representation is given. The outcome of
this algorithm is a sequence of pairs of convex functions that converge
uniformly to a pair of convex functions if the conditions of the formulated
theorems are satisfied. A geometric interpretation is also given
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