14,553 research outputs found
Functions of perturbed operators
We prove that if 0<\a<1 and is in the H\"older class \L_\a(\R), then
for arbitrary self-adjoint operators and with bounded , the
operator is bounded and \|f(A)-f(B)\|\le\const\|A-B\|^\a. We
prove a similar result for functions of the Zygmund class \L_1(\R):
\|f(A+K)-2f(A)+f(A-K)\|\le\const\|K\|, where and are self-adjoint
operators. Similar results also hold for all H\"older-Zygmund classes
\L_\a(\R), \a>0. We also study properties of the operators for
f\in\L_\a(\R) and self-adjoint operators and such that belongs
to the Schatten--von Neumann class \bS_p. We consider the same problem for
higher order differences. Similar results also hold for unitary operators and
for contractions.Comment: 6 page
A quantitative study of spin noise spectroscopy in a classical gas of K atoms
We present a general derivation of the electron spin noise power spectrum in
alkali gases as measured by optical Faraday rotation, which applies to both
classical gases at high temperatures as well as ultracold quantum gases. We
show that the spin-noise power spectrum is determined by an electron spin-spin
correlation function, and we find that measurements of the spin-noise power
spectra for a classical gas of K atoms are in good agreement with the
predicted values. Experimental and theoretical spin noise spectra are directly
and quantitatively compared in both longitudinal and transverse magnetic fields
up to the high magnetic field regime (where Zeeman energies exceed the
intrinsic hyperfine energy splitting of the K ground state)
Toeplitz Schur multipliers of for
We study Toeplitz Schur miltipliers of Schatten-von Neumann class for $0 Mots-clé, Keywords : Schur multipliers, Schatten-von Neumann classes, commutative locally compact groups
An Interesting Class of Operators with unusual Schatten-von Neumann behavior
We consider the class of integral operators Q_\f on of the form
(Q_\f f)(x)=\int_0^\be\f (\max\{x,y\})f(y)dy. We discuss necessary and
sufficient conditions on to insure that is bounded, compact,
or in the Schatten-von Neumann class \bS_p, . We also give
necessary and sufficient conditions for to be a finite rank
operator. However, there is a kind of cut-off at , and for membership in
\bS_{p}, , the situation is more complicated. Although we give
various necessary conditions and sufficient conditions relating to
Q_{\phi}\in\bS_{p} in that range, we do not have necessary and sufficient
conditions. In the most important case , we have a necessary condition and
a sufficient condition, using and modulus of continuity,
respectively, with a rather small gap in between. A second cut-off occurs at
: if \f is sufficiently smooth and decays reasonably fast, then \qf
belongs to the weak Schatten-von Neumann class \wS{1/2}, but never to
\bS_{1/2} unless \f=0.
We also obtain results for related families of operators acting on
and .
We further study operations acting on bounded linear operators on
related to the class of operators Q_\f. In particular we
study Schur multipliers given by functions of the form and
we study properties of the averaging projection (Hilbert-Schmidt projection)
onto the operators of the form Q_\f.Comment: 87 page
Simulations of magnetic and magnetoelastic properties of Tb2Ti2O7 in paramagnetic phase
Magnetic and magnetoelastic properties of terbium titanate pyrochlore in
paramagnetic phase are simulated. The magnetic field and temperature
dependences of magnetization and forced magnetostriction in Tb2Ti2O7 single
crystals and polycrystalline samples are calculated in the framework of
exchange charge model of crystal field theory and a mean field approximation.
The set of electron-deformation coupling constants has been determined.
Variations of elastic constants with temperature and applied magnetic field are
discussed. Additional strong softening of the crystal lattice at liquid helium
temperatures in the magnetic field directed along the rhombic symmetry axis is
predicted.Comment: 13 pages, 4 figures, 2 table
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