459 research outputs found
A Meinardus theorem with multiple singularities
Meinardus proved a general theorem about the asymptotics of the number of
weighted partitions, when the Dirichlet generating function for weights has a
single pole on the positive real axis. Continuing \cite{GSE}, we derive
asymptotics for the numbers of three basic types of decomposable combinatorial
structures (or, equivalently, ideal gas models in statistical mechanics) of
size , when their Dirichlet generating functions have multiple simple poles
on the positive real axis. Examples to which our theorem applies include ones
related to vector partitions and quantum field theory. Our asymptotic formula
for the number of weighted partitions disproves the belief accepted in the
physics literature that the main term in the asymptotics is determined by the
rightmost pole.Comment: 26 pages. This version incorporates the following two changes implied
by referee's remarks: (i) We made changes in the proof of Proposition 1; (ii)
We provided an explanation to the argument for the local limit theorem. The
paper is tentatively accepted by "Communications in Mathematical Physics"
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Impurity-induced tuning of quantum well states in spin-dependent resonant tunneling
We report exact model calculations of the spin-dependent tunneling in double
magnetic tunnel junctions in the presence of impurities in the well. We show
that the impurity can tune selectively the spin channels giving rise to a wide
variety of interesting and novel transport phenomena. The tunneling
magnetoresistance, the spin polarization and the local current can be
dramatically enhanced or suppressed by impurities. The underlying mechanism is
the impurity-induced shift of the quantum well states (QWS) which depends on
the impurity potential, impurity position and the symmetry of the QWS.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let
The magnetic order of GdMn2Ge2 studied by neutron diffraction and x ray resonant magnetic scattering
Recoil Correction to Hydrogen Energy Levels: A Revision
Recent calculations of the order (Z\alpha)^4(m/M)Ry pure recoil correction to
hydrogen energy levels are critically revised. The origins of errors made in
the previous works are elucidated. In the framework of a successive approach,
we obtain the new result for the correction to S levels. It amounts to -16.4
kHz in the ground state and -1.9 kHz in the 2S state.Comment: 15 pages, Latex, no figure
Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems
We propose the integrable (pseudo)spherical generalization of the
four-dimensional anisotropic oscillator with additional nonlinear potential.
Performing its Kustaanheimo-Stiefel transformation we then obtain the
pseudospherical generalization of the MICZ-Kepler system with linear and
potential terms. We also present the generalization of the
parabolic coordinates, in which this system admits the separation of variables.
Finally, we get the spherical analog of the presented MICZ-Kepler-like system.Comment: 7 page
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