3,347 research outputs found
Searching for Apery-Style Miracles [Using, Inter-Alia, the Amazing Almkvist-Zeilberger Algorithm]
Roger Apery's seminal method for proving irrationality is "turned on its
head" and taught to computers, enabling a one second redux of the original
proof of zeta(3), and many new irrationality proofs of many new constants,
alas, none of them is both famous and not-yet-proved-irrational.Comment: 16 pages. Exclusively published in the Personal Journal of Shalosh B.
Ekhad and Doron Zeilberger, May 2014, and this arxiv.org. Accompanied my
Maple package NesApery, available from
http://www.math.rutgers.edu/~zeilberg/tokhniot/NesAper
Molecular principles underlying dual RNA specificity in the Drosophila SNF protein
The first RNA recognition motif of the Drosophila SNF protein is an example of an RNA binding protein with multi-specificity. It binds different RNA hairpin loops in spliceosomal U1 or U2 small nuclear RNAs, and only in the latter case requires the auxiliary U2A′ protein. Here we investigate its functions by crystal structures of SNF alone and bound to U1 stem-loop II, U2A′ or U2 stem-loop IV and U2A′, SNF dynamics from NMR spectroscopy, and structure-guided mutagenesis in binding studies. We find that different loop-closing base pairs and a nucleotide exchange at the tips of the loops contribute to differential SNF affinity for the RNAs. U2A′ immobilizes SNF and RNA residues to restore U2 stem-loop IV binding affinity, while U1 stem-loop II binding does not require such adjustments. Our findings show how U2A′ can modulate RNA specificity of SNF without changing SNF conformation or relying on direct RNA contacts
Dynamics of spin 1/2 quantum plasmas
The fully nonlinear governing equations for spin 1/2 quantum plasmas are
presented. Starting from the Pauli equation, the relevant plasma equations are
derived, and it is shown that nontrivial quantum spin couplings arise, enabling
studies of the combined collective and spin dynamics. The linear response of
the quantum plasma in an electron--ion system is obtained and analyzed.
Applications of the theory to solid state and astrophysical systems as well as
dusty plasmas are pointed out.Comment: 4 pages, 2 figures, to appear in Physical Review Letter
Graviton mediated photon-photon scattering in general relativity
In this paper we consider photon-photon scattering due to self-induced
gravitational perturbations on a Minkowski background. We focus on four-wave
interaction between plane waves with weakly space and time dependent
amplitudes, since interaction involving a fewer number of waves is excluded by
energy-momentum conservation. The Einstein-Maxwell system is solved
perturbatively to third order in the field amplitudes and the coupling
coefficients are found for arbitrary polarizations in the center of mass
system. Comparisons with calculations based on quantum field theoretical
methods are made, and the small discrepances are explained.Comment: 5 pages, 3 figure
The Complex Langevin method: When can it be trusted?
We analyze to what extent the complex Langevin method, which is in principle
capable of solving the so-called sign problems, can be considered as reliable.
We give a formal derivation of the correctness and then point out various
mathematical loopholes. The detailed study of some simple examples leads to
practical suggestions about the application of the method.Comment: 14 pages, including several eps figures and tables; clarification and
minor corrections added, to appear in PR
A possibility to measure elastic photon--photon scattering in vacuum
Photon--photon scattering in vacuum due to the interaction with virtual
electron-positron pairs is a consequence of quantum electrodynamics. A way for
detecting this phenomenon has been devised based on interacting modes generated
in microwave waveguides or cavities [G. Brodin, M. Marklund and L. Stenflo,
Phys. Rev. Lett. \textbf{87} 171801 (2001)]. Here we materialize these ideas,
suggest a concrete cavity geometry, make quantitative estimates and propose
experimental details. It is found that detection of photon-photon scattering
can be within the reach of present day technology.Comment: 7 pages, 3 figure
Specific heat anomalies of open quantum systems
The evaluation of the specific heat of an open, damped quantum system is a
subtle issue. One possible route is based on the thermodynamic partition
function which is the ratio of the partition functions of system plus bath and
of the bath alone. For the free damped particle it has been shown, however,
that the ensuing specific heat may become negative for appropriately chosen
environments. Being an open system this quantity then naturally must be
interpreted as the change of the specific heat obtained as the difference
between the specific heat of the heat bath coupled to the system degrees of
freedom and the specific heat of the bath alone. While this difference may
become negative, the involved specific heats themselves are always positive;
thus, the known thermodynamic stability criteria are perfectly guaranteed. For
a damped quantum harmonic oscillator, instead of negative values, under
appropriate conditions one can observe a dip in the difference of specific
heats as a function of temperature. Stylized minimal models containing a single
oscillator heat bath are employed to elucidate the occurrence of the anomalous
temperature dependence of the corresponding specific heat values. Moreover, we
comment on the consequences for the interpretation of the density of states
based on the thermal partitionfunction.Comment: 7 pages, 6 figures, new title and some modifications of the main tex
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