newmaterial, physics2, spinchains
<p>H. Boos, V. Korepin and F. Smirnov,<a target="_blank" href="http://xxx.lanl.gov/abs/hep-th/0304077">"New formulae for solutions of quantum Knizhnik-Zamolodchikov equations on level -4"</a>
<p>[abstract:] "We present a new form of solution to the quantum Knizhnik-Zamolodchikov equation [qKZ] on level -4 in a special case corresponding to the Heisenberg XXX spin chain. Our form is equivalent to the integral representation obtained by Jimbo and Miwa in 1996 \cite{JM}. An advantage of our form is that it is reduced to the product of single integrals. This fact is deeply related to a cohomological nature of our formulae. Our approach is also based on the deformation of hyper-elliptic integrals and their main property - deformed Riemann bilinear relation. Jimbo and Miwa also suggested a nice conjecture which relates solution of the qKZ on level -4 to any correlation function of the XXX model. This conjecture together with our form of solution to the qKZ makes it possible to prove a conjecture that any correlation function of the XXX model can be expressed in terms of the Riemann $\zeta$-function at odd arguments and rational coefficients suggested in \cite{bk1,bk2}. This issue will be discussed in our next publication. "

newmaterial, NTscattering, physics1

<p>S. Joffily, <a target="_blank" href="http://xxx.lanl.gov/abs/math-ph/0303014">"Jost function, prime numbers and Riemann zeta function"</a>

<p>[abstract:] "The large complex zeros of the Jost function (poles of the S matrix) in the complex wave number-plane for s-wave scattering by truncated potentials are associated to the distribution of large prime numbers as well as to the asymptotic behavior of the imaginary parts of the zeros of the Riemann zeta function on the critical line. A variant of the Hilbert and Polya conjecture is proposed and considerations about the Dirac sea as "virtual resonances'' are briefly discussed."


newmaterial, physics2, spinchains, renormalisation
<p>K. Sakai, M. Shiroishi, Y. Nishiyama and M. Takahashi, 
<a target="_blank" href="http://xxx.lanl.gov/abs/cond-mat/0302564">"Third Neighbor Correlators of Spin-1/2 Heisenberg Antiferromagnet"</a>

<p>[abstract:] "We exactly evaluate the third neighbor correlator <S_j^z S_{j+3}^z> and all the possible non-zero correlators <S^{alpha}_j S^{beta}_{j+1} S^{gamma}_{j+2} S^{delta}_{j+3}> of the spin-1/2 Heisenberg $XXX$ antiferromagnet in the ground state without magnetic field. All the correlators are expressed in terms of certain combinations of logarithm ln2, the Riemann zeta function zeta(3), zeta(5) with rational coefficients. The results accurately coincide with the numerical ones obtained by the density-matrix renormalization group method and the numerical diagonalization."


newmaterial, miscellaneous

<p>V. Kisil, <a target="_blank" href="http://xxx.lanl.gov/abs/math.CV/0302186">"Axially symmetric generalization of the Cauchy-Riemann system and modified Clifford analysis"</a>

<p>[abstract:] "The main aim of this paper is to describe the most adequate generalization of the Cauchy-Riemann system fixing properties of classical functions in octonionic case. An octonionic generalization of the Laplace transform is introduced. Octonionic generalizations of the inversion transformation, the gamma function and the Riemann zeta-function are given." 


newmaterial, miscellaneous

<p>J.S. Dowker and K. Kirsten, <a target="_blank" href="http://xxx.lanl.gov/abs/hep-th/03011432">"The Barnes zeta-function, sphere determinants and Glaisher- Kinkelin-Bendersky constants"</a>
<p>[abstract:] "Summations and relations involving the Hurwitz and Riemann zeta-functions are extended first to Barnes zeta-functions and then to zeta-functions of general type. The analysis is motivated by the evaluation of determinants on spheres which are treated both by a direct expansion method and by regularised sums. Comments on existing calculations are made. A Kaluza-Klein technique is introduced providing a determinant interpretation of the Glaisher-Kinkelin-Bendersky constants which are then generalised to arbitrary zeta-functions. This technique allows an improved treatment of sphere determinants." 


newmaterial, physics2, physics1

<p>P. Leboeuf and A.G. Monastra, <a target="_blank" href="http://xxx.lanl.gov/abs/nucl-th/0302083">"Quantum thermodynamic fluctuations of a chaotic Fermi-gas model"</a>

<p>[abstract:] "We investigate the thermodynamics of a Fermi gas whose single-particle energy levels are given by the complex zeros of the Riemann zeta function. This is a model for a gas, and in particular for an atomic nucleus, with an underlying fully chaotic classical dynamics. The probability distributions of the quantum fluctuations of the grand potential and entropy of the gas are computed as a function of temperature and compared, with good agreement, with general predictions obtained from random matrix theory and periodic orbit theory (based on prime numbers). In each case the universal and non-universal regimes are identified."