We study the Navier-Stokes and Euler equations of incompressible hydrodynamics in two spatial dim... more We study the Navier-Stokes and Euler equations of incompressible hydrodynamics in two spatial dimensions. Taking the divergence of the momentum equation leads, as usual, to a Poisson equation for the pressure: in this paper we study this equation using Monge-Ampere structures. In two dimensional flows where the laplacian of the pressure is positive, a Kahler geometry is described on the
Symmetry, Integrability and Geometry: Methods and Applications, 2007
... at Root of Unity* Nikolai IORGOV , Vladimir ROUBTSOV §, Vitaly SHADURA and Yuri TYKHYY ... more ... at Root of Unity* Nikolai IORGOV , Vladimir ROUBTSOV §, Vitaly SHADURA and Yuri TYKHYY ... Université d'Angers, 2 bd. Lavoisier, 49045, Angers, France E-mail: volodya@tonton. univ-angers.fr § ITEP, Moscow, 25 B. Cheremushkinskaja, 117259, Moscow, Russia ...
We study the single particle band dispersion in High Temperature Superconductors, using the nearl... more We study the single particle band dispersion in High Temperature Superconductors, using the nearly antiferromagnetic Fermi liquid (NAFL) description of their planar quasi-particles.(P. Monthoux and D. Pines, Phys. Rev. B 47, 6069 (1993).) We solve numerically a set of Eliashberg-like, strong coupling equations and obtain the quasi-particle self energy as a function of temperature and the spin-fermion interaction coupling strength, g. We consider optimally doped as well as underdoped materials by performing calculations in both the mean field, z=2, and the z=1 pseudoscaling regimes of the underlying spin fluctuation spectra. We find that the band dispersion undergoes a strong renormalization, resulting in a temperature dependent Fermi surface. Our results are in agreement with the analytical predictions of Chubukov et al,(A. V. Chubukov et al, J. Phys: Cond. Matt., 48, 10017 (1996).) although significant temperature evolution is obtained only for extremely large values of g. We use the results for the self energy to calculate the ARPES spectra and transport coefficients and compare them to the experimentally obtained results in cuprates.
ABSTRACT We study the Navier-Stokes and Euler equations of incompressible hydrodynamics in two an... more ABSTRACT We study the Navier-Stokes and Euler equations of incompressible hydrodynamics in two and three spatial dimensions and show how the constraint of incompressiblility leads to equations of Monge--Amp\`ere type for the stream function, when the Laplacian of the pressure is known. In two dimensions a K\"ahler geometry is described, which is associated with the Monge--Amp\`ere problem. This K\"ahler structure is then generalised to `two-and-a-half dimensional' flows, of which Burgers' vortex is one example. In three dimensions, we show how a generalized Calabi--Yau structure emerges in a special case.
We study the Navier-Stokes and Euler equations of incompressible hydrodynamics in two spatial dim... more We study the Navier-Stokes and Euler equations of incompressible hydrodynamics in two spatial dimensions. Taking the divergence of the momentum equation leads, as usual, to a Poisson equation for the pressure: in this paper we study this equation using Monge-Ampere structures. In two dimensional flows where the laplacian of the pressure is positive, a Kahler geometry is described on the
Symmetry, Integrability and Geometry: Methods and Applications, 2007
... at Root of Unity* Nikolai IORGOV , Vladimir ROUBTSOV §, Vitaly SHADURA and Yuri TYKHYY ... more ... at Root of Unity* Nikolai IORGOV , Vladimir ROUBTSOV §, Vitaly SHADURA and Yuri TYKHYY ... Université d'Angers, 2 bd. Lavoisier, 49045, Angers, France E-mail: volodya@tonton. univ-angers.fr § ITEP, Moscow, 25 B. Cheremushkinskaja, 117259, Moscow, Russia ...
We study the single particle band dispersion in High Temperature Superconductors, using the nearl... more We study the single particle band dispersion in High Temperature Superconductors, using the nearly antiferromagnetic Fermi liquid (NAFL) description of their planar quasi-particles.(P. Monthoux and D. Pines, Phys. Rev. B 47, 6069 (1993).) We solve numerically a set of Eliashberg-like, strong coupling equations and obtain the quasi-particle self energy as a function of temperature and the spin-fermion interaction coupling strength, g. We consider optimally doped as well as underdoped materials by performing calculations in both the mean field, z=2, and the z=1 pseudoscaling regimes of the underlying spin fluctuation spectra. We find that the band dispersion undergoes a strong renormalization, resulting in a temperature dependent Fermi surface. Our results are in agreement with the analytical predictions of Chubukov et al,(A. V. Chubukov et al, J. Phys: Cond. Matt., 48, 10017 (1996).) although significant temperature evolution is obtained only for extremely large values of g. We use the results for the self energy to calculate the ARPES spectra and transport coefficients and compare them to the experimentally obtained results in cuprates.
ABSTRACT We study the Navier-Stokes and Euler equations of incompressible hydrodynamics in two an... more ABSTRACT We study the Navier-Stokes and Euler equations of incompressible hydrodynamics in two and three spatial dimensions and show how the constraint of incompressiblility leads to equations of Monge--Amp\`ere type for the stream function, when the Laplacian of the pressure is known. In two dimensions a K\"ahler geometry is described, which is associated with the Monge--Amp\`ere problem. This K\"ahler structure is then generalised to `two-and-a-half dimensional' flows, of which Burgers' vortex is one example. In three dimensions, we show how a generalized Calabi--Yau structure emerges in a special case.
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Papers by V. Roubtsov