199,630 research outputs found
Tkachenko modes and structural phase transitions of the vortex lattice of a two-component Bose-Einstein condensate
No full textWe consider a rapidly rotating two-component Bose-Einstein condensate (BEC) containing a vortex lattice. We calculate the dispersion relation for small oscillations of vortex positions (Tkachenko modes) in the mean-field quantum Hall regime, taking into account the coupling of these modes with density excitations. Using an analytic form for the density of the vortex lattice, we numerically calculate the elastic constants for different lattice geometries. We also apply this method to calculate the elastic constant for the single-component triangular lattice. For a two-component BEC, there are two kinds of Tkachenko modes, which we call acoustic and optical in analogy with phonons. For all lattice types, acoustic Tkachenko mode frequencies have quadratic wave-number dependence at long wavelengths, while the optical Tkachenko modes have linear dependence. For triangular lattices the dispersion of the Tkachenko modes are isotropic, while for other lattice types the dispersion relations show directional dependence consistent with the symmetry of the lattice. Depending on the intercomponent interaction there are five distinct lattice types, and four structural phase transitions between them. Two of these transitions are second order and are accompanied by the softening of an acoustic Tkachenko mode. The remaining two transitions are first order and while one of them is accompanied by the softening of an optical mode, the other does not have any dramatic effect on the Tkachenko spectrum. We also find an instability of the vortex lattice when the intercomponent repulsion becomes stronger than the repulsion within components
Tkachenko modes of the square vortex lattice in a two-component Bose-Einstein condensate
No full textWe study Tkachenko modes of the square vortex lattice of a two-component Bose-Einstein condensate (BEC) in the mean-field quantum Hall regime, considering the coupling of these modes with density excitations. We derive the hydrodynamic equations and obtain the dispersion relations of the excitation modes. We find that there are two types of excitations, gapped inertial modes and gapless Tkachenko modes. These modes have two branches which we call acoustic and optical modes in analogy with phonons. The former has quadratic while the latter has linear wave-number dependence in both inertial and Tkachenko modes. Acoustic Tkachenko mode is found to be anisotropic while the other three modes are isotropic. The anisotropy of the acoustic Tkachenko mode reflects the four-fold symmetry of the square lattice
Static properties of a warm dense uniform electron gas
No full textCopyright 2021 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in J. Ara, Ll. Coloma, and I. M. Tkachenko , "Static properties of a warm dense uniform electron gas", Physics of Plasmas 28, 112704 (2021) https://doi.org/10.1063/5.0062259[EN] We show how the static dielectric function and other static characteristics of dense warm charged Fermi liquids can be obtained exclusively from the system static structure factor. The non-perturbative self-consistent method of moments is employed to extend onto quantum fluids, a similar reduction stemming from the fluctuation-dissipation theorem and other exact relations for classical one-component plasmas. The results are compared to and complement the numerical data obtained recently by the path-integral Monte Carlo method. Alternative theoretical approaches are discussed and employed as well.I.M.T. is grateful to M. Bonitz and T. Dornheim for several valuable discussions. The authors appreciate that M. Bonitz and T. Dornheim provided accurate path integral Monte Carlo simulation results. I.M.T. also acknowledges fruitful discussions with Yu. V. Arkhipov and L. Conde and the financial support provided by the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan (Project No. AP09260349).Ara-Bernad, J.; Coloma, L.; Tkachenko Gorski, IM. (2021). Static properties of a warm dense uniform electron gas. Physics of Plasmas. 28(11):1-17. https://doi.org/10.1063/5.0062259S117281
The role of collective motion in examples of coarsening and self-assembly
No full textThe simplest prescription for building a patterned structure from its constituents is to add particles, one at a time, to an appropriate template. However, self-organizing molecular and colloidal systems in nature can evolve in much more hierarchical ways. Specifically, constituents (or clusters of constituents) may aggregate to form clusters (or clusters of clusters) that serve as building blocks for later stages of assembly. Here we evaluate the character and consequences of such collective motion in a set of prototypical assembly processes. We do so using computer simulations in which a system's capacity for hierarchical dynamics can be controlled systematically. By explicitly allowing or suppressing collective motion, we quantify its effects. We find that coarsening within a two dimensional attractive lattice gas (and an analogous off-lattice model in three dimensions) is naturally dominated by collective motion over a broad range of temperatures and densities. Under such circumstances, cluster mobility inhibits the development of uniform coexisting phases, especially when macroscopic segregation is strongly favored by thermodynamics. By contrast, the assembly of model viral capsids is not frustrated but is instead facilitated by collective moves, which promote the orderly binding of intermediates consisting of several monomers
Observation of Tkachenko Oscillations in Rapidly Rotating Bose-Einstein Condensates
No full textPhys.Rev.Lett.91:100402,2003 We directly image Tkachenko waves in a vortex lattice in a dilute-gas
Bose-Einstein condensate. The low (sub-Hz) resonant frequencies are a
consequence of the small but nonvanishing elastic shear modulus of the
vortex-filled superfluid. The frequencies are measured for rotation rates as
high as 98% of the centrifugal limit for the harmonically confined gas.
Agreement with a hydrodynamic theory worsens with increasing rotation rate,
perhaps due to the increasing fraction of the volume displaced by the vortex
cores. We also observe two low-lying m=0 longitudinal modes at about 20 times
higher frequency
Local moment problem
No full textThe work is devoted to the local moment problem, which consists in finding of non-decreasing functions on the real axis
having given first 2n+1; n = 0,1,2,...; power moments on the whole axis and also 2m+1 first power moments on a certain finite
axis interval. Considering the local moment problem as a combination of the Hausdorff and Hamburger truncated moment
problems we obtain the conditions of its solvability and describe the class of its solutions with minimal number of growth
points if the problem is solvable.Adamyan, V.; Tkachenko Gorski, IM. (2014). Local moment problem. Proceedings in Applied Mathematics and Mechanics. 14(1):981-982. doi:10.1002/pamm.201410471S981982141N.I. Akhiezer The classical moment problem and some related questions in analysis, Hafner Publishing N.Y. Company (1965).M.G. Krein Nudel'man A.A., The Markov moment problem and extremal problems, Translation of Mathematical Monographs AMS, 50 (1977).V. Adamyan I. Tkachenko Solution of the Truncated Matrix Hamburger Moment Problem According to M.G. Krein. Operator Theory: Advances and Applications, vol. 118(Proceedings of the Mark Krein International Conference on Operator Theory and Applications, vol.II, Operator Theory and Related Topics), Birkhäuser Verlag Basel, (2000), 32 - 51.V. Adamyan I. Tkachenko M. Urrea Solution of the Stieltjes truncated moment problem, J. Applied Analysis, vol. 9, N.1 (2003) 57-74.V. Adamyan I. Tkachenko Solution of the Stieltjes Truncated Matrix Moment Problem, Opuscula Mathematica, v. 25/1 (2005), 5-24.V. Adamyan I. Tkachenko General Solution of the Stieltjes Truncated Matrix Moment Problem, Operator Theory: Advances and Applications v. 163 (2005), 1- 22
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