We prove the phase segregation phenomenon to occur in the ground state solutions of an interacting system of two self-coupled repulsive Hartree equations for large nonlinear and nonlocal interactions. A self-consistent numerical investigation visualizes the approach to this segregated regime.
@article{bwmeta1.element.doi-10_2478_s11533-009-0004-9,
author = {Walter Aschbacher and Marco Squassina},
title = {On phase segregation in nonlocal two-particle Hartree systems},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {230-248},
zbl = {1179.35255},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0004-9}
}
Walter Aschbacher; Marco Squassina. On phase segregation in nonlocal two-particle Hartree systems. Open Mathematics, Tome 7 (2009) pp. 230-248. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0004-9/
[1] Ablowitz M.J., Prinari B., Trubatch A.D., Discrete and continuous nonlinear Schrödinger systems, London Mathematical Society, Lecture Note Series 302, Cambridge University Press, 2004 | Zbl 1057.35058
[2] Anderson M.H., Ensher J.R., Matthews M.R., Wieman C.E., Cornell E.A., Observation of Bose-Einstein condensation in a diluite atomic vapor, Science, 1995, 269, 198–201 http://dx.doi.org/10.1126/science.269.5221.198[Crossref]
[3] Aschbacher W.H., Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation, Electron. J. Diff. Eqns., 2009, 12, 1–22 | Zbl 1173.35642
[4] Aschbacher W.H., Fröhlich J., Graf G.M., Schnee K., Troyer M., Symmetry breaking regime in the nonlinear Hartree equation, J. Math. Phys., 2002, 43, 3879–3891 http://dx.doi.org/10.1063/1.1488673[Crossref] | Zbl 1060.81012
[5] Bao W., Ground states and dynamics of multicomponent Bose-Einstein condensates, Multiscale Model. Simul., 2004, 2, 210–236 http://dx.doi.org/10.1137/030600209[Crossref] | Zbl 1062.82034
[6] Caliari M., Squassina M., Location and phase segregation of ground and excited states for 2D Gross-Pitaevskii systems, Dyn. Partial Differ. Equ., 2008, 5, 117–137 | Zbl 1158.35322
[7] Conti M., Terracini S., Verzini G., Nehari’s problem and competing species systems, Ann. Inst. H. Poincaré Anal. Non Linéaire, 2002, 19, 871–888 http://dx.doi.org/10.1016/S0294-1449(02)00104-X[Crossref] | Zbl 1090.35076
[8] Dalfovo F., Giorgini S., Pitaevskii L.P., Stringari S., Theory of trapped Bose-condensed gases, Rev. Mod. Phys., 1999, 71, 463–512 http://dx.doi.org/10.1103/RevModPhys.71.463[Crossref]
[9] Erdös L., Schlein B., Yau H.-T., Rigorous derivation of the Gross-Pitaevskii equation, Phys. Rev. Lett., 2007, 98, 040404 [WoS]
[10] Esry B.D., Greene C.H., Burke J.P., Bohn J.L., Hartree-Fock theory for double condensates, Phys. Rev. Lett., 1997, 78, 3594–3597 http://dx.doi.org/10.1103/PhysRevLett.78.3594[Crossref]
[11] Gross E.P., Structure of a quantized vortex in boson systems, Nuovo Cimento, 1961, 20, 454–477 http://dx.doi.org/10.1007/BF02731494[Crossref] | Zbl 0100.42403
[12] Lieb E.H., Seiringer R., Yngvason J., Bosons in a trap: a rigorous derivation of the Gross-Pitaevskii energy functional, Phys. Rev. A, 2000, 61, 043602
[13] Myatt C.J., Burt E.A., Ghrist R.W., Cornell E.A., Wieman C.E., Production of two overlapping Bose-Einstein condensates by sympathetic cooling, Phys. Rev. Lett., 1997, 78, 586–589 http://dx.doi.org/10.1103/PhysRevLett.78.586[Crossref]
[14] Öhberg P., Stenholm S., Hartree-Fock treatment of two-component Bose-Einstein condensate, Phys. Rev. A, 1998, 57, 1272–1279 http://dx.doi.org/10.1103/PhysRevA.57.1272[Crossref]
[15] Pitaevskii L.P., Vortex lines in an imperfect Bose gas, Sov. Phys. JETP, 1961, 13, 451–454
[16] Riboli F., Modugno M., Topology of the ground state of two interacting Bose-Einstein condensates, Phys. Rev. A, 2002, 65, 063614
[17] Rüegg Ch., Cavadini N., Furrer A., Güdel H-U., Krämer K., Mutka H., Wildes A., Habicht K., Vorderwisch P., Bose-Einstein condensation of the triplet states in the magnetic insulator TlCuCl3, Nature, 2003, 423,(6935):62–65 http://dx.doi.org/10.1038/nature01617[Crossref]
[18] Timmermans E., Phase separation of Bose-Einstein condensates, Phys. Rev. Lett., 1998, 81, 5718–5721 http://dx.doi.org/10.1103/PhysRevLett.81.5718[Crossref]