Vortex formation in a two-dimensional Bose gas
We discuss the stability of a homogeneous two-dimensional Bose gas at finite temperature against the formation of isolated vortices. We consider a patch of several healing lengths in size and compute its free energy using the Euclidean formalism. Since we deal with an open system, which is able to e...
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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
2010
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| Sumario: | We discuss the stability of a homogeneous two-dimensional Bose gas at finite temperature against the formation of isolated vortices. We consider a patch of several healing lengths in size and compute its free energy using the Euclidean formalism. Since we deal with an open system, which is able to exchange particles and angular momentum with the rest of the condensate, we use the symmetry-breaking (as opposed to the particle number conserving) formalism, and include configurations with all values of angular momenta in the partition function. At finite temperature, there appear sphaleron configurations associated with isolated vortices. The contribution from these configurations to the free energy is computed in the dilute gas approximation. We show that the Euclidean action of linearized perturbations of a vortex is not positive definite. As a consequence the free energy of the 2D Bose gas acquires an imaginary part. This signals the instability of the gas. This instability may be identified with the Berezinskii-Kosterlitz-Thouless transition. © 2010 IOP Publishing Ltd. |
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| Bibliografía: | Mermin, N.D., Wagner, H., Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models (1966) Phys. Rev. Lett., 17, p. 1133 Hohenberg, P.C., Existence of long-range order in one and two dimensions (1967) Phys. Rev., 158, p. 383 Coleman, S., There are no Goldstone bosons in two dimensions (1973) Commun. Math. Phys., 31, p. 259 Berezinskii, V.L., Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group: I. Classical systems (1971) Sov. Phys.-JETP, 32, p. 493 Kosterlitz, J.M., Thouless, D.J., Ordering, metastability and phase transitions in two-dimensional systems (1973) J. Phys. C: Solid State Phys., 6, p. 1181 Al Khawaja, U., Andersen, J.O., Proukakis, N.P., Stoof, H.T.C., Low-dimensional Bose gases (2002) Phys. Rev. A, 66, p. 013615 How, P.-T., Leclair, A., Critical point of the two-dimensional Bose gas: An S-matrix approach (2010) Nucl. Phys., 824, p. 415 Gräter, M., Wetterich, C., Kosterlitz-Thouless phase transition in the two-dimensional linear σ model (1995) Phys. Rev. Lett., 75, p. 378 Gersdorff, G.V., Wetterich, C., Nonperturbative renormalization flow and essential scaling for the Kosterlitz-Thouless transition (2001) Physical Review B - Condensed Matter and Materials Physics, 64 (5), pp. 0545131-0545135. , 054513 Floerchinger, S., Wetterich, C., Superfluid Bose gas in two dimensions (2009) Phys. Rev. A, 79, p. 013601 Popov, V.N., Quantum vortices and phase transitions in Bose systems (1973) Sov. Phys.-JETP, 37, p. 341 Popov, V.N., (1987) Functional Integrals and Collective Excitations, , (Cambridge: Cambridge University Press) chapter 8 Chu, H.-C., Williams, G.A., Quenched Kosterlitz-Thouless superfluid transition (2000) Phys. Rev. Lett., 86, p. 2585 Arovas, D.P., Auerbach, A., Quantum tunneling of vortices in two-dimensional superfluids (2008) Phys. Rev. B, 78, p. 094508 Lindner, N.H., Auerbach, A., Arovas, D.P., Vortex quantum dynamics of two-dimensional lattice bosons (2008) Phys. Rev. Lett., 102, p. 070403 Joseph Wang, C.-C., Duine, R.A., MacDonald, A.H., Quantum vortex dynamics in two-dimensional neutral superfluids (2010) Phys. Rev. A, 81, p. 013609 Gross, E.P., Hydrodynamics of a superfluid condensate (1963) J. Math. Phys., 4, p. 195 Ginzburg, V.L., Pitaevskii, L.P., On the theory of superfluidity (1958) Sov. Phys.-JETP, 34, p. 858 Pu, H., Law, C.K., Eberly, J.H., Bigelow, N.P., Coherent disintegration and stability of vortices in trapped Bose condensates (1999) Physical Review A - Atomic, Molecular, and Optical Physics, 59 (2-3), pp. 1533-1537 Prokof'Ev, N., Ruebenacker, O., Svistunov, B., Critical point of a weakly interacting two-dimensional Bose gas (2001) Physical Review Letters, 87 (1-27), pp. 2704021-2704024. , 270402 Prokof'Ev, N., Svistunov, B., Two-dimensional weakly interacting Bose gas in the fluctuation region (2002) Phys. Rev. A, 66, p. 043608 Davis, M.J., Morgan, S.A., Burnett, K., Simulations of thermal Bose fields in the classical limit (2002) Phys. Rev. A, 66, p. 053618 Hutchinson, D.A.W., Blakie, P.B., Phase transitions in ultra-cold two-dimensional Bose gases (2006) Int. J. Mod. Phys., 20 (30-31), p. 5224 Simula, T.P., Blakie, P.B., Thermal activation of vortex-antivortex pairs in quasi-two-dimensional Bose-Einstein condensates (2006) Phys. Rev. Lett., 96, p. 020404 Shumayer, D., Hutchinsin, D.A.W., Thermodynamically activated vortex-dipole formation in a two-dimensional Bose-Einstein condensate (2007) Phys. Rev. A, 75, p. 015601 Simula, T.P., Davis, M.J., Blakie, P.B., Superfluidity of an interacting trapped quasi-two-dimensional Bose gas (2008) Phys. Rev. A, 77, p. 023618 Holzmann, M., Chevallier, M., Krauth, W., Semiclassical theory of the quasi-two-dimensional trapped Bose gas (2008) Europhys. Lett., 82, p. 30001 Bisset, R.N., Baillie, D., Blakie, P.B., Analysis of the Holzmann-Chevallier-Krauth theory for the trapped quasi-two-dimensional Bose gas (2009) Phys. Rev. A, 79, p. 013602 Bisset, R.N., Davis, M.J., Simula, T.P., Blakie, P.B., Quasi-condensation and coherence in the quasi-two-dimensional trapped Bose gas (2009) Phys. Rev. A, 79, p. 033626 Bisset, R.N., Blakie, P.B., Quantitative test of the mean-field description of a trapped two-dimensional Bose gas (2009) Phys. Rev. A, 80, p. 045603 Bisset, R.N., Blakie, P.B., Transition region properties of a trapped quasi-two-dimensional degenerate Bose gas (2009) Phys. Rev. A, 80, p. 035602 Hadzibabic, Z., Krüger, P., Cheneau, M., Battelier, B., Dalibard, J., Berezinskii-Kosterlitz-Thouless crossover in a trapped atomic gas (2007) Nature, 441, p. 1118 Krüger, P., Hadzibabic, Z., Dalibard, J., Critical point of an interacting two-dimensional atomic Bose gas (2007) Phys. Rev. Lett., 99, p. 040402 Cladé, P., Ryu, C., Ramanathan, A., Helmerson, K., Phillips, W.D., Observation of a 2D Bose gas: From thermal to quasi-condensate to superfluid (2009) Phys. Rev. Lett., 102, p. 170401 Calzetta, E., Hu, B.-L., (2008) Nonequilibrium Quantum Field Theory, , (Cambridge: Cambridge University Press) chapter 13.3 Rubakov, V., (2002) Classical Theory of Gauge Fields, , (Princeton, NJ: Princeton University Press) Langer, J.S., Theory of nucleation rates (1968) Phys. Rev. Lett., 21, p. 973 Langer, J.S., Statistical theory of the decay of metastable states (1969) Ann. Phys., 54, p. 258 Coleman, S., Fate of the false vacuum: Semiclassical theory (1977) Phys. Rev. D, 15, p. 2929 Callan, C.G., Coleman, S., Fate of the false vacuum: II. First quantum corrections (1977) Phys. Rev. D, 16, p. 1762 Coleman, S., (1985) Aspects of Symmetry, , (Cambridge: Cambridge University Press) chapter 7 Affleck, I.K., De Luccia, F., Induced vacuum decay (1979) Phys. Rev. D, 20, p. 3168 Affleck, I., Quantum-statistical metastability (1981) Phys. Rev. Lett., 46, p. 388 Haldane, F.D.M., Effective harmonic-fluid approach to low-energy properties of one-dimensional quantum fluids (1981) Phys. Rev. Lett., 47, p. 1840 Calzetta, E., Hu, B.L., Rey, A.M., Bose-Einstein-condensate superfluid-Mott-insulator transition in an optical lattice (2006) Phys. Rev. A, 73, p. 023610 Hadzibabic, Z., Dalibard, J., (2009) Two-dimensional Bose Fluids: An Atomic Physics Perspective Lifshitz, L.M., Pitaevskii, L.P., (1990) Statistical Physics, Part 2, 9. , (Course of Theoretical Physics) (Oxford: Pergamon) chapter 30 Barnett, R., Chen, E., Refael, G., Vortex synchronization in Bose-Einstein condensates: A time-dependent Gross-Pitaevskii equation approach (2010) New J. Phys., 13, p. 043004 Altland, A., Simons, B., (2006) Condensed Matter Field Theory, , (Cambridge: Cambridge University Press) chapter 9 Negele, J.W., Orland, H., (1998) Quantum Many-Particle Systems Feynman, R.P., (1972) Statistical Mechanics, , (Reading, MA: Addison-Wesley) chapter 3 Rajaraman, R., (1987) Solitons and Instantons, , (New York: Elsevier) chapter 10 Gelfand, I.M., Yaglom, A.M., Integration in functional spaces and its applications in quantum physics (1960) J. Math. Phys., 1, p. 48 Dunne, G.V., Functional determinants in quantum field theory (2008) J. Phys. A: Math. Theor., 41, p. 304006 Holzmann, M., Krauth, W., Kosterlitz-Thouless transition of the quasi two-dimensional trapped Bose gas (2008) Phys. Rev. Lett., 100, p. 190402 |
| ISSN: | 09534075 |
| DOI: | 10.1088/0953-4075/43/9/095004 |