Functional renormalization group for quantized anharmonic oscillator. (English) Zbl 1220.81095
Summary: Functional renormalization group methods formulated in the real-time formalism are applied to the \(O(N)\) symmetric quantum anharmonic oscillator, considered as a \(0+1\)-dimensional quantum field-theoric model, in the next-to-leading order of the gradient expansion of the one- and two-particle irreducible effective action. The infrared scaling laws and the sensitivity-matrix analysis show the existence of only a single, symmetric phase. The Taylor expansion for the local potential converges fast while it is found not to work for the field-dependent wavefunction renormalization, in particular for the double-well bare potential. Results for the gap energy for the bare anharmonic oscillator potential hint on improving scheme-independence in the next-to-leading order of the gradient expansion, although the truncated perturbation expansion in the bare quartic coupling provides strongly scheme-dependent results for the infrared limits of the running couplings.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81T17 | Renormalization group methods applied to problems in quantum field theory |
| 81Q15 | Perturbation theories for operators and differential equations in quantum theory |
| 41A58 | Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) |
References:
| [1] | Zappala, D., Phys. Lett. A, 290, 35 (2001) · Zbl 1021.81012 |
| [2] | Hedden, R.; Meden, V.; Pruschke, Th.; Schönhammer, K., J. Phys.: Cond. Matter, 16, 5279 (2004) |
| [3] | Huang, S.; Agarwal, G. S., Phys. Rev., A80, 033807 (2009) |
| [4] | V. Barsan, 0912.1988 [cond-mat.stat-mech].; V. Barsan, 0912.1988 [cond-mat.stat-mech]. |
| [5] | Scalapino, D. J.; Sears, M.; Ferrell, R. A., Phys. Rev., B6, 3409 (1972) |
| [6] | Krumhansl, J. A.; Schrieffer, J. R., Phys. Rev., B11, 3535 (1975) |
| [7] | Kowalewska-Kudłaszyk, A.; Kalaga, J. K.; Leoński, W., Phys. Lett., A373, 1334 (2009) · Zbl 1228.81172 |
| [8] | Gevorgyan, T. V.; Shahinyan, A. R.; Kryuchkyan, G. Yu., Phys. Rev., A79, 053828 (2009) |
| [9] | Skokos, Ch.; Krimer, D. O.; Komineas, S.; Flach, S., Phys. Rev., E79, 056211 (2009) |
| [10] | Kingsbury, K.; Amey, C.; Kapulkin, A.; Pattanayak, A., Phys. Rev. Lett., 102, 119402 (2009) |
| [11] | Bender, C. M.; Wu, T. T., Phys. Rev., 184, 1231 (1969) |
| [12] | Bender, C. M.; Wu, T. T., Phys. Rev., D7, 1620 (1973) |
| [13] | Bender, C. M.; Cooper, F.; Guralnik, G. S.; Sharp, D. H., Phys. Rev., D19, 1865 (1979) |
| [14] | Bender, C. M.; Dunne, G. V., Phys. Rev., D40, 3504 (1989) |
| [15] | Auberson, G.; Peyranre, M. C., Phys. Rev., A65, 032120 (2002) |
| [16] | Fessatidis, V.; Mancini, J. D.; Prie, J. D.; Zhou, Y.; Majewski, A., Phys. Rev., A60, 1713 (1999) |
| [17] | Jáuregui, R.; Récamier, J., Phys. Rev., A46, 2240 (1992) |
| [18] | Handy, C. R., Phys. Rev., A46, 1663 (1992) |
| [19] | Agrawal, R. K.; Varma, V. S., Phys. Rev., A49, 5089 (1994) |
| [20] | Hatsuda, T.; Kunihiro, T.; Tanaka, T., Phys. Rev. Lett., 78, 3229 (1997) |
| [21] | Meißner, H.; Steinborn, E. O., Phys. Rev., A56, 1189 (1997) |
| [22] | Kashiwa, T., Phys. Rev. D, 59, 085002 (1999) |
| [23] | Sangchul, Oh., Phys. Rev., A77, 012326 (2008) |
| [24] | Egusquiza, I. L.; Basagoiti, M. A.V., Phys. Rev., A57, 1586 (1998) |
| [25] | Yukalov, V. I.; Yukalova, E. P.; Gluzman, S., Phys. Rev., A58, 96 (1998) |
| [26] | Frasca, M., Nuovo Cim., B117, 867 (2002) |
| [27] | Martin-Delgado, M. A.; Sierra, G., Phys. Rev. Lett., 83, 1514 (1999) |
| [28] | Kapoyannis, A. S.; Tetradis, N., Phys. Lett., A276, 225 (2000) · Zbl 1274.81172 |
| [29] | Aoki, K-I; Horikoshi, A.; Taniguchi, M.; Terao, H., Prog. Theor. Phys., 108, 571 (2002) · Zbl 1022.81043 |
| [30] | H. Gies, <http://arxiv.org/abs/hep-ph/0611146>; H. Gies, <http://arxiv.org/abs/hep-ph/0611146> |
| [31] | Wilson, K. G., Rev. Mod. Phys., 55, 583 (1983) |
| [32] | Wegner, F. J.; Houghton, A., Phys. Rev., A8, 401 (1973) |
| [33] | Polchinski, J., Nucl. Phys., B231, 269 (1984) |
| [34] | Wetterich, C., Phys. Lett., B301, 90 (1993) |
| [35] | Litim, D. F., J. High Energy Phys., 11, 059 (2001) |
| [36] | Morris, T., Int. J. Mod. Phys., A9, 2411 (1994) |
| [37] | Symanzik, K., Commun. Math. Phys., 18, 227 (1970) · Zbl 0195.55902 |
| [38] | Alexandre, J.; Polonyi, J., Ann. Phys., 288, 37 (2001) · Zbl 0972.81121 |
| [39] | Polonyi, J.; Sailer, K., Phys. Rev., D71, 025010 (2005) |
| [40] | Luttinger, J. M.; Ward, J. C., Phys. Rev., 118, 1417 (1960) · Zbl 0098.21705 |
| [41] | Baym, G., Phys. Rev., 127, 1391 (1962) · Zbl 0104.45101 |
| [42] | De Dominicis, C.; Martin, P. C., J. Math. Phys., 5, 14 (1964) |
| [43] | Cornwall, J. M.; Jackiw, R.; Tomboulis, E., Phys. Rev., D10, 2428 (1974) · Zbl 1110.81324 |
| [44] | Haymaker, R. W., Nuovo Cim., 14, 1 (1991) |
| [45] | Dupuis, N., Eur. Phys. J., B48, 319 (2005) |
| [46] | Pawlowski, J. M., Ann. Phys., 322, 2831 (2007) · Zbl 1132.81041 |
| [47] | Mazza, M.; Zappala, D., Phys. Rev., D64, 105013 (2001) |
| [48] | Margaritis, A.; Ódor, G.; Patkos, A., Z. Phys., C39, 109 (1998) |
| [49] | Landau, L. D.; Lifshitz, E. M., Quantum Mechanics, (Nonrelativistic Theory (1965), Pergamon Press: Pergamon Press Oxford) · Zbl 0081.22207 |
| [50] | Kuhn, W., Z. Phys., 33, 408 (1925) · JFM 51.0747.05 |
| [51] | Nagy, S.; Nándori, I.; Polonyi, J.; Sailer, K., Phys. Rev., D77, 025026 (2008) |
| [52] | Feynman, R., Statistical Mechanics (1972), W.A.Benjamin, Inc.: W.A.Benjamin, Inc. Massachusetts, chapt. 3 |
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