Abstract
A theory of real-time quantum many-body dynamics is evaluated in detail. It is based on a generating functional of correlation functions where the closed time contour extends only to a given time. Expanding the contour from this time to a later time leads to a dynamic flow of the generating functional. This flow describes the dynamics of the system and has an explicit causal structure. In the present work it is evaluated within a vertex expansion of the effective action leading to time-evolution equations for Green functions. These equations are applicable for strongly interacting systems as well as for studying the late-time behavior of non-equilibrium time evolution. For the specific case of a bosonic \(\mathcal{N}\)-component φ 4-theory with contact interactions an s-channel truncation is identified to yield equations identical to those derived from the 2PI effective action in next-to-leading order of a \(1/\mathcal{N}\) expansion. The presented approach allows to directly obtain non-perturbative dynamic equations beyond the widely used 2PI approximations.
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References
T. Gasenzer, J.M. Pawlowski, Phys. Lett. B 670, 135 (2008)
C.D. Fertig, K.M. O’Hara, J.H. Huckans, S.L. Rolston, W.D. Phillips, J.V. Porto, Phys. Rev. Lett. 94, 120403 (2005)
T. Kinoshita, T. Wenger, D.S. Weiss, Nature 440, 900 (2006)
S. Hofferberth, I. Lesanovsky, B. Fischer, T. Schumm, J. Schmiedmayer, Nature 449, 324 (2007)
S. Ritter, A. Öttl, T. Donner, T. Bourdel, M. Köhl, T. Esslinger, Phys. Rev. Lett. 98, 090402 (2007)
J. Estève, C. Gross, A. Weller, S. Giovanazzi, M.K. Oberthaler, Nature Phys. 455, 1216 (2008)
T. Gericke, P. Würtz, D. Reitz, T. Langen, H. Ott, Nature Phys. 4, 949 (2008)
W.S. Bakr, J.I. Gillen, A. Peng, S. Fölling, M. Greiner, Nature 462, 74 (2009)
M. Karski, L. Förster, J.M. Choi, W. Alt, A. Widera, D. Meschede, Phys. Rev. Lett. 102, 053001 (2009)
T. Heinzel, Mesoscopic Electronics in Solid State Nanostructures (VCH-Wiley, Berlin, 2006)
P.C. Hohenberg, B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977)
M. Strickland, J. Phys. G 34, S429 (2007)
R. Micha, I.I. Tkachev, Phys. Rev. D 70, 043538 (2004)
C. Wetterich, Phys. Lett. B 301, 90 (1993)
C. Bagnuls, C. Bervillier, Phys. Rept. 348, 92 (2001)
J. Berges, N. Tetradis, C. Wetterich, Phys. Rept. 363, 223 (2002)
J. Polonyi, Cent. Eur. J. Phys. 1, 1 (2003)
M. Salmhofer, C. Honerkamp, Prog. Theor. Phys. 105, 1 (2001)
B. Delamotte, D. Mouhanna, M. Tissier, Phys. Rev. B 69, 134413 (2004)
H. Gies, Lect. Notes 2006 ECT∗ School “Renormalization group and effective field theory approaches to many-body systems”, Trento, arXiv:hep-ph/0611146 (2006)
D.F. Litim, J.M. Pawlowski, in: The Exact Renormalization Group, ed. by A. Krasnitz et al. (World Scientific, Singapore, 1999)
D.F. Litim, J.M. Pawlowski, J. High Energy Phys. 11, 026 (2006)
J.M. Pawlowski, Ann. Phys. 322, 2831 (2007)
L. Canet, B. Delamotte, O. Deloubriere, N. Wschebor, Phys. Rev. Lett. 92, 195703 (2004)
J.I. Latorre, C.A. Lutken, E. Rico, G. Vidal, Phys. Rev. A 71, 034301 (2005)
S. Kehrein, Phys. Rev. Lett. 95, 056602 (2005)
A. Mitra, S. Takei, Y.B. Kim, A.J. Millis, Phys. Rev. Lett. 97, 236808 (2006)
J. Zanella, E. Calzetta, hep-th/0611222 (2006)
L. Canet, H. Chate, J. Phys. A 40, 1937 (2007)
R. Gezzi, T. Pruschke, V. Meden, Phys. Rev. B 75, 045324 (2007)
S.G. Jakobs, V. Meden, H. Schoeller, Phys. Rev. Lett. 99, 150603 (2007)
T. Korb, F. Reininghaus, H. Schoeller, J. König, Phys. Rev. B 76, 165316 (2007)
S. Matarrese, M. Pietroni, J. Cosmol. Astropart. Phys. 0706, 026 (2007)
C. Karrasch, R. Hedden, R. Peters, T. Pruschke, K. Schönhammer, V. Meden, J. Phys.: Condens. Matter 20, 345205 (2008)
S.G. Jakobs, M. Pletyukhov, H. Schoeller, J. Phys. A: Math. Theor. 43, 103001 (2010)
H. Schoeller, Eur. Phys. J. ST 168, 179 (2009)
C. Wetterich, Phys. Rev. Lett. 78, 3598 (1997)
C. Wetterich, Phys. Rev. E 56, 2687 (1997)
L.M.A. Bettencourt, C. Wetterich, Phys. Lett. B 430, 140 (1998)
G. Vidal, Phys. Rev. Lett. 93, 040502 (2004)
A. Daley, C. Kollath, U. Schollwöck, G. Vidal, J. Stat. Mech.: Theory Exp. P04005 (2004)
S.R. White, A.E. Feiguin, Phys. Rev. Lett. 93, 076401 (2004)
S.R. Manmana, A. Muramatsu, R.M. Noack, AIP Conf. Proc. 789, 269 (2005)
U. Schollwöck, Rev. Mod. Phys. 77, 259 (2005)
J. Berges, Nucl. Phys. A 699, 847 (2002)
G. Aarts, D. Ahrensmeier, R. Baier, J. Berges, J. Serreau, Phys. Rev. D 66, 045008 (2002)
J. Berges, AIP Conf. Proc. 739, 3 (2005), hep-ph/0409233
B. Mihaila, Phys. Rev. D 68, 036002 (2003)
F. Cooper, J.F. Dawson, B. Mihaila, Phys. Rev. D 67, 051901(R) (2003)
F. Cooper, J.F. Dawson, B. Mihaila, Phys. Rev. D 67, 056003 (2003)
J. Berges, J. Serreau, Phys. Rev. Lett. 91, 111601 (2003)
A. Arrizabalaga, J. Smit, A. Tranberg, J. High Energy Phys. 10, 017 (2004)
J. Berges, S. Borsanyi, J. Serreau, Nucl. Phys. B 660, 51 (2003)
J. Berges, S. Borsanyi, C. Wetterich, Phys. Rev. Lett. 93, 142002 (2004)
T. Gasenzer, J. Berges, M.G. Schmidt, M. Seco, Phys. Rev. A 72, 063604 (2005)
G. Aarts, A. Tranberg, Phys. Rev. D 74, 025004 (2006)
J. Berges, T. Gasenzer, Phys. Rev. A 76, 033604 (2007)
T. Gasenzer, Eur. Phys. J. ST 168, 89 (2009), arXiv:0812.0004 [cond-mat.other]
J.M. Luttinger, J.C. Ward, Phys. Rev. 118, 1417 (1960)
G. Baym, Phys. Rev. 127, 1391 (1962)
J.M. Cornwall, R. Jackiw, E. Tomboulis, Phys. Rev. D 10, 2428 (1974)
C. Scheppach, J. Berges, T. Gasenzer, Phys. Rev. A 81, 033611 (2010)
A.V. Gorshkov, M. Hermele, V. Gurarie, C. Xu, P.S. Julienne, J. Ye, P. Zoller, E. Demler, M.D. Lukin, A.M. Rey, arXiv:0905.2610v1 [cond-mat.quant-gas] (2009)
J. Rammer, Quantum Field Theory of Non-equilibrium States (Cambridge University Press, Cambridge, 2007)
J. Schwinger, J. Math. Phys. 2, 407 (1961)
K.T. Mahanthappa, Phys. Rev. 126, 329 (1962)
P.M. Bakshi, K.T. Mahanthappa, J. Math. Phys. 4(1), 12 (1963)
L.V. Keldysh, Sov. Phys. JETP 20, 1018 (1965)
L.V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964)
D. Boyanovsky, H.J. de Vega, R. Holman, M. Simionato, Phys. Rev. D 60, 065003 (1999)
D. Boyanovsky, H.J. de Vega, Ann. Phys. 307, 335 (1999)
S.-I. Ei, K. Fujii, T. Kunihiro, Ann. Phys. 280, 236 (2000)
Y. Hatta, T. Kunihiro, Ann. Phys. 298, 24 (2000)
D.R. Hartree, Proc. Camb. Philos. Soc. 24, 89 (1928)
D.R. Hartree, Proc. Camb. Philos. Soc. 24, 111 (1928)
V. Fock, Z. Phys. 61, 126 (1930)
L.P. Kadanoff, G. Baym, Quantum Statistical Mechanics (Addison-Wesley, New York, 1995)
J.-P. Blaizot, A. Ipp, R. Mendez-Galain, N. Wschebor, Nucl. Phys. A 784, 376 (2007)
J. Berges, Phys. Rev. D 70, 105010 (2004)
E.P. Gross, Nuovo Cimento 20, 454 (1961)
L.P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40, 646 (1961)
L.P. Pitaevskii, Sov. Phys. JETP 13, 451 (1961)
G. Aarts, J. Berges, Phys. Rev. Lett. 88, 041603 (2002)
M. Alford, J. Berges, J.M. Cheyne, Phys. Rev. D 70, 125002 (2004)
K. Temme, T. Gasenzer, Phys. Rev. A 74, 053603 (2006)
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Gasenzer, T., Keßler, S. & Pawlowski, J.M. Far-from-equilibrium quantum many-body dynamics. Eur. Phys. J. C 70, 423–443 (2010). https://doi.org/10.1140/epjc/s10052-010-1430-3
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DOI: https://doi.org/10.1140/epjc/s10052-010-1430-3