Stochastic bosonization for a d3 Fermi system
Accardi, L. ; Lu, Y. G. ; Mastropietro, V.
Annales de l'I.H.P. Physique théorique, Tome 67 (1997), p. 185-213 / Harvested from Numdam
Publié le : 1997-01-01
@article{AIHPA_1997__66_2_185_0,
     author = {Accardi, L. and Lu, Y. G. and Mastropietro, Vieri},
     title = {Stochastic bosonization for a $d \ge 3$ Fermi system},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {67},
     year = {1997},
     pages = {185-213},
     zbl = {0874.60092},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1997__66_2_185_0}
}
Accardi, L.; Lu, Y. G.; Mastropietro, V. Stochastic bosonization for a $d \ge 3$ Fermi system. Annales de l'I.H.P. Physique théorique, Tome 67 (1997) pp. 185-213. http://gdmltest.u-ga.fr/item/AIHPA_1997__66_2_185_0/

[AcFriLu] L. Accardi, A. Frigerio and Y.G. Lu, The weak coupling limit as a quantum functional central limit, Comm. Math. Phys. Vol. 131, 1990, pp. 537-570. | MR 1065896 | Zbl 0703.60096

[Ac90] L. Accardi, Noise and dissipation in quantum theory, Reviews in Math. phys., Vol. 2, 1990, pp. 127-176. | MR 1090278 | Zbl 0718.60131

[AcLu93a] L. Accardi and Y.G. Lu, From Markovian approximation to a new type of quantum stochastic calculus. to appear in: Quantum Probability and Related Topics, World Scientific, OP-PQ VII, 1993, Volterra preprint N. 68, 1991. | MR 1186651

[AcLu93b] L. Accardi and Y.G. Lu, Wiener Noise Versus Wigner Noise in Quantum Electrodynamics. Quantum Probability and Related Topics, World Scientific, QP-VIII, 1993, Volterra Preprint N. 131, 1993. | MR 1258315

[AcLuVo94a] L. Accardi, Y.G. Lu and I. Volovich, Stochastic bosonization in arbitrary dimensions, in: Proceeding of the Udine Conference in memory of Alberto Frigerio, Udine 12-14 September 1994, C. Cecchini, G. Grillo (Eds.), Tipografia Universitaria di Udine, 1995.

[AcLuVo94b] L. Accardi, Y.G. Lu and I. Volovich, Non-Commutative (quantum) probability, Master Fields and Stochastic Bosonization, Preprint Volterra, 1994, ID-9412241.

[AcMa] L. Accardi and V. Mastropietro, Stochastic bosonization for an interacting d ≥ 3 Fermi system, Ann. Inst. Henri-Poincaré, Vol. 66, No. 2, 1997, pp. 215-235. | Numdam | MR 1449192 | Zbl 0874.60093

[Da] E.B. Davies, Markovian master equation, Comm. Math. Phys., Vol. 39, 1974, pp. 91-110. | MR 359633 | Zbl 0294.60080

[DeDuLeLi S. De Smedt, D. Durr, J.L. Lebowitz and C. Liverani, Quantum System with a Thermal Environment: Rigorous Treatment of a Simple Model. Comm. Math. Phys., Vol. 120, 1988, pp. 195-231. | MR 973532 | Zbl 0657.60085

[FoKaMa] G.W. Ford, M. Kac and P. Mazur, Statistical mechanics of Assemblies of coupled oscillators, J. Math. Phys., Vol. 6, 4, 1965, pp. 504-515. | MR 180277 | Zbl 0127.21605

[GoVeVe] D. Goderis, A. Verbeure and P. Vets, Dynamics of fluctuations for quantum lattice systems, Comm. Math. Phys., Vol. 128, 1990, pp. 533-549. | MR 1045883 | Zbl 0702.46050

[KoMeSc] P. Kopietz, K. Meden and K. Schonhammer, Anomalous scaling and spin charge separation in coupled chains, Phys. Rev. Lett., Vol. 74, No. 15, 1995, pp. 2997-3000.

[KwHoMa] H.-J. Kwon, A. Houghton and J.B. Marston, Gauge interactions and bosonized fermion liquids, Phys. Rev. Lett., Vol. 73, No. 2, 1994, pp. 284- 287.

[JaPi] V. Jaksic and C. Pillet, On a model for Quantum Friction I: Fermi's Golded rule and Dynamics at Zero Temperature, Preprint.

[Ha] H. Haken, Quantum field theory of solids, North Holland, 1988.

[HoKwMa] A. Houghton, H.-J. Kwon and J.B. Marston, Stability and single-particle properties of bosonized Fermi liquids, Phys. Rev., B, Vol. 50, No. 3, 1994, pp. 1351-1362.

[HoKwMaSc] A. Houghton, H.-J. Kwon, J.B. Marston and R. Shankar, Coulomb interaction and the Fermi liquid state: solution by bosonization, J. Phys. Cond. Matter, Vol. 6, No. 26, 1994, pp. 4909-4916.

[HoMa] A. Houghton and J.B. Marston, Bosonization and fermion liquids in dimensions greater than one, Phys. Rev. B, Vol. 48, No. 11, 1993, pp. 7790-7808.

[HuPa] R.L. Hudson and K.R. Parthasaraty, Quantum Ito's formula and stochastic evolution, Comm. Math. Phys, Vol. 93, 1994, pp. 301-323. | Zbl 0546.60058

[Lu92] Y.G. Lu, The weak coupling limit for quadratic interaction. J. Math. Phys., Vol. 33, No. 8, 1992. | MR 1180417 | Zbl 0762.60104

[Ma] V. Mastropietro, Schwinger functions in Thirring and Luttinger models, Il Nuovo Cimento, Vol. 108B, No. 10, 1993, pp. 1095-1107.

[MaLi] D. Maths and E. Lieb, An exact solution of a many fermion system an its associated boson field, J. Math. Phys., Vol. 6, 1965, pp. 304-332. | MR 172638

[Pu] J.V. Pule', The Bloch equations, Comm. Math. Phys., Vol. 38, 1974, pp. 241- 256. | MR 359650

[ScMeKo] K. Schonhammer, V. Meden and P. Kopietz, Spin charge separation and anomalous scaling in coupled chains, J. Low. Temp. Phys., Vol. 89, Nos. 3-4, 1995, pp. 587-597.

[So] L. Solyom, The Fermi gas model of one dimensional conductors, Advances in Physics, Vol. 28, 1979, pp. 201-265.

[VH] L. Van Hove, Quantum mechanical perturbations giving rise to a statistical transport equation, Physical , Vol. 21, 1955, pp. 517-540. | MR 71346 | Zbl 0106.20903