Derivation of a Matrix-valued Boltzmann Equation for the Hubbard Model
作者： Martin L R Fürst , Jani Lukkarinen , Peng Mei , Herbert Spohn
DOI: 10.1088/1751-8113/46/48/485002
关键词:
摘要: For the spin-$\{1}{2}$ Fermi-Hubbard model we derive kinetic equation valid for weak interactions by using time-dependent perturbation expansion up to second order. In recent theoretical and numerical studies has been merely stated without further details. this contribution provide required background material.
core.ac.uk
arxiv.org
sci-hub.se 参考文章(14)
Robert Zwanzig, Nonequilibrium statistical mechanics Oxford University Press. ,(2001)
D. Benedetto, F. Castella, R. Esposito, M. Pulvirenti, From the N-body Schrödinger Equation to the Quantum Boltzmann Equation: a Term-by-Term Convergence Result in the Weak Coupling Regime Communications in Mathematical Physics. ,vol. 277, pp. 1- 44 ,(2007) , 10.1007/S00220-007-0347-7
Martin L. R. Fürst, Christian B. Mendl, Herbert Spohn, Matrix-valued Boltzmann equation for the Hubbard chain. Physical Review E. ,vol. 86, pp. 031122- ,(2012) , 10.1103/PHYSREVE.86.031122
Léon van Hove, Quantum-mechanical perturbations giving rise to a statistical transport equation Physica D: Nonlinear Phenomena. ,vol. 21, pp. 517- 540 ,(1954) , 10.1016/S0031-8914(54)92646-4
T. G. Ho, L. J. Landau, FERMI GAS ON A LATTICE IN THE VAN HOVE LIMIT Journal of Statistical Physics. ,vol. 87, pp. 821- 845 ,(1997) , 10.1007/BF02181246
N. M. Hugenholtz, DERIVATION OF THE BOLTZMANN-EQUATION FOR A FERMI GAS Journal of Statistical Physics. ,vol. 32, pp. 231- 254 ,(1983) , 10.1007/BF01012709
A. K. Geim, K. S. Novoselov, The rise of graphene Nature Materials. ,vol. 6, pp. 183- 191 ,(2007) , 10.1038/NMAT1849
N. M. R. Peres, M. A. N. Araújo, Daniel Bozi, Phase diagram and magnetic collective excitations of the Hubbard model for graphene sheets and layers Physical Review B. ,vol. 70, pp. 195122- ,(2004) , 10.1103/PHYSREVB.70.195122
Martin L. R. Fürst, Christian B. Mendl, Herbert Spohn, Matrix-valued Boltzmann equation for the nonintegrable Hubbard chain. Physical Review E. ,vol. 88, pp. 012108- 012108 ,(2013) , 10.1103/PHYSREVE.88.012108
Jani Lukkarinen, Herbert Spohn, Weakly nonlinear Schrödinger equation with random initial data Inventiones Mathematicae. ,vol. 183, pp. 79- 188 ,(2011) , 10.1007/S00222-010-0276-5