We analyze a modified version of the Coleman-Hepp model, which is able to take into account energy-exchange processes between the incoming particle and the linear array made up of N spin-12 systems. We bring to light the presence of a Wiener dissipative process in the weak-coupling, macroscopic (N → ∞) limit. In such and a limit a restricted portion of the total Hilbert space, the particle undergoes a sort of Brownian motion, while the free Hamiltonian of the spin array serves as a Wiener process. No partial trace is computed over the states of the spin system (which plays the role of “reservoir”). The mechanism of appearance of the stochastic process is discussed and contrasted to other noteworthy examples in the literature. The links with van Hove's “λ2T” limits are emphasized.We analyze a modified version of the Coleman-Hepp model, which is able to take into account energy-exchange processes between the incoming particle and the linear array made up of N spin-12 systems. We bring to light the presence of a Wiener dissipative process in the weak-coupling, macroscopic (N → ∞) limit. In such and a limit a restricted portion of the total Hilbert space, the particle undergoes a sort of Brownian motion, while the free Hamiltonian of the spin array serves as a Wiener process. No partial trace is computed over the states of the spin system (which plays the role of “reservoir”). The mechanism of appearance of the stochastic process is discussed and contrasted to other noteworthy examples in the literature. The links with van Hove's “λ2T” limits are emphasized.

Jan 1, 19979 citations

Nonrelativistic Perturbation Theory

CO-PUBLISHED WITH IMPERIAL COLLEGE PRESS eBooksNov 1, 20060 citations

Effects of Fermi-surface topology on the electronic properties of the two-dimensionalt-t’ model

Liang Chen, Pierre Bénard

We present a study of the two-dimensional t-t' model in the parameter regime of \ensuremath{\Vert}t'\ensuremath{\Vert}>\ensuremath{\Vert}t\ensuremath{\Vert}/2. As a function of band filling, the Fermi surface exhibits rich geometrical and topological properties, which have significant impact on the physical properties of the normal state. In particular, the Fermi surface becomes nested when the chemical potential reaches - ${\mathit{t}}^{2}$ /t', where the nesting vectors are [2 arccos(t/2t'),0] and [0,2 arccos(t/2t')]. The normal-state properties, such as the transport properties and charge and spin fluctuations, are analyzed in relation with the geometrical properties of the Fermi surface. We show that these properties lead to an optical charge-density wave mode within the random-phase approximation, even if the Hubbard interaction is repulsive. Implications for the recently introduced antiferromagnetic--van Hove model are also discussed.We present a study of the two-dimensional t-t' model in the parameter regime of \ensuremath{\Vert}t'\ensuremath{\Vert}>\ensuremath{\Vert}t\ensuremath{\Vert}/2. As a function of band filling, the Fermi surface exhibits rich geometrical and topological properties, which have significant impact on the physical properties of the normal state. In particular, the Fermi surface becomes nested when the chemical potential reaches -${\mathit{t}}^{2}$/t', where the nesting vectors are [2 arccos(t/2t'),0] and [0,2 arccos(t/2t')]. The normal-state properties, such as the transport properties and charge and spin fluctuations, are analyzed in relation with the geometrical properties of the Fermi surface. We show that these properties lead to an optical charge-density wave mode within the random-phase approximation, even if the Hubbard interaction is repulsive. Implications for the recently introduced antiferromagnetic--van Hove model are also discussed.

Physical review. B, Condensed matterJul 1, 19955 citations

{\mathit{t}}^{2}

/t', where the nesting vectors are [2 arccos(t/2t'),0] and [0,2 arccos(t/2t')]. The normal-state properties, such as the transport properties and charge and spin fluctuations, are analyzed in relation with the geometrical properties of the Fermi surface. We show that these properties lead to an optical charge-density wave mode within the random-phase approximation, even if the Hubbard interaction is repulsive. Implications for the recently introduced antiferromagnetic--van Hove model are also discussed.