Download Modern Many-Particle Physics: Atomic Gases, Quantum Dots and by Enrico Lipparini PDF

By Enrico Lipparini

A big a part of this booklet is dedicated to the outline of homogenous platforms, resembling electron gasoline in several dimensions, the quantum good in an extreme magnetic box, liquid helium and nuclear topic. even if, the main appropriate half is devoted to the learn of finite platforms: metal clusters, quantum dots, the condensate of chilly and diluted atoms in magnetic traps, helium drops and nuclei. The e-book specializes in tools of having reliable numerical approximations to energies and linear reaction in accordance with approximations to first-principles Hamiltonians. those tools are illustrated and utilized to Bose and Fermi platforms at 0 and finite temperature. sleek Many-Particle Physics is directed in the direction of scholars who've taken a traditional path in quantum mechanics and own a easy realizing of condensed subject phenomena

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The experimental values were taken from Knight et al. (1985). PPJM indicates the approximation with pseudo-potential of Bachelet et al. (1982), PHJM indicates the approximation with the pseudo-Hamiltonian of Bachelet et al. (1989). As can be seen from the table, the pseudo-potential and pseudo-Hamiltonian models, when compared to jellium model (JM), much reduce the discrepancy between experimental and LDA results. Quantum dots Recently, nanotechnologies (1 nanometre = 1 0 - 9 metres) based on semiconductor heterostructures (for example, GaAs/Ga x Alj_ x As) allowed the realization of quantum wires and dots: these are specific objects to study the physics of low-dimensionality electrons.

128) is a condition which is imposed on /k,k' by translational invariance. 121). 130) enable for the determination of the Landau parameter F(. In order to establish a connection between F£ and a measurable quantity, let us assume that the hydrodynamic regime holds, and let us look for Euler-like equations for the density variations. 131) m —' oe k m kk' where we have used the result ^ k kjl(5n(k, r, t))coil = 0, which results from the current being conserved during collisions. However, the fact that the collision term does not change the quasiparticle density and their current, does not mean that it is not relevant in the hydrodynamic regimes where WT -C 1.

4) be stationary with respect to variations of (2-5) we obtain the Hartree-Fock equations: V2 2m + «ext(r)) ^ ( r , ") + E / dr'V*(r', (r - r') x [ ^ ( r , c 7 ) ^ ( r ' , o - ' ) - ^ ( r ' , c T ' ) ^ ( r , o - ) ] =enpi(r,a). 8) and cr||u' means that the spins must be parallel, since otherwise the exchange term vanishes. e. 9)] is non-local. In the Hartree theory only the local (direct) term U(r) is considered. The HF equations form a system of TV coupled integral-differential equations.

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