Modern Many-Particle Physics - Atomic Gases, Quantum Dots and Quantum Fluids

Abstract

This book is printed on acid-free paper. PrefaceThis book is the fruit of my lectures on the Theory of Many Body Systems which I have been teaching for many years in the degree course in Physics at the University of Trento. As often happens, the outline of the book was my students' notes; in particular, the notes of the students of the academic year 1999-2000 which were extremely useful for me. Chapter 6 on the Monte Carlo methods is the work of Francesco Pederiva, a research assistant in our Department. During the course, Francesco, apart from illustrating the method, teaches the students all the computer programmes, continually referred to in the book, by means of practical exercises in our computational laboratory. In particular, he teaches the Hartree-Fock, Brueckner-Hartree-Fock, Kohn-Sham, Diffusion Monte Carlo programmes for the static properties, RPA, and Time-Dependent HF and LSDA for Boson and Fermion finite systems. These programmes are available to anyone who is interested in using them.The book is directed towards students who have had a conventional course in quantum mechanics and have some basic understanding of condensed matter phenomena. I have often gone into extensive mathematical details, trying to be as clear as possible and I hope that the reader will be able to rederive many of the formulas presented without too much difficulty.In the book, even though a lot of space is devoted to the description of the homogeneous systems, such as electron gas in different dimensions, quantum wells in intense magnetic field, liquid helium and nuclear matter, the most relevant part is dedicated to the study of finite systems. Particular attention is paid to those systems realized recently in the laboratories throughout the world: metal clusters, quantum dots and the condensates of cold and dilute atoms in magnetic traps. However, some space is also devoted to the more traditional finite systems, like the helium drops and the nuclei. I have tried to treat all these systems in the most unifying way possible, attempting to bring all the analogies to light. My intention was to narrow the gap between the usual undergraduate lecture course and the literature on these systems presented in scientific journals. VI PrefaceIt is important to remark that the book takes a "Quantum chemist's" approach to many-body theories. It focuses on methods of getting good numerical approximations to energies and linear response based on approximations to first-principle Hamiltonians. There is another approach to many-body physics that focuses on symmetries and symmetry breaking, quantum field theory and renormalization groups, and aims to extracting the emergent features of the many body systems. This works with "effective" model theories, and does not attempt to do "06 initio computations". These two ways of dealing with many-body systems complement each other, and find common ground in the study of atomic gases, metal clusters, quantum dots and quantum Hall effect systems that are the main application of the book.

Addition energies and density dipole response of quantum rings under the influence of in-plane electric fields

“…[32][33][34] Of particular interest are the m −1 , m 1 , and m 3 moments. For the dipole operator along the x direction, F = D x = e͚ i=1 N x i , they read Fig.…”

Spin-orbit effects on the Larmor dispersion relation in GaAs quantum wells

“…Although other approaches may be also considered, we have considered the exchange-correlation potential W xc ͑n , , V͒ in the local-spin current density approximation ͑LSCDA͒. 26,27 It depends on the density n, magnetization = n ↑ − n ↓ , and local vorticity V, and is evaluated from the exchange-correlation energy per electron E xc as W xc = ‫͑ץ‬nE xc ͒ / ‫ץ‬ . The last term in Eq.…”

“…27 We are going to see that, in the absence of SO coupling, not only the exact Hamiltonian, but also the one in which the residual interaction is treated in the TDLSCDA fulfill the equation…”

“…27 The poles of t ͑q , ͒ yield ͑q͒. The transverse spin response without inclusion of spin-orbit coupling has been studied in the past in the random-phase approximation 28 ͑RPA͒ and time-dependent Hartree-Fock 29 approximations.…”

Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials

“…A simple but reliable theoretical tool for the study of these trapped degenerate gases is the density-functional theory [6]. In particular, the Gross-Pitaevskii equation (GPE), which accurately describes BECs in dilute gases, is the Euler-Lagrange equation produced by the Thomas-Fermi (TF) density functional which takes into account the inhomogeneity of the condensate [4].…”