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Problems in Quantum Theory of Many-Particle Systems : lecture note

Léon Van Hove, Nicolaas Marinus Hugenholtz, L. P. Howland

Jan 1, 19610 citations

Quantum Many Particle Physics

Pinaki Majumdar

This set of lectures focuses on some problems in itinerant Bose and Fermi systems. The first lecture will be an introduction to many-particle physics. In the second we will discuss phase transitions and symmetry breaking and the mean field approach to condensation in Bose systems. In the third we will look at strong interactions in ‘normal’ Fermi systems. The final lecture will be on strong coupling superconductivity which involves both strong interactions and symmetry breaking.

Texts and readings in physical sciencesJan 1, 200147 citations

Quantum Interacting Particle Systems

QP-PQ, quantum probability and white noise analysisJan 1, 20025 citations

Lecture 11: Time Independent Formalisms. Flux-Across Surfaces. Enss Method. Inverse Scattering

Gianfausto Dell’Antonio

At the beginning of Lecture 10 we have remarked that scattering Theory in Quantum as in Classical Mechanics, describes those effects of the interaction of a system of N particles which can be measured when the components of the system have become spatially separated so that the mutual interactions have become negligible. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Atlantis studies in mathematical physicsJan 1, 20160 citations

Analysis of Classical and Quantum Interacting Particle Systems

Bogusław Zegarliński

QP-PQ, quantum probability and white noise analysisJul 1, 200226 citations

The second quantization method for indistinguishable particles (Lecture Notes in Physics, UFABC 2010)

V. S. Shchesnovich

Summary of the lectures: 1. Creation and annihilation operators for the system of indistinguishable particles 1.1 The permutation group and the states of a system of indistinguishable particles 1.2 Dimension of the Hilbert space of a system of indistinguishable particles 1.3 Definition and properties of the creation and annihilation operators 1.4 TheFockspace 1.5 The representations of state vectors and operators 1.5.1 N-particlewave-functions 1.5.2 The second-quantization representation of operators 1.5.3 Examples 1.6 Evolution of operators in the Heisenberg picture 1.7 Statistical operators of indistinguishable particles 1.7.1 The averages of the s-particle operators 1.7.2 The general structure of the one-particle statistical operator 2 Quadratic Hamiltonian and the diagonalization 2.1 Diagionalization of the Hamiltonian quadratic in the fermion operators 2.2 Diagionalization of the Hamiltonian quadratic in the boson operators 2.2.1 Diagonalization of the quadratic bosonic Hamiltonian possessing a zero mode 2.3 Long range order, condensation and the Bogoliubov spectrum of weakly interacting Bose gas 2.3.1 The excitation spectrum of weakly interacting Bose gas inabox 2.3.2 The excitation spectrum of an interacting Bose gas in an externalpotential 2.4 The Jordan-Wigner transformation: fermionization of interacting 1D spin chainsSummary of the lectures: 1. Creation and annihilation operators for the system of indistinguishable particles 1.1 The permutation group and the states of a system of indistinguishable particles 1.2 Dimension of the Hilbert space of a system of indistinguishable particles 1.3 Definition and properties of the creation and annihilation operators 1.4 TheFockspace 1.5 The representations of state vectors and operators 1.5.1 N-particlewave-functions 1.5.2 The second-quantization representation of operators 1.5.3 Examples 1.6 Evolution of operators in the Heisenberg picture 1.7 Statistical operators of indistinguishable particles 1.7.1 The averages of the s-particle operators 1.7.2 The general structure of the one-particle statistical operator 2 Quadratic Hamiltonian and the diagonalization 2.1 Diagionalization of the Hamiltonian quadratic in the fermion operators 2.2 Diagionalization of the Hamiltonian quadratic in the boson operators 2.2.1 Diagonalization of the quadratic bosonic Hamiltonian possessing a zero mode 2.3 Long range order, condensation and the Bogoliubov spectrum of weakly interacting Bose gas 2.3.1 The excitation spectrum of weakly interacting Bose gas inabox 2.3.2 The excitation spectrum of an interacting Bose gas in an externalpotential 2.4 The Jordan-Wigner transformation: fermionization of interacting 1D spin chains

arXiv:1308.3275Aug 14, 20134 citations

Lectures on Quantum Interacting Particle Systems

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