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Documents  Seiringer, Robert | enregistrements trouvés : 9

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Research talks;Mathematical Physics

We present a mathematically rigorous justification of the Local Density Approximation in density functional theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density (the lowest possible energy of all quantum states having this density) and the integral over the Uniform Electron Gas energy of this density. The error involves gradient terms and justifies the use of the Local Density Approximation in situations where the density is very flat on sufficiently large regions in space. (Joint work with Mathieu Lewin and Elliott Lieb) We present a mathematically rigorous justification of the Local Density Approximation in density functional theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density (the lowest possible energy of all quantum states having this density) and the integral over the Uniform Electron Gas energy of this density. The error involves gradient terms and justifies the use of the ...

82B03 ; 81V70 ; 49K21

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- xiii; 180 p.
ISBN 978-3-642-29510-2

Lecture notes in mathematics , 2051

Localisation : Collection 1er étage

problème des N corps # théorie quantique # système interactif # théorie quantique des champs # condensat de Bose-Einstein # treillis # vortex quantique # gaz de Coulomb # localisation d'Anderson # matrice aléatoire

82B10 ; 81V70 ; 82B28 ; 82B44 ; 82-06 ; 81-06 ; 00B25

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Research talks;Mathematical Physics

These lectures will be an introduction to the quantum Heisenberg model and other related systems. We will review the Hilbert space, the spin operators, the Hamiltonian, and the free energy. We will restrict ourselves to equilibrium systems. The main questions deal with the nature of equilibrium states and the phase transitions. We will review some of the main results such as the Mermin-Wagner theorem and the method of reflection positivity, that allows to prove the existence of phase transitions. Finally, we will discuss certain probabilistic representations and their consequences. These lectures will be an introduction to the quantum Heisenberg model and other related systems. We will review the Hilbert space, the spin operators, the Hamiltonian, and the free energy. We will restrict ourselves to equilibrium systems. The main questions deal with the nature of equilibrium states and the phase transitions. We will review some of the main results such as the Mermin-Wagner theorem and the method of reflection positivity, that ...

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Research talks;Mathematical Physics

These lectures will be an introduction to the quantum Heisenberg model and other related systems. We will review the Hilbert space, the spin operators, the Hamiltonian, and the free energy. We will restrict ourselves to equilibrium systems. The main questions deal with the nature of equilibrium states and the phase transitions. We will review some of the main results such as the Mermin-Wagner theorem and the method of reflection positivity, that allows to prove the existence of phase transitions. Finally, we will discuss certain probabilistic representations and their consequences. These lectures will be an introduction to the quantum Heisenberg model and other related systems. We will review the Hilbert space, the spin operators, the Hamiltonian, and the free energy. We will restrict ourselves to equilibrium systems. The main questions deal with the nature of equilibrium states and the phase transitions. We will review some of the main results such as the Mermin-Wagner theorem and the method of reflection positivity, that ...

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Research talks;Mathematical Physics

These lectures will be an introduction to the quantum Heisenberg model and other related systems. We will review the Hilbert space, the spin operators, the Hamiltonian, and the free energy. We will restrict ourselves to equilibrium systems. The main questions deal with the nature of equilibrium states and the phase transitions. We will review some of the main results such as the Mermin-Wagner theorem and the method of reflection positivity, that allows to prove the existence of phase transitions. Finally, we will discuss certain probabilistic representations and their consequences. These lectures will be an introduction to the quantum Heisenberg model and other related systems. We will review the Hilbert space, the spin operators, the Hamiltonian, and the free energy. We will restrict ourselves to equilibrium systems. The main questions deal with the nature of equilibrium states and the phase transitions. We will review some of the main results such as the Mermin-Wagner theorem and the method of reflection positivity, that ...

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Research talks;Mathematical Physics

We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins $S= 1/2$. We rigorously prove the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial contribution to the free energy at low temperatures. The proof combines a bosonic representation of the model introduced by Holstein and Primakoff with probabilistic estimates, localization bounds and functional inequalities.
Joint work with Michele Correggi and Alessandro Giuliani
We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins $S= 1/2$. We rigorously prove the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial contribution to the free energy at low temperatures. The proof combines a bosonic representation of the model introduced by Holstein and Primakoff with probabilistic estimates, localization bounds and functional ...

82D05 ; 82D40 ; 82D45 ; 82B10

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Research talks;Mathematical Physics

These lectures will be an introduction to the quantum Heisenberg model and other related systems. We will review the Hilbert space, the spin operators, the Hamiltonian, and the free energy. We will restrict ourselves to equilibrium systems. The main questions deal with the nature of equilibrium states and the phase transitions. We will review some of the main results such as the Mermin-Wagner theorem and the method of reflection positivity, that allows to prove the existence of phase transitions. Finally, we will discuss certain probabilistic representations and their consequences. These lectures will be an introduction to the quantum Heisenberg model and other related systems. We will review the Hilbert space, the spin operators, the Hamiltonian, and the free energy. We will restrict ourselves to equilibrium systems. The main questions deal with the nature of equilibrium states and the phase transitions. We will review some of the main results such as the Mermin-Wagner theorem and the method of reflection positivity, that ...

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- 203 p.
ISBN 978-3-7643-7336-8

Oberwolfach seminars , 0034

Localisation : Ouvrages RdC (Math)

mécanique statistique # équilibre quantique en mécanique statistique # système de plusieurs corps # théorie quantique # superfluide # gaz de Bose # inégalité de Poincaré # condensation de Bose-Einstein # équation de Gross-Pitaevskii

82B10 ; 82-02 ; 81V70 ; 81-02 ; 82C10 ; 82D50

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- xv; 293 p.
ISBN 978-0-521-19118-0

Localisation : Ouvrage RdC (LIEB)

Théorie quantique # modèle de Thomas-Fermi # physique mathématique

81-02 ; 81S25

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