bogoliubov transformation pdf – bogoliubov de gennes hamiltonian
The Bogoliubov transformation of bosons correspond to the linear canonical transformation of oscillators in classical mechanics because bosons are quanta of oscillators, and we know the linear canonical transformations are symplectic due to the symplectic structure of the classical phase space, So to be more specific, what are the restrictions on Bogoliubov transformations? Let us consider
Manquant :
Quantum Theory of Condensed Matter
· Fichier PDF
BCS Theory of Superconductivity
· Fichier PDF
Bogoliubov transformations For more details on how exactly these transformations come about in external field problems see for example: Part V of Friedrichs’ book [1] Capri [2] Schroer Seiler and Swieca [3], and Seiler [4], Stated more precisely, one needs the answers to the following questions: when is a Bogoliubov transformation unitarily
Cited by : 29
Mathematical Analysis of the BCS-Bogoliubov Theory 1
· Fichier PDF
transformation Bogoliubov transformation bs = X j usj aj +vsj a ⁄ j: 10 2 By \diagonalized” we mean that in terms of the new canonical variables fbsg the Hamiltonian will read H = X s Es b ⁄ sbs; 11 that is will be equivalent to a set of non-interacting harmonic oscillators normal modes Before we show how to relate the u and v coe–cients to the matrices A and B, let us
bogoliubov transformation pdf
Bogoliubov transformation This theory is called the Bogoliubov theory The ground state of the BCS Hamiltonian is discussed by several authors In 1961 Mattis and Lieb [5] studied the wavefunction of the ground state of the BCS Hamiltonian under the condition that in the ground state, all the electrons in the neighborhood of the Fermi surface are paired, See Richardson [7] and von Delft [3
Bogoliubov theory of the weakly interacting Bose gas
· Fichier PDF
Bogoliubov-Valatin-Transformation Calculation of the condensation energy 3 Finite Temperatures Excitation Energies and the Energy Gap Determination of T c Temperature dependence of the energy gap Thermodynamic quantities 4/52, Outlines Cooper-Pairs BCS Theory Finite Temperatures Outline 1 Cooper-Pairs Formation of Pairs Origin of Attractive Interaction 2 BCS Theory The model Hamiltonian
Outline RG LGT Fermions Feynman Wilson Gauss Ising Bogoliubov Higgs Cite The great unification The renormalization procedure will be to take the continuum limit a mass m If this is fixed in physical units then in lattice units it must diverge as a → 0, This corresponds to a second order phase transition on the lattice, A lattice field theory in Euclidean time and D dimensions of space
second quantisation canonical transformations and self-consistent field approximations Recent Graduate Texts A Altland and B D Simons Quantum Field Theory in Condensed Matter Physics CUP 2006, An acces-sible introduction to the subject, S, Sachdev Quantum Phase Transitions, CUP 1999, An advanced survey of theoretical approaches to this subject, H, Bruus and K, Flensberg Many Body
Bogoliubov Transformation in Classical Mechanics
· Fichier PDF
Bogoliubov Transformation Group Structure Any F-even unitary matrix in 2M will correspond to some Bogoliubov transformation The set of such matrices forms a group a subgroup of the unitary group of degree 2M Let us now make a unitary rotation of all matrices A and define: with Consequently, matrices B are real and orthogonal! They form the O2M group – orthogonal group in 2M, O2M can be
Taille du fichier : 275KB
On the Nature of Strong Bogoliubov Transformations for
· Fichier PDF
by Bogoliubov transformations1 P T Nam1 M Napi orkowski 1 J P Solovej 2 1Institute of Science and Technology Austria 2Department of Mathematics University of Copenhagen GDR Dynqua meeting, Grenoble 1 J, Funct, Anal, in press Marcin Napi orkowski Quadratic Hamiltonians and Bogoliubov transformations, Bosonic quadratic Hamiltonians on Fock space General form of quadratic …
Canonical Transformations in Quantum Field Theory
· Fichier PDF
known as the Bogoliubov transformation The two parameters up and v¡p are determined uniquely by the following requirements The new operators ^b p and ^b+ p are assumed to obey the same Bosonic commutation relation as the real particle operators, ^ap and ^a+ p: h ^b p;^b+ p0 i = ^b p ^b+ p0 ¡ ^b+ p0 ^b p = –pp0: 4,21 This commutation relation imposes the constraint for the two
Bogoliubov Hamiltonians and one-parameter groups of
· Fichier PDF
transformations in the context of QFT: we consider explicitly two particularly important cases of linear transformations namely the boson translation and the Bogoliubov transformation for bosons † The boson translation Let us consider first QM a is an oscillator operator defined by h a;a y …
Introduction to Lattice Field Theory
· Fichier PDF
quantum mechanics
Bogoliubov transformations are the standard tool of the quantum field theory It is interesting that they can be applied also in quantum information theory QIT, One of the most important notions of QIT is entanglement—a uniquely quantum phenomenon connected with the question whether the state of a composite quantum system may be determined by the states of its constituent subsystems
Diagonalization of bosonic quadratic Hamiltonians
· Fichier PDF
Bogoliubov Transformation Group Structure
· Fichier PDF
Bogoliubov Hamiltonians and one-parameter groups of Bogoliubov transformations Laurent Bruneaua CPT-CNRS UMR 6207 Université du Sud Toulon-Var Boíte Postale 20132 F-83957 La Garde Cedex France Jan Derezińskib Department of Mathematical Methods in Physics, Warsaw University, Hoża 74, 00-682, Warszawa, Poland Received 24 July 2006; accepted 8 December 2006; published online 12 …
BOGOLIUBOV TRANSFORMATIONS AND ENTANGLEMENT OF …
· Fichier PDF