Spectrum of the BCS Reduced Hamiltonian in the Theory of Superconductivity
スポンサーリンク
概要
- 論文の詳細を見る
The spectrum and eigenstates of Bardeen-Cooper-Schrieffer's reduced Hamiltonian in the theory of superconductivity are investigated in a mathematically rigorous manner. The Hamiltonian is defined first for a finite number of electrons contained in a finite volume. The interaction Hamiltonian is assumed to take a simple form. The Hamiltonian after the Bogoliubov transformation (transformed Hamiltonian) has a limit in the weak topology of Hilbert space when the volume tends to infinity with the number density of electrons kept constant. In the limit the interaction part vanishes and the free part gives a continuous excitation spectrum of Bogolons (transformed electrons). It should be noticed that the operator norm of the former does not tend to zero and has no strong limit as well as the total Hamiltonian. An equivalent boson which consists of two Bogolons with opposite momenta and spins is introduced. In the Fock space for the bosons the Hamiltonian has a strong limit for infinite volume. The limit operator has the same excitation spectrum of Bogolons as the free Hamiltonian and the existence of the lower limit of the spectrum is shown for some special class of the interactions. For large volume the limit operator is a good approximation to the transformed Hamiltonian. The ground state of the free part of the transformed Hamiltonian (i.e. the ground state of Bardeen-Cooper-Schrieffer's calculation) is not the exact eigenstate of the transformed total Hamiltonian and the difference does not vanish when the volume tends to infinity.
- 理論物理学刊行会の論文
- 1965-11-25
著者
関連論文
- Effects of Liquid Property on Air Entrainment and Oxygen Transfer Rates of a Plunging Jet Reactor
- Numerical Study of Impurity Effects on Quasiparticles within S-wave and Chiral P-wave Vortices
- Vortex Core of Chiral p-wave Superconductors(New Developments in Strongly Correlated Electron Systems)
- Phase-Sensitive Impurity Effects in Vortex Core of Moderately Clean Chiral Superconductors : Condensed Matter: Electronic Properties, etc.
- Propagation of Hydromagnetic Waves in Collisionless Plasma. I
- Absence of Anomalous Tunneling of Bogoliubov Excitations for Arbitrary Potential Barrier under the Critical Condensate Current(General)
- Analytical Formulation of the Local Density of States around a Vortex Core in Unconventional Superconductors(Condensed matter: electronic structure and electrical, magnetic, and optical properties)
- Analytical Result on Electronic States around a Vortex Core in a Noncentrosymmetric Superconductor(Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties)
- Determinants of Ligand Specificity in Groups I and IV WW Domains
- Fractional Exclusion Statistics for the Multicomponent Sutherland Model
- Numerical Study of the S=1 Antiferromagnetic Spin Chain with Bond Alternation
- Fractional Exclusion Statistics for the t-J Model with Long Range Exchange and Hopping
- Fredholm Determinant and the Solution of the Korteweg-de Vries Equation : General and Mathematical Physics
- Quasi-Hole Structures in the Electron-Removal Spectrum of Fractional Quantum Hall Systems
- Tetragonal-to-Orthorhombic Transition and Disappearance of Superconductivity in the Pb-Doped Bi_2Sr_2CuO_y System
- Elementary Excitations and Dynamical Correlation Functions of the Calogero-Sutherland Model with Internal Symmetry
- Partially Solvable Anisotropic t-J Model with Long-Range Interactions
- On the β-γ Angular Correlations of Tm^ and Sb^ : VT Interaction
- Humoral Defense of the Nematode Ascaris suum : Antibacterial, Bacteriolytic and Agglutinating Activities in the Body Fluid
- Spin-Charge Separation at Finite Temperature in the Supersymmetric t-J Model with Long-Range Interactions
- Mechanism of Anomalous Tunneling in Condensed Bose System(Condensed matter: structure and mechanical and thermal properties)
- Regular Perturbation and Asymptotic Limits of Operators in Fixed-Source Theory
- Regular Perturbation and Asymptotic Limits of Operators in Quantum Field Theory
- Spectrum Method for a General Evolution Equation
- Recursion Operators for N×N Matrix Nonlinear Evolution Equations : Condensed Matter and Statistical Physics
- Interactions of Hydromagnetic Waves
- Hydromagnetic Plane Steady Flow in Compressible Ionized Gases
- Propagation of Hydromagnetic Waves in a Collisionless Plasma
- Spectrum of the BCS Reduced Hamiltonian in the Theory of Superconductivity
- Magnetohydrostatic Equilibrium for Fluid Enclosed in an Axisymmetric Toroidal Surface
- Bound States and Asymptotic Fields
- Spectral Problem of N×N Matrix Differential Operators on the Line
- Kramer–Pesch Effect in Chiral p-Wave Superconductors
- Fractional Exclusion Statistics for the Multicomponent Sutherland Model
- Fredholm Determinants and the Cauchy Problem of a Class of Nonlinear Evolution Equations
- Inverse Scattering Method for the Initial Value Problem of the Nonlinear Equation of Evolution (Part V. Initial Value Problems)