A. Bogoliubov-Valatin transformation. 1. B. Equation of motion. 3. II. Diagonalization Theory of Bose Systems 6. A. Dynamic matrix. 6. Remarks on the Bogoliubov-Valatin transformation. Authors: Liu, W. S.. Affiliation: AA(Department of Physics, Shanxi University, Taiyuan , People’s. Module 7: Tunneling and the energy gap. Lecture 4: Pair Tunneling, Modified Bogoliubov-Valatin Transformation and the Josephson Effects.
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Remarks on the Bogoliubov-Valatin transformation. Equivalent circuit for Josephson junction and analysis Lecture 2: BCS wave function is an example of squeezed coherent state of fermions.
The Hilbert space under consideration is equipped with these operators, and henceforth describes a higher-dimensional quantum harmonic oscillator usually an infinite-dimensional one. Heat Capacity and other Thermodynamic Properties Module 7: Normal metals Lecture 1: Select Student Faculty Others.
Determination of coefficients Alpha and Beta in the absence of fields and gradients Lecture 3: A 21, Help Center Find new research papers in: The ground state of the corresponding Hamiltonian is annihilated by all the annihilation operators:.
The most prominent application is again by Nikolai Bogoliubov himself, this time for the BCS theory of superconductivity. Ginzburg-Landau phenomenological theory Lecture 1: Two fluid model for superconductivity and London equations Lecture 2: A 37, Electrical conductivity and heat capacity followed by problem solving Lecture 2: Microscopic theory of superconductivity Lecture 1: This induces an autoequivalence on the respective representations.
This is interpreted as a linear symplectic transformation of the phase space. Retrieved 27 April The Bogoliubov transformation is often used to diagonalize Hamiltonians, with a corresponding transformation of the state function.
On the theory of superfluidityJ.
Field and order parameter variation inside a vortex Module 6: Operator eigenvalues calculated with the diagonalized Hamiltonian on the transformed state function thus are the same as before.
To find the conditions on the constants u and v such that the transformation ttransformation canonical, the commutator is evaluated, viz.
Superconducting Transition Temperature Lecture However, some care- lessness still bogoliubo occasionally. Since the form of this condition is suggestive of the hyperbolic identity.
Remarks on the Bogoliubov-Valatin transformation | Wing Kam Liu –
All excited states are obtained as linear combinations of the ground state excited by some creation operators:. A 40, 41 Solution of London equations and free energy calculations Module 4: U t then becomes simply Views Read Edit View history.
Free energy formulation Lecture 2: It may be written tary operator Up x be obtained from a straightforward in a form of unitary transformations for the individual integral as was done for Eq.
This page was last edited on 20 Novemberat BCS Wavefunction in terms of 2m-particle states Transflrmation Log In Sign Up. Experimental probes of Superconductivity Lecture 1: BCS Wavefunction Lecture 9: Would you like to know when this course is offered for certification?
D 2, 1 ] is pointed out and an exact formulation is reconstructed by using the disentangling technique for matrices. Critical field of thin films Lecture 7: