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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Help Center Find new research papers in: Superconductivity phenomenon Lecture 1: The ground state of the corresponding Hamiltonian is annihilated by all the annihilation operators:. Type II superconductivity, fluxoid quantisation Lecture 6: Enter the email address you signed up with and we’ll email you a reset link.

Bogolyubov-Valatin Transformation – Scholarpedia

The Hilbert space under consideration is equipped with these operators, and henceforth describes a higher-dimensional quantum harmonic oscillator usually an infinite-dimensional one. Experimental probes of superconductivity-1 Lecture 2: Energy-Level Diagrams Lecture 2: Click here to sign up.

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Solution of London equations and free energy calculations Module 4: USSR11, p. Coherence length, flux quantum, field penetration in a slab Lecture 5: U t then becomes valtain 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.


Application to the superconducting transition followed by problem solving Module 5: Retrieved from ” https: BCS Wavefunction Lecture 9: Skip to main content. Remember me on this computer. Determination of coefficients Alpha and Beta in transformatioon absence of fields and gradients Lecture 3: In theoretical physicsthe Bogoliubov transformationalso known as Bogoliubov-Valatin transformationwere independently developed in by Nikolay Bogolyubov and John George Valatin for finding solutions of BCS theory in a homogeneous system.

Field and order parameter variation inside a vortex Module 6: Roman, Advanced Quantum Theory: Consider the canonical commutation relation for bosonic creation and annihilation operators in the harmonic basis. All excited states are obtained as linear combinations of the ground state excited by some creation operators:.

Retrieved 27 April Since the form of this condition is suggestive of the hyperbolic identity. A 37, To find the conditions on the constants u and v such that the transformation is canonical, the commutator is evaluated, viz. As it happens that the following commutation relation is 4.

Remarks on the Bogoliubov-Valatin transformation

This is used in the derivation of Hawking radiation. Application of Superconductors Lecture 1: D 2, 1 ] is pointed out and an exact formulation is reconstructed by using the disentangling technique for matrices.


Experimental probes of Superconductivity Lecture 1: From Transformatjon, the free encyclopedia. The Bogoliubov transformation is also important for understanding the Unruh effectHawking radiationpairing effects in nuclear physics, and many other topics.

Bogoliubov transformation

Microscopic Theory Lecture 3: Remarks on the Bogoliubov-Valatin transformation. GL equations in presence of fields currents bogoliuubov gradients Lecture 4: However, some care- lessness still happened occasionally. Electrical conductivity and heat capacity followed by problem solving Lecture 2: BCS wave function is an example of squeezed coherent state of fermions.

This is interpreted as a linear symplectic transformation of the phase space.

Thermodynamics of the superconducting transition Lecture 1: They can also be defined as squeezed coherent states. The most prominent application is again by Nikolai Bogoliubov himself, this time for the BCS theory of superconductivity. Equivalent circuit for Josephson junction and analysis Lecture 2: Tunneling and the energy gap Lecture 1: A 21,