Bogoliubov transformation
E461415
The Bogoliubov transformation is a mathematical change of basis used in quantum field theory and many-body physics to diagonalize Hamiltonians by mixing creation and annihilation operators, enabling the description of quasiparticles and phenomena like superconductivity.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Bogoliubov transformation canonical | 3 |
| Bogoliubov quasiparticles | 1 |
| Bogoliubov transformations | 1 |
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
canonical transformation
ⓘ
change of basis ⓘ linear transformation ⓘ mathematical transformation ⓘ |
| appliesTo |
bosonic operators
ⓘ
fermionic operators ⓘ |
| expresses | new quasiparticle operators as linear combinations of old operators ⓘ |
| field |
condensed matter physics
ⓘ
many-body physics ⓘ quantum field theory ⓘ statistical mechanics ⓘ |
| goal | to obtain a Hamiltonian that is diagonal in quasiparticle operators ⓘ |
| hasProperty |
canonical
ⓘ
invertible ⓘ linear in creation and annihilation operators ⓘ symplectic in bosonic case ⓘ unitary in fermionic case ⓘ |
| involves | coherence factors u and v ⓘ |
| mathematicallyFormulatedAs | linear transformation between two sets of ladder operators ⓘ |
| namedAfter | Nikolay Bogoliubov NERFINISHED ⓘ |
| preserves |
canonical anticommutation relations
ⓘ
canonical commutation relations ⓘ |
| relatedTo |
BCS ground state
NERFINISHED
ⓘ
Bogoliubov quasiparticles NERFINISHED ⓘ Bogoliubov–de Gennes equations NERFINISHED ⓘ Hartree–Fock–Bogoliubov theory NERFINISHED ⓘ Nambu spinor formalism ⓘ quasiparticle operators ⓘ |
| usedFor |
defining quasiparticles
ⓘ
describing superconductivity ⓘ describing superfluidity ⓘ diagonalizing Hamiltonians ⓘ diagonalizing quadratic Hamiltonians ⓘ mixing creation and annihilation operators ⓘ quantizing fields with pairing terms ⓘ removing anomalous terms in Hamiltonians ⓘ solving BCS theory of superconductivity ⓘ treating interacting Bose gases ⓘ treating interacting Fermi systems ⓘ |
| usedIn |
BCS theory of superconductivity
NERFINISHED
ⓘ
Bogoliubov theory of weakly interacting Bose gas NERFINISHED ⓘ Hawking radiation calculations ⓘ Unruh effect analysis ⓘ mean-field approximations ⓘ particle creation in curved spacetime ⓘ quantum optics ⓘ squeezed state formalism ⓘ theory of superfluid helium ⓘ |
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Bogoliubov transformations
this entity surface form:
Bogoliubov quasiparticles