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*Chapter 1.9 and 7.1 of Nazarov & Danon textbook.
*Chapter 1.9 and 7.1 of Nazarov & Danon textbook.


== LECTURE 2: Second quantization formalism for bosons ==
== LECTURE 2: Quantization of the electromagnetic field ==
* Example: AC Stark effect for two-level atom in quantized electromagnetic field vs. Floquet theory.
* Example: Nonclassical light and photon statistics.
* Example: Light-matter interaction.
 
===References===
*[[Media:WYSIN=quantization_of_free_electromagnetic_field_photons_and_operators.pdf|Quantization of the free electromagnetic field: Photons and operators]]
*M. Haas, U. D. Jentschura, and C. H. Keitel, ''Comparison of classical and second quantized description of the dynamic Stark shift'', Am. J. Phys. '''74''', 77 (2006). [https://doi.org/10.1119/1.2140742 [PDF]]
 
 
== LECTURE 3: Second quantization formalism for bosons ==
* Example: Pair distribution function, density-density correlation function and structure factor.
* Example: Pair distribution function, density-density correlation function and structure factor.
* Example: Magnons in ferromagnets and antiferromagnets.
* Example: Magnons in ferromagnets and antiferromagnets.
Line 19: Line 29:
*J. M. Zhang and R. X. Dong, ''Exact diagonalization: The Bose–Hubbard model as an example'', Eur. J. Phys. '''31''', 591 (2010). [https://iopscience.iop.org/article/10.1088/0143-0807/31/3/016 [PDF]]
*J. M. Zhang and R. X. Dong, ''Exact diagonalization: The Bose–Hubbard model as an example'', Eur. J. Phys. '''31''', 591 (2010). [https://iopscience.iop.org/article/10.1088/0143-0807/31/3/016 [PDF]]


== LECTURE 3: Second quantization formalism for fermions ==  
== LECTURE 4: Second quantization formalism for fermions ==  
* Example: Hubbard dimer and trimer.
* Example: Hubbard dimer and trimer.
* Example: Mean-field magnetic phase diagram of Hubbard model.
* Example: Mean-field magnetic phase diagram of Hubbard model.
Line 32: Line 42:
* E. Erlandsen, A. Kamra, A. Brataas, and A. Sudbø, ''Enhancement of superconductivity mediated by antiferromagnetic squeezed magnons'', Phys. Rev. B '''100''', 100503(R) (2019). [https://doi.org/10.1103/PhysRevB.100.100503 [PDF]]
* E. Erlandsen, A. Kamra, A. Brataas, and A. Sudbø, ''Enhancement of superconductivity mediated by antiferromagnetic squeezed magnons'', Phys. Rev. B '''100''', 100503(R) (2019). [https://doi.org/10.1103/PhysRevB.100.100503 [PDF]]


== LECTURE 4: Time-dependent perturbation theory: Dyson vs. Magnus series ==
== LECTURE 5: Time-dependent perturbation theory: Dyson vs. Magnus series ==
* Example: Dyson vs. Magnus expansion for driven harmonic oscillator.
* Example: Dyson vs. Magnus expansion for driven harmonic oscillator.


Line 39: Line 49:
* S. Blanes, F. Casas, J. A. Oteo, and J. Ros, ''A pedagogical approach to the Magnus expansion'', Eur. J. Phys. '''31''', 907 (2010). [http://personales.upv.es/serblaza/2010EJP.pdf [PDF]]
* S. Blanes, F. Casas, J. A. Oteo, and J. Ros, ''A pedagogical approach to the Magnus expansion'', Eur. J. Phys. '''31''', 907 (2010). [http://personales.upv.es/serblaza/2010EJP.pdf [PDF]]


== LECTURE 5: Floquet theory of periodically driven quantum systems ==
== LECTURE 6: Floquet theory of periodically driven quantum systems ==
*Example: AC Stark effect for two-level atom in classical electromagnetic wave.
*Example: AC Stark effect for two-level atom in classical electromagnetic wave.
*Example: Floquet topological insulators.
*Example: Floquet topological insulators.
Line 45: Line 55:
===References===
===References===
* A. Eckardt and E. Anisimovas, ''High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective'', New J. Phys. '''17''', 093039  (2015). [https://iopscience.iop.org/article/10.1088/1367-2630/17/9/093039/pdf [PDF]].
* A. Eckardt and E. Anisimovas, ''High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective'', New J. Phys. '''17''', 093039  (2015). [https://iopscience.iop.org/article/10.1088/1367-2630/17/9/093039/pdf [PDF]].
== LECTURE 6: Quantization of the electromagnetic field ==
* Example: AC Stark effect for two-level atom in quantized electromagnetic field vs. Floquet theory.
* Example: Nonclassical light and photon statistics.
* Example: Light-matter interaction.
===References===
*[[Media:WYSIN=quantization_of_free_electromagnetic_field_photons_and_operators.pdf|Quantization of the free electromagnetic field: Photons and operators]]
*M. Haas, U. D. Jentschura, and C. H. Keitel, ''Comparison of classical and second quantized description of the dynamic Stark shift'', Am. J. Phys. '''74''', 77 (2006). [https://doi.org/10.1119/1.2140742 [PDF]]


== LECTURE 7: Dissipative quantum mechanics with application to qubits ==
== LECTURE 7: Dissipative quantum mechanics with application to qubits ==

Revision as of 08:54, 10 August 2021

LECTURE 1: Second quantization formalism for harmonic oscillator

  • Example: Coherent (quasiclassical) and squeezed states.
  • Example: Isotropic three-dimensional harmonic oscillator.
  • Example: Phonons in solids.

References

  • Chapter 1.9 and 7.1 of Nazarov & Danon textbook.

LECTURE 2: Quantization of the electromagnetic field

  • Example: AC Stark effect for two-level atom in quantized electromagnetic field vs. Floquet theory.
  • Example: Nonclassical light and photon statistics.
  • Example: Light-matter interaction.

References


LECTURE 3: Second quantization formalism for bosons

  • Example: Pair distribution function, density-density correlation function and structure factor.
  • Example: Magnons in ferromagnets and antiferromagnets.
  • Example: Bogoliubov theory of superfluidity.
  • Example: Bose-Hubbard model for cold atoms in optical lattices.

References

  • Chapters 3, 4.5 and 6 of Nazarov & Danon textbook.
  • W. E. Lawrence, Algebraic identities relating first- and second-quantized operators, Am. J. Phys. 68, 167 (2000). [PDF]
  • C. Timm, Lecture Notes on Theory of Magnetism
  • J. M. Zhang and R. X. Dong, Exact diagonalization: The Bose–Hubbard model as an example, Eur. J. Phys. 31, 591 (2010). [PDF]

LECTURE 4: Second quantization formalism for fermions

  • Example: Hubbard dimer and trimer.
  • Example: Mean-field magnetic phase diagram of Hubbard model.
  • Example: Mean-field vs. exact Richardson solution of BCS model of superconductivity.
  • Example: Hartree-Fock theory of electrons in metals.

References

  • Chapters 3 and 5 of Nazarov & Danon textbook.
  • C. Timm, Lecture Notes on Theory of Superconductivity
  • D. J. Carrascal, J. Ferrer, J. C. Smith, and K. Burke, The Hubbard dimer: A density functional case study of a many-body problem, J. Phys.: Condens. Matter 29, 019501 (2017). [PDF]
  • Y. Claveau, B. Arnaud and S. Di Matteo, Mean-field solution of the Hubbard model: the magnetic phase diagram, Eur. J. Phys. 35, 035023 (2014). [PDF]
  • E. Erlandsen, A. Kamra, A. Brataas, and A. Sudbø, Enhancement of superconductivity mediated by antiferromagnetic squeezed magnons, Phys. Rev. B 100, 100503(R) (2019). [PDF]

LECTURE 5: Time-dependent perturbation theory: Dyson vs. Magnus series

  • Example: Dyson vs. Magnus expansion for driven harmonic oscillator.

References

  • Chapter 1 of Nazarov and Danon textbook.
  • S. Blanes, F. Casas, J. A. Oteo, and J. Ros, A pedagogical approach to the Magnus expansion, Eur. J. Phys. 31, 907 (2010). [PDF]

LECTURE 6: Floquet theory of periodically driven quantum systems

  • Example: AC Stark effect for two-level atom in classical electromagnetic wave.
  • Example: Floquet topological insulators.

References

  • A. Eckardt and E. Anisimovas, High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective, New J. Phys. 17, 093039 (2015). [PDF].

LECTURE 7: Dissipative quantum mechanics with application to qubits

  • Example: Damped harmonic oscillator.
  • Example: Qubit coupled to dissipative environment (spin-boson model).
  • Example: Linblad master equation and quantum jump solution.

References

  • Chapters 11 and 12 of Nazarov & Danon textbook.

LECTURE 8: Relativistic quantum mechanics

References

  • Chapter 13 of Nazarov & Danon textbook.
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