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From [https://press.uchicago.edu/ucp/books/book/chicago/B/bo24041257.html ''The Beautiful Cure: The Revolution in Immunology and What it Means for Your Health''] by [https://www.davislab.manchester.ac.uk/ Daniel M. Davis] (Professor of Immunology with a Ph.D. in physics):
'''How to select a good topic and style of presentation (for the format and goals of PHYS800):'''
<pre> “Science is many things. A method, a journey, a route to power, a body of knowledge, a thing you loved or hated at school, a jigsaw puzzle with an infinite number of pieces, a force for good and bad which has produced both food and bombs. Arguably, its greatest success has been, and will be for some time to come, in curing diseases.”
<pre>-> Pick a topic that is of relevance to your research or your broader field. It does not have to be too advanced, so it could be something that is missing, or it is improperly covered, in standard textbooks.  
</pre>
-> Pick a model on which your topic can be clearly explained, with all details included. Examples from previous presentations include: one or few qubits; one or few spins; one or two atoms, or an infinite tight-binding chain; Hubbard dimer; etc.
 
-> Present using: traditional blackboard; handwritten notes in PDF format which can be annotated as you talk; PPT slides; Jupyter (or Mathematica) notebook in case you are using code snippets to run numerical (or analytical) calculations on simple models.  
[https://www.frankawilczek.com/ Frank Wilczek] on Einstein's productive years:
<pre> “The later part of Einstein’s career-more than half, chronologically, covering thirty years—was devoted to (let’s call it) Theory of Everything physics, and it was essentially fruitless. During Einstein’s great creative period he dealt with much more specific, less grandiose problems. His special theory of relativity came out of worrying about technical difficulties in the electrodynamics of moving bodies. His general theory of relativity came out of worrying about how to make a theory of gravity consistent with special relativity. His pioneering work on Brownian motion and Bose-Einstein statistics came out of worrying about the relationship between fundamental physics and thermodynamics; specifically, about fluctuations. His seminal work on photons came out of thinking about specific, puzzling experimental results, notably the observed spectrum of blackbody radiation.”
</pre>
 
[https://www.frankawilczek.com/ Frank Wilczek] on Einstein's unproductive years:
<pre> “Why did Einstein loathe the implications of quantum mechanics? This question belongs to psychology more than physics. There was certainly no empirical reason for his distaste-on the contrary, quantum mechanics went from success to brilliant success. Einstein apparently just didn’t like the way probability enters into the laws of quantum theory, and he may have sensed difficulties in reconciling quantum theory with his baby, relativity. A normal scientific reaction would have been to respect the overwhelming success of what people were doing in quantum theory, assimilate that work, and try to tinker with it (maybe hoping to remove the probabilities) or build on it (to include relativity). In fact, we know that great results were there to be had along those directions, such as the Bell inequalities and the Dirac equation. But instead of trying to tinker or build, Einstein went into denial.”
</pre>
</pre>


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===Fundamentals===
===Fundamentals===
*B. Blankleider and A. N. Kvinikhidze, ''Shortest derivation of time-independent perturbation theory'', Am. J. Phys. '''93''', 652 (2025). [https://doi.org/10.1119/5.0152132 [PDF]]
*M. T. Ahari, G. Ortiz, and B. Seradjeha, ''On the role of self-adjointness in the continuum formulation of topological quantum phases'', Am. J. Phys. '''84''', 858 (2016). [https://doi.org/10.1119/1.4961500 [PDF]]
*M. T. Ahari, G. Ortiz, and B. Seradjeha, ''On the role of self-adjointness in the continuum formulation of topological quantum phases'', Am. J. Phys. '''84''', 858 (2016). [https://doi.org/10.1119/1.4961500 [PDF]]
*M. M. Nieto, Quantum Phase and quantum phase operators: Some physics and some history, Phys. Scr. '''T48''', 5 (1993). [https://doi.org/10.1088/0031-8949/1993/T48/001 [PDF]]
*M. M. Nieto, ''Quantum phase and quantum phase operators: Some physics and some history'', Phys. Scr. '''T48''', 5 (1993). [https://doi.org/10.1088/0031-8949/1993/T48/001 [PDF]]
* A. C. Hirshfeld and P. Henselder, ''Deformation quantization in the teaching of quantum mechanics'', Am. J. Phys. '''70''', 537 (2002). [https://doi.org/10.1119/1.1450573 [PDF]]
* A. C. Hirshfeld and P. Henselder, ''Deformation quantization in the teaching of quantum mechanics'', Am. J. Phys. '''70''', 537 (2002). [https://doi.org/10.1119/1.1450573 [PDF]]


===Algebraic approach via operator identities===
===Algebraic approach via operators and their identities===
*[https://quantum.georgetown.domains/courses.html#graduates ''Quantum Mechanics without Calculus'' graduate course videos by Prof. J. K. Freericks]
*[https://quantum.georgetown.domains/courses.html#graduates ''Quantum Mechanics done right'' graduate course videos by Prof. J. K. Freericks]
*E. Munguía-González, S. Rego, and J. K. Freericks, ''Making squeezed-coherent states concrete by determining their wavefunction'', Am. J. Phys. '''89''', 885 (2021). [https://doi.org/10.1119/10.0004872 [PDF]]
*E. Munguía-González, S. Rego, and J. K. Freericks, ''Making squeezed-coherent states concrete by determining their wavefunction'', Am. J. Phys. '''89''', 885 (2021). [https://doi.org/10.1119/10.0004872 [PDF]]
*A. M. Orjuela and J. K. Freericks,  ''Free expansion of a Gaussian wavepacket using operator manipulations'', [https://arxiv.org/abs/2305.00059 arXiv:2305.00059].
*A. M. Orjuela and J. K. Freericks,  ''Free expansion of a Gaussian wavepacket using operator manipulations'', Am. J. Phys. '''91''', 463 (2023). [https://doi.org/10.1119/5.0083964 [PDF]]


===Time-evolution===
===Time-evolution===
* [[Media:evolution_operator_decomposition.pdf|Decompositions of ordered operator exponentials for time-evolution in computational quantum physics]]
* [[Media:evolution_operator_decomposition.pdf|Overview of decompositions of ordered operator exponentials for time-evolution of quantum systems]]
* M. S. Rudner and N. H. Lindner, ''The Floquet engineer's handbook'', [https://arxiv.org/abs/2003.08252 arXiv:2003.08252].
* L. A. J. Guttieres, M. D. Petrović, J. K. Freericks, ''Computational projects with the Landau–Zener problem in the quantum mechanics classroom'', Am. J. Phys. '''91''', 885 (2023). [https://doi.org/10.1119/5.0139717 [PDF]]
*M. A. Sentef, J. Li, F. Künzel, and M. Eckstein, ''Quantum to classical crossover of Floquet engineering in correlated quantum systems'', Phys. Rev. Res. {\bf 2}, 033033 (2020). [https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.2.033033 [PDF]]
*R. Merlin, ''Rabi oscillations, Floquet states, Fermi's golden rule, and all that: Insights from an exactly solvable two-level model'', Am. J. Phys. '''89''', 26 (2021). [https://doi.org/10.1119/10.0001897 [PDF]]
*R. Merlin, ''Rabi oscillations, Floquet states, Fermi's golden rule, and all that: Insights from an exactly solvable two-level model'', Am. J. Phys. '''89''', 26 (2021). [https://doi.org/10.1119/10.0001897 [PDF]]
*S. Blanes, F. Casas, J. A. Oteo, and J. Ros, ''A pedagogical approach to the Magnus expansion'', Eur. J. Phys. '''31''', 907 (2010). [https://iopscience.iop.org/article/10.1088/0143-0807/31/4/020 [PDF]]
*S. Blanes, F. Casas, J. A. Oteo, and J. Ros, ''A pedagogical approach to the Magnus expansion'', Eur. J. Phys. '''31''', 907 (2010). [https://iopscience.iop.org/article/10.1088/0143-0807/31/4/020 [PDF]]
*C. J. Eckhardt, G. Passetti, M. Othman, C. Karrasch, F. Cavaliere, M. A. Sentef, and D. M. Kennes, ''Quantum Floquet engineering with an exactly solvable tight-binding chain in a cavity'', Communications Physics '''5''', 122 (2022). [https://www.nature.com/articles/s42005-022-00880-9.pdf [PDF]]
*C. J. Eckhardt, G. Passetti, M. Othman, C. Karrasch, F. Cavaliere, M. A. Sentef, and D. M. Kennes, ''Quantum Floquet engineering with an exactly solvable tight-binding chain in a cavity'', Commun. Phys. '''5''', 122 (2022). [https://www.nature.com/articles/s42005-022-00880-9.pdf [PDF]]
* M. S. Rudner and N. H. Lindner, ''The Floquet engineer's handbook'', [https://arxiv.org/abs/2003.08252 arXiv:2003.08252].
 
==Open Quantum Systems==
*F. Campaioli, J. H. Cole, and H. Hapuarachchi, ''Tutorial on quantum master equations: Tips and tricks for quantum optics, quantum computing and beyond'', PRX QUANTUM '''5''', 020202 (2024). [https://arxiv.org/pdf/2303.16449 [PDF]] + [https://github.com/frnq/qme/tree/main Python scripts]
*D. Manzano, ''A short introduction to the Lindblad master equation'', AIP Adv. '''10''', 025106 (2020). [https://doi.org/10.1063/1.5115323 [PDF]]
*F. Nathan and M. S. Rudner, ''Universal Lindblad equation for open quantum systems'', Phys. Rev. B '''102''', 115109 (2020). [https://doi.org/10.1103/PhysRevB.102.115109 [PDF]]
*Y. Tanimura, ''Numerically “exact” approach to open quantum dynamics: The hierarchical equations of motion (HEOM)'', J. Chem. Phys. '''153''', 020901 (2020). [https://doi.org/10.1063/5.0011599 [PDF]]
 
==Decoherence==
*B. Gu and I. Franco, ''When can quantum decoherence be mimicked by classical noise?'', J. Chem. Phys. '''151''', 014109 (2019). [https://aip.scitation.org/doi/10.1063/1.5099499 [PDF]]
*J. Kincaida, K. McLelland, and M. Zwolak,  ''Measurement-induced decoherence and information in double-slit interference'', Am. J. Phys. '''84''', 522 (2016). [https://doi.org/10.1119/1.4943585 [PDF]]
 
==Quantum Information Science==
*A. Ekert and P. L. Knight, ''Entangled quantum systems and the Schmidt decomposition'', Am. J. Phys. '''63''', 415 (1995). [http://dx.doi.org/10.1119/1.17904 [PDF]]
*T. Grover, ''Highly entangled quantum matter'' [https://pirsa.org/15030117 [Video]]


==Quantum Optics==
==Quantum Optics==
* Q.-H. Chen, T. Liu, Y.-Y. Zhang, and K.-L. Wang, ''Exact solutions to the Jaynes-Cummings model without the rotating-wave approximation'', Europhys. Lett. '''96''',  14003 (2011). [https://iopscience.iop.org/article/10.1209/0295-5075/96/14003 [PDF]]
*M. Bina, ''The coherent interaction between matter and radiation: A tutorial on the Jaynes-Cummings model'', Eur. Phys. J. Special Topics '''203''', 163 (2012). [https://link.springer.com/article/10.1140/epjst/e2012-01541-3 [PDF]]
* [https://iopscience.iop.org/issue/0953-4075/46/22 50 years of Jaynes-Cummings physics]
* G. Grynberg, A. Aspect, and Claude Fabre, ''Introduction to Quantum Optics: From the Semi-classical Approach to Quantized Light'' (Cambridge University Press, Cambridge, 2010). [https://www.cambridge.org/core/books/introduction-to-quantum-optics/F45DCE785DC8226D4156EC15CAD5FA9A [PDF]]
*Map of [http://info.phys.unm.edu/~ideutsch/Classes/Phys566F23/index.html Quantum Optics]:
[[Image:map_quantum_optics.jpg|center|500px]]


==Quantum-Classical Methods==
==Quantum-Classical Methods (particularly in Chemical Physics or Physical Chemistry)==
* F. Agostini and B. F. E. Curchod, ''Different flavors of nonadiabatic molecular dynamics'', WIREs Comput. Mol. Sci. '''9''', e1417 (2019).  [https://doi.org/10.1002/wcms.1417 [PDF]]
* F. Agostini and B. F. E. Curchod, ''Different flavors of nonadiabatic molecular dynamics'', WIREs Comput. Mol. Sci. '''9''', e1417 (2019).  [https://doi.org/10.1002/wcms.1417 [PDF]]
* F. Agostini, ''An exact-factorization perspective on quantum-classical approaches to excited-state dynamics'', Euro. Phys. J. B '''91''', 143 (2018). [https://link.springer.com/article/10.1140/epjb/e2018-90085-9 [PDF]]
* F. Agostini, ''An exact-factorization perspective on quantum-classical approaches to excited-state dynamics'', Euro. Phys. J. B '''91''', 143 (2018). [https://link.springer.com/article/10.1140/epjb/e2018-90085-9 [PDF]]


==Quantum Information Science==
==Topological concepts in quantum materials==
*A. Ekert and P. L. Knight, ''Entangled quantum systems and the Schmidt decomposition'', Am. J. Phys. '''63''', 415 (1995). [http://dx.doi.org/10.1119/1.17904 [PDF]]
* D. C. Ralph, ''Berry curvature, semiclassical electron dynamics, and topological materials: Lecture notes for Introduction to Solid State Physics'', arXiv:2001.04797 [https://arxiv.org/pdf/2001.04797 [PDF]]
* T. Grover, [https://pirsa.org/15030117 ''Highly entangled quantum matter'']
 
==Quantum Many-Body Systems==


==Open Quantum Systems and Quantum Master Equations==
===Quantum spins and magnets===
*G. Schaller, [https://www1.itp.tu-berlin.de/schaller/download/NEQME2.pdf ''Nonequilibrium master equations''].
*B. K. Nikolić, [[Media:PHYS800_hubbard_dimer.pdf|From Hubbard dimer to effective antiferromagnetic Hubbard model for two spins]]
*D. Manzano, ''A short introduction to the Lindblad master equation'', AIP Adv. '''10''', 025106 (2020). [https://doi.org/10.1063/1.5115323 [PDF]]
*B. K. Nikolić, [[Media:PHYS800_magnons.pdf|Ground state and low-energy magnon excitations of ferro- and antiferromagnets]]
*C. Le Bris, P. Rouchon, and J. Roussel, ''Adaptive low-rank approximation and denoised Monte Carlo approach for high-dimensional Lindblad equations'', Phys. Rev. A '''92''', 062126 (2015). [https://doi.org/10.1103/PhysRevA.92.062126 [PDF]]
*K. Joel, D. Kollmar, and L. F. Santos, ''An introduction to the spectrum, symmetries, and dynamics of spin-1/2 Heisenberg chains'', Am. J. Phys. '''81''', 450 (2013). [https://pubs.aip.org/aapt/ajp/article/81/6/450/149628/An-introduction-to-the-spectrum-symmetries-and [PDF]]
*Y. Tanimura, ''Numerically “exact” approach to open quantum dynamics: The hierarchical equations of motion (HEOM)'', J. Chem. Phys. '''153''', 020901 (2020). [https://doi.org/10.1063/5.0011599 [PDF]]
*F. Mila, ''Quantum spin liquids'', Eur. J. Phys. 21, '''499''' (2000). [https://doi.org/10.1088/0143-0807/21/6/302 [PDF]]
*V. Reimer, M. R. Wegewijs, K. Nestmann, and M. Pletyukhov, ''Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables'', J. Chem. Phys. '''151''', 044101 (2019). [https://doi.org/10.1063/1.5094412 [PDF]]
*P. Wrzosek, K. Wohlfeld, D. Hofmann, T. Sowiński, and M. A. Sentef, ''Quantum walk versus classical wave: Distinguishing ground states of quantum magnets by spacetime dynamics'', Phys. Rev. B '''102''', 024440 (2020). [https://doi.org/10.1103/PhysRevB.102.024440 [PDF]]
*M. Hoffmann and S. Blügel, ''Systematic derivation of realistic spin models for beyond-Heisenberg solids'', Phys. Rev. B '''101''', 024418 (2020). [https://doi.org/10.1103/PhysRevB.101.024418 [PDF]]
*S. Kitamura, T. Oka, and H. Aoki, ''Probing and controlling spin chirality in Mott insulators by circularly polarized laser'', Phys. Rev. B '''96''', 014406 (2017). [https://doi.org/10.1103/PhysRevB.96.014406 [PDF]]
* A. Szilva, Y. Kvashnin, E. A. Stepanov, O. Eriksson, A. I. Lichtenstein, and M. I. Katsnelson, ''Quantitative theory of magnetic interactions in solids'', Rev. Mod. Phys. '''95''', 035004 (2023). [https://doi.org/10.1103/RevModPhys.95.035004 [PDF]]


==Decoherence==
==Superconductivity==
*B. Gu and I. Franco, ''When can quantum decoherence be mimicked by classical noise?'', J. Chem. Phys. '''151''', 014109 (2019). [https://aip.scitation.org/doi/10.1063/1.5099499 [PDF]]
*[[Media:bdg_kwant.ipynb|Bogoliubov-de Gennes equations via KWANT]]
*J. Kincaida, K. McLelland, and M. Zwolak,  ''Measurement-induced decoherence and information in double-slit interference'', Am. J. Phys. '''84''', 522 (2016). [https://doi.org/10.1119/1.4943585 [PDF]]


==Quantum Many-Body Systems==
===Computational algorithms===
*I. P. McCulloch, ''From density-matrix renormalization group to matrix product states'', J. Stat. Mech. P10014 (2007). [https://iopscience.iop.org/article/10.1088/1742-5468/2007/10/P10014 [PDF]]
*G. Catarina and B. Murta, ''Density-matrix renormalization group: a pedagogical introduction'', Eur. Phys. J. B '''96''', 111 (2023). [https://link.springer.com/content/pdf/10.1140/epjb/s10051-023-00575-2.pdf?pdf=button [PDF]]
*J. Hauschild and F. Pollmann, ''Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)'', SciPost Phys. Lect. Notes '''5''' (2018). [https://scipost.org/SciPostPhysLectNotes.5/pdf [PDF]]
*J. Hauschild and F. Pollmann, ''Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)'', SciPost Phys. Lect. Notes '''5''' (2018). [https://scipost.org/SciPostPhysLectNotes.5/pdf [PDF]]
*F. Mila, ''Quantum spin liquids'', Eur. J. Phys. 21, '''499''' (2000). [https://doi.org/10.1088/0143-0807/21/6/302 [PDF]]
* A. Chiocchetta, D. Kiese, C. P. Zelle, F. Piazza,  and S. Diehl, ''Cavity-induced quantum spin liquids'', Nat. Commun. '''12''', 5901 (2021). [https://www.nature.com/articles/s41467-021-26076-3.pdf [PDF]


==Quantum Field Theory==
==Path Integrals==
*Y. BenTov, ''Schwinger-Keldysh path integral for the quantum harmonic oscillator'', [https://arxiv.org/abs/2102.05029 arXiv:2102.05029]
*D. H. Rischke, ''"In-out" (or Feynman) path integrals in quantum mechanics'' [https://itp.uni-frankfurt.de/~drischke/Script_Path_Integrals_GU2021.pdf [PDF]]
*Y. BenTov, ''"In-in" (or Schwinger-Keldysh) path integral in quantum mechanics'', arXiv:2102.05029 (2021). [https://arxiv.org/pdf/2102.05029 [PDF]]
 
==Quantum Field Theory (for AMO and Condensed Matter Physics)==
*G. Fletcher, ''Functional integrals and the BCS theory of superconductivity'',  Am. J. Phys. '''58''', 50 (1990). [https://pubs.aip.org/aapt/ajp/article/58/1/50/1053498/Functional-integrals-and-the-BCS-theory-of [PDF]]
*K. Byczuk and P. Jakubczyk, ''Generalized Gaussian integrals with application to the Hubbard–Stratonovich transformation'', Am. J. Phys. '''91''',  840 (2023). [https://doi.org/10.1119/5.0141045 [PDF]]
*Y. Tanizaki, Y. Hidaka, and T. Hayata, ''Lefschetz-thimble analysis of the sign problem in one-site fermion model'', New J. Phys. '''18''', 033002 (2016).  [https://iopscience.iop.org/article/10.1088/1367-2630/18/3/033002/pdf [PDF]]
*P. Millington and P. M Saffin, ''Visualising quantum effective action calculations in zero dimensions'',  J. Phys. A: Math. Theor. '''52''', 405401 (2019). [https://iopscience.iop.org/article/10.1088/1751-8121/ab37e6/pdf [PDF]]


==Numeric and Symbolic Packages==
==Numeric and Symbolic Packages==

Latest revision as of 13:12, 21 November 2025

How to select a good topic and style of presentation (for the format and goals of PHYS800): 

-> Pick a topic that is of relevance to your research or your broader field. It does not have to be too advanced, so it could be something that is missing, or it is improperly covered, in standard textbooks. 
-> Pick a model on which your topic can be clearly explained, with all details included. Examples from previous presentations include: one or few qubits; one or few spins; one or two atoms, or an infinite tight-binding chain; Hubbard dimer; etc.  
-> Present using: traditional blackboard; handwritten notes in PDF format which can be annotated as you talk; PPT slides; Jupyter (or Mathematica) notebook in case you are using code snippets to run numerical (or analytical) calculations on simple models.

Quantum Mechanics

Fundamentals

  • B. Blankleider and A. N. Kvinikhidze, Shortest derivation of time-independent perturbation theory, Am. J. Phys. 93, 652 (2025). [PDF]
  • M. T. Ahari, G. Ortiz, and B. Seradjeha, On the role of self-adjointness in the continuum formulation of topological quantum phases, Am. J. Phys. 84, 858 (2016). [PDF]
  • M. M. Nieto, Quantum phase and quantum phase operators: Some physics and some history, Phys. Scr. T48, 5 (1993). [PDF]
  • A. C. Hirshfeld and P. Henselder, Deformation quantization in the teaching of quantum mechanics, Am. J. Phys. 70, 537 (2002). [PDF]

Algebraic approach via operators and their identities

Time-evolution

  • Overview of decompositions of ordered operator exponentials for time-evolution of quantum systems
  • L. A. J. Guttieres, M. D. Petrović, J. K. Freericks, Computational projects with the Landau–Zener problem in the quantum mechanics classroom, Am. J. Phys. 91, 885 (2023). [PDF]
  • R. Merlin, Rabi oscillations, Floquet states, Fermi's golden rule, and all that: Insights from an exactly solvable two-level model, Am. J. Phys. 89, 26 (2021). [PDF]
  • S. Blanes, F. Casas, J. A. Oteo, and J. Ros, A pedagogical approach to the Magnus expansion, Eur. J. Phys. 31, 907 (2010). [PDF]
  • C. J. Eckhardt, G. Passetti, M. Othman, C. Karrasch, F. Cavaliere, M. A. Sentef, and D. M. Kennes, Quantum Floquet engineering with an exactly solvable tight-binding chain in a cavity, Commun. Phys. 5, 122 (2022). [PDF]
  • M. S. Rudner and N. H. Lindner, The Floquet engineer's handbook, arXiv:2003.08252.

Open Quantum Systems

  • F. Campaioli, J. H. Cole, and H. Hapuarachchi, Tutorial on quantum master equations: Tips and tricks for quantum optics, quantum computing and beyond, PRX QUANTUM 5, 020202 (2024). [PDF] + Python scripts
  • D. Manzano, A short introduction to the Lindblad master equation, AIP Adv. 10, 025106 (2020). [PDF]
  • F. Nathan and M. S. Rudner, Universal Lindblad equation for open quantum systems, Phys. Rev. B 102, 115109 (2020). [PDF]
  • Y. Tanimura, Numerically “exact” approach to open quantum dynamics: The hierarchical equations of motion (HEOM), J. Chem. Phys. 153, 020901 (2020). [PDF]

Decoherence

  • B. Gu and I. Franco, When can quantum decoherence be mimicked by classical noise?, J. Chem. Phys. 151, 014109 (2019). [PDF]
  • J. Kincaida, K. McLelland, and M. Zwolak, Measurement-induced decoherence and information in double-slit interference, Am. J. Phys. 84, 522 (2016). [PDF]

Quantum Information Science

  • A. Ekert and P. L. Knight, Entangled quantum systems and the Schmidt decomposition, Am. J. Phys. 63, 415 (1995). [PDF]
  • T. Grover, Highly entangled quantum matter [Video]

Quantum Optics

  • M. Bina, The coherent interaction between matter and radiation: A tutorial on the Jaynes-Cummings model, Eur. Phys. J. Special Topics 203, 163 (2012). [PDF]
  • 50 years of Jaynes-Cummings physics
  • G. Grynberg, A. Aspect, and Claude Fabre, Introduction to Quantum Optics: From the Semi-classical Approach to Quantized Light (Cambridge University Press, Cambridge, 2010). [PDF]
  • Map of Quantum Optics:

Quantum-Classical Methods (particularly in Chemical Physics or Physical Chemistry)

  • F. Agostini and B. F. E. Curchod, Different flavors of nonadiabatic molecular dynamics, WIREs Comput. Mol. Sci. 9, e1417 (2019). [PDF]
  • F. Agostini, An exact-factorization perspective on quantum-classical approaches to excited-state dynamics, Euro. Phys. J. B 91, 143 (2018). [PDF]

Topological concepts in quantum materials

  • D. C. Ralph, Berry curvature, semiclassical electron dynamics, and topological materials: Lecture notes for Introduction to Solid State Physics, arXiv:2001.04797 [PDF]

Quantum Many-Body Systems

Quantum spins and magnets

  • B. K. Nikolić, From Hubbard dimer to effective antiferromagnetic Hubbard model for two spins
  • B. K. Nikolić, Ground state and low-energy magnon excitations of ferro- and antiferromagnets
  • K. Joel, D. Kollmar, and L. F. Santos, An introduction to the spectrum, symmetries, and dynamics of spin-1/2 Heisenberg chains, Am. J. Phys. 81, 450 (2013). [PDF]
  • F. Mila, Quantum spin liquids, Eur. J. Phys. 21, 499 (2000). [PDF]
  • P. Wrzosek, K. Wohlfeld, D. Hofmann, T. Sowiński, and M. A. Sentef, Quantum walk versus classical wave: Distinguishing ground states of quantum magnets by spacetime dynamics, Phys. Rev. B 102, 024440 (2020). [PDF]
  • M. Hoffmann and S. Blügel, Systematic derivation of realistic spin models for beyond-Heisenberg solids, Phys. Rev. B 101, 024418 (2020). [PDF]
  • S. Kitamura, T. Oka, and H. Aoki, Probing and controlling spin chirality in Mott insulators by circularly polarized laser, Phys. Rev. B 96, 014406 (2017). [PDF]
  • A. Szilva, Y. Kvashnin, E. A. Stepanov, O. Eriksson, A. I. Lichtenstein, and M. I. Katsnelson, Quantitative theory of magnetic interactions in solids, Rev. Mod. Phys. 95, 035004 (2023). [PDF]

Superconductivity

Computational algorithms

  • G. Catarina and B. Murta, Density-matrix renormalization group: a pedagogical introduction, Eur. Phys. J. B 96, 111 (2023). [PDF]
  • J. Hauschild and F. Pollmann, Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy), SciPost Phys. Lect. Notes 5 (2018). [PDF]

Path Integrals

  • D. H. Rischke, "In-out" (or Feynman) path integrals in quantum mechanics [PDF]
  • Y. BenTov, "In-in" (or Schwinger-Keldysh) path integral in quantum mechanics, arXiv:2102.05029 (2021). [PDF]

Quantum Field Theory (for AMO and Condensed Matter Physics)

  • G. Fletcher, Functional integrals and the BCS theory of superconductivity, Am. J. Phys. 58, 50 (1990). [PDF]
  • K. Byczuk and P. Jakubczyk, Generalized Gaussian integrals with application to the Hubbard–Stratonovich transformation, Am. J. Phys. 91, 840 (2023). [PDF]
  • Y. Tanizaki, Y. Hidaka, and T. Hayata, Lefschetz-thimble analysis of the sign problem in one-site fermion model, New J. Phys. 18, 033002 (2016). [PDF]
  • P. Millington and P. M Saffin, Visualising quantum effective action calculations in zero dimensions, J. Phys. A: Math. Theor. 52, 405401 (2019). [PDF]

Numeric and Symbolic Packages

  • SNEG Mathematica package for analytical calculations in second quantization.
  • QuSpin Python package for numerical calculations (exact diagonalization and quantum dynamics) of arbitrary boson, fermion and spin many-body systems.
  • HOQST Julia package for numerical calculations of time evolution of open quantum systems, such as qubits in dissipative environment.
  • QuTiP Python package for numerical calculations of time evolution of open quantum systems, such as qubits in dissipative environment. 
conda config --append channels conda-forge
conda install qutip
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