Lev Landau’s “Theoretical Minimum” [UPDATED]

Check here for posts containing reference materials and notes for Theoretical Minimum

The great Soviet physicist Lev Landau developed a famous entry exam to test his students. This “Theoretical Minimum” contained everything of what he considered elementary for a young theoretical physicist. Despite its name, it was and still is, extremely rigorous and comprehensive.

Nowadays students are examined by collaborators of Landau Institute for Theoretical Physics. Each exam, as it was before, consists of problems solving. For every exam there is one or several examiners with whom the potential candidate is to establish contact in order to make an appointment for particular exam. Normally the student wishing to attempt the examination is expected to do so at Landau Institute for Theoretical Physics at Moscow, but it is not feasible for overseas candidates.  Therefore, in such cases the examiner would send the candidate problems via email and the detailed solutions should be sent back in 3-7 days. The solutions are to be submitted in LaTeX PDF format.

The syllabus for each exam corresponds to the contents of volumes in the Course of Theoretical Physics by Lev Landau & Evgeny Lifshitz. Usually one is expected to master every paragraph of the book, literally! Here is the detailed syllabus :

  • Mathematics-I : Three Problems in indefinite Integration, differential equations and limits, vector algebra and tensor analysis.
  • Mechanics : Volume 1. Theoretical mechanics, except section § 27, 29, 30, 37, 51
  • Field Theory : Volume 2. The Classical Theory of Fields, except section § 50, 54-57, 59-61, 68, 70, 74, 77, 97, 98, 102, 106, 108, 109, 115-119
  • Mathematics-II : Theory of functions of a complex variable, evaluating integrals, solution of equations deductions using contour integrals (Laplace’s method), calculate asymptotics of integrals, special functions (Bessel, Legendre, elliptic, the hypergeometric function, the gamma function).
  • Quantum Mechanics : Volume 3. Quantum Mechanics : Non-Relativistic Theory, except sections § 29, 49, 51, 57, 77, 80, 84, 85, 87, 88, 90, 101, 104, 105, 106, 110, 114, 138, 152.
  • Quantum Electrodynamics : Volume 4. Quantum Electrodynamics, except section § 9, 14, 16, 31, 35, 38, 41, 46, 48, 51, 52, 55, 57, 66, 70, 82, 84, 85, 87, 89, 91, 95, 97, 100, 101, 106, 109, 112, 115-144
  • Statistical Physics-I : Volume 5. Statistical Physics Part I, except sections § 22, 30, 50, 60, 68, 70, 72, 79, 80, 84, 95, 99, 100, 125-127, 134-141, 150-153, 155-160
  • Continuum mechanics : Volume 6. Fluid Mechanics, except sections § 11, 13, 14, 21, 23, 25, 28, 30-32, 34-48, 53-59, 63, 67-78, 80, 83, 86, 88, 90, 91, 94-141; Volume 7. Theory of Elasticity, except sections § 11, 13, 14, 21, 23, 25, 28, 30-32, 34-48, 53-59, 63, 67-78, 80, 83, 86, 88, 90, 91, 94-141
  • Electrodynamics of continuous media : Volume 8. Electrodynamics of continrous media, except § 1 to 5, 9, 15, 16, 18, 25, 28, 34, 35, 42, 44, 56, 57, 61, 64, 69, 74, 79-81, 84, 91-112, 123, 126.
  • Statistical Physics-II : Volume 9. Statistical Physics Part II, only § 1-5, 7, 18, 22, 27, 29, 36, 40, 43, 48, 50, 55, 61, 63, 65, 69
  • Physical Kinetics : Volume 10. Physical Kinetics, only § 1 to 8, 11, 12, 14, 21, 22, 24, 27, 30, 32-34, 41-44, 66-69, 75, 78, 82, 86, 101.

As a side note, the exam Quantum Mechanics also serves as graduate entrance exam for the institute. I will be posting my notes and those which will be helpful for those who wish to attempt it soon.

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Simulation for Quantum Science [Part 3]

QCAD: Quantum circuit emulator

QCAD is a {surprisingly!} windows-based environment for quantum computing simulation which helps designing circuits and simulating them. Developed by Hiroshi Watanabe Masaru Suzuki and Junnosuke Yamazaki at University of Tokoyo and Nagoya University.

Extremely useful tool for designing Quantum circuits using graphical user interface (GUI). The designed cricuits can also be exported as EPS (Encapsulated Postscript) for use with LaTeX. I have not tried exporting the circuits but it does sound very useful.

 

Quantum Computer Emulator (QCE)

QCE is a software tool that emulates various hardware designs of Quantum Computers. QCE simulates the physical processes that govern the operation of a hardware quantum processor, strictly according to the laws of quantum mechanics. QCE also provides an environment to debug and execute quantum algorithms under realistic experimental conditions. The software consists of a Graphical User Interface (GUI) and the simulator itself. Developed and maintained by Zernike Institute for Advanced Materials, University of Groningen.

QCE runs smoothly on Windows XP and is known to support Windows 98/NT/2000/ME/XP environment. It gives a detailed exposition is given of the implementation of the CNOT and the To oli gate, the quantum Fourier transform, Grover’s database search algorithm, Shor’s algorithm, and more.

A paper titled “QCE: A Simulator for Quantum Computer Hardware” by K.F.L. Michielsen and H.A. De Raedt offers detailed information regarding QCE although the paper could have more clearer snapshots of the emulator in action.

 

jQuantum – Quantum Computer Simulation Applet

jQuantum is a quantum computer simulator. It simulates the implementation of quantum circuits on a small quantum register up to about 15 qubits. Its main intention is to create images—images which may help to learn and understand quantum circuits, and which perhaps will serve as building blocks for inventing new quantum algorithms. Hosted and supported by South Westphalia University of Applied Sciences.

Awesome Python Libraries

This is extension of this post by David Cerezo Sanchez where he posted the following useful Python libraries :

  • SymPy, a Python library for symbolic mathematics
  • Pattern, web mining module for Python
  • NLTK, natural language processing with Python
  • Scapy, interactive packet manipulation program
  • Bitey and llvm-py, to import and modify LLVM bytecode

All of them extremely useful but there are some that I would like to add :

  • scipy, for advanced math, signal processing, optimization and statistics
  • NumPy, for linear algebra, Fourier transform, and random number capabilities
  • matplotlib, for 2D plotting
  • Twisted, to implement network protocol parsing and handling for TCP servers
  • Python for iOS, not a library but very useful tool for using python on iOS devices

Quantum Systems in Python

Recently read an extremely interesting post here by Markus Baden introduced to me the wonderful tool called Quantum Optics Toolbox in Python aka qutip. Developed by Robert Johansson and Paul Nation. It is truly the most marvelous tool, granted I just started to use it. The best thing is that one of the developer Robert Johansson has recently posted lecture notes for qutip. These notes contains ready to execute code which user can directly start playing with. Here are the notes in html format :

while the PDF of these are available on the github.

I am only disappointed that the latest version 2x and above wont be supporting windows officially.  Times like this make me happy that I am comfortable with Linux, though I still wish Mac prizes would drop down…