File:7623.jpg This is the second core course in the sequence (PHYS 616 + PHYS 813) aimed to introduce physics graduate students to basic concepts and tools of statistical physics. PHYS 616, or equivalent taken at some other institution, is prerequisite to enroll in this course.
Quantum statistical mechanics governs most of condensed matter physics (metals, semiconductors, glasses, ...) and parts of molecular physics and astrophysics (white dwarfs, neutron stars). It spawned the origin of quantum mechanics (Planck's theory of the black-body radiation spectrum) and provides framework for our understanding of other exotic quantum phenomena (Bose-Einstein condensation, superfluids, and superconductors).
The course will focus on practical introduction to QSM via examples and hands-on tutorials using computer algebra system such as Mathematica. The examples will be drawn from the application of QSM to condensed matter physics, phase transitions in magnetic systems, astrophysics, and plasma physics, as are the areas of relevance to research in DPA.
Main Course Topics:
Second quantization formalism for bosons and fermions.
Applications of second quantization: Hartree-Fock method, magnons, superconductivity and superfluidity.
Time-dependent perturbation theory: Dyson vs. Magnus expansions.
Floquet theory of periodically driven time-dependent quantum systems.
Quantization of the electromagnetic field.
Nonclassical light.
Light-matter interaction.
Dissipative quantum mechanics with application to qubits.
Relativistic quantum mechanics.
News
Fall 2021 course starts on August 31 at 3:30PM in Sharp Lab 118.
Lecture in Progress
LECTURE 1: Second quantization formalism for harmonic oscillator
Quick Links
The course utilizes hands-on Computer Labs based on:
QuSpin Python package for numerical calculations (exact diagonalization and quantum dynamics) of arbitrary boson, fermion and spin many-body systems,
QuTiP Python package for numerical calculations of time evolution of open quantum systems, such as qubits in dissipative environment,
It also offers students Research-Project Based Learning track where a scientific paper can be completed by the end of the semester as exemplified by:
U. Bajpai, A. Suresh, and B. K. Nikolić, Quantum many-body states and Green functions of nonequilibrium electron-magnon systems: Localized spin operators vs. their mapping to Holstein-Primakoff bosons, Phys. Rev. B 104, 184425 (2021). [PDF]
P. Mondal, A. Suresh, and B. K. Nikolić, When can localized spins interacting with conduction electrons in ferro- or antiferromagnets be described classically via the Landau-Lifshitz equation: Transition from quantum many-body entangled to quantum-classical nonequilibrium states, Phys. Rev. B 104, 214401 (2021). [PDF]
Course Motto
In teaching, writing, and research, there is no greater clarifier than a well-chosen example.
Formalism should not be introduced for its own sake, but only when it is needed for some particular problem.
Physics comes in two parts: the precise mathematical formulation of the laws, and the conceptual interpretation of the mathematics. However, if words of conceptual interpretation actually convey the wrong meaning of the mathematics, they must be replaced by more accurate words. (W. J. Mullin)
