METHODS OF COMPUTATIONAL PHYSICS (Spring 2023)

Course Number: Phys 516
Class Number: 50614R
Instructor: Aiichiro Nakano; office: VHE 610; phone: (213) 821-2657; email: anakano@usc.edu
TA: Ghazaleh Ostovar; email: ostovar@usc.edu
Lecture: 9:00-9:50 M W F, KAP 145
Office Hour: 16:00-17:20 F, VHE 610
Blackboard: https://blackboard.usc.edu
Class homepage: https://aiichironakano.github.io/phys516.html
Textbooks:
T. Pang, "An Introduction to Computational Physics, 2nd Ed." (Cambridge Univ. Press, 2010)--sample C, Fortran 77, and Fortran 90 programs available on line.
W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, "Numerical Recipes, 3rd Ed." (Cambridge Univ. Press, 2007)--available online (C, Fortran 77, and Fortran 90).
R. Li and A. Nakano, Simulation with Python (APress, 2022)--codes.

Prerequisites: Basic knowledge of calculus and undergraduate physics; familiarity with a programming language such as C or Fortran -- A nice introduction to computing: (1) Y. Patt and S. Patel, Introduction to Computing Systems: From Bits and Gates to C and beyond, (2) T. Hey and G. Papay, The Computing Universe; Software skills for computational physicists: A. Scopatz and K. D. Huff, Effective Computation in Physics, USC students have free access through Safari Online.

Course Description

Students will learn basic elements of computational methods and acquire hands-on experience in their practical use in the context of computer simulations to solve physics problems. For details, please see course information sheet.

Molecular dynamics simulation of the oxidation of an aluminum nanoparticle.

Announcements

• 1/9 (M): Class begins.
• 1/13 (F): Physics happy hour at 3 pm in the ACB courtyard.
• 1/13 (F): Assignment 1 discussion at office hour (4:30 pm in VHE 610).
• 1/16 (M): MLK Birthday--no class.
• 1/18 (W): Please note that the office hour has been extended: 4:00-5:20 pm on Fridays.
• 1/18 (W): Assignment 1 due at 11:59 pm.
• 1/20 (F): Assignment 2, part 1 discussion at office hour (4:00 pm in VHE 610).
• 1/20 (F): USC Center for Advanced Computing Research (CARC) workshop on "Scientific computing: overview of an HPC cluster and essential Linux commands" at 1 pm; register here.
• 1/26 (Th): Weekly CARC workshops begin: CP2K quantum molecular dynamics simulation taught by Dr. Marco Olguin (4-6 pm on Thursdays); register here.
• 1/27 (F): Assignment 2, part 2 discussion at office hour.
• 1/27 (F): Assignment 2 due at 11:59 pm.
• 2/3 (F): Please see Berkeley seminar series on Quantum computing for high energy physics.
• 2/3 (F): Physics happy hour at 3 pm in the ACB courtyard.
• 2/3 (F): Assignment 3 discussion at office hour.
• 2/6 (M): Assignment 3 due at 11:59 pm.
• 2/6 (M), 8 (W), 10 (F): Class will meet remotely due to my family's COVID-19 positive case; please use the Zoom link on Blackboard.
• 2/10 (F): Want to see Lagrangian formulation of molecular dynamics (MD)? See: (1) Extended-Lagrangian charge-equilibration MD; and (2) Path-integral formulation of quantum mechanics (see derivation).
• 2/10 (F): No office hour, but enjoy fun get-together.
• 2/17 (F): Assignment 4 discussion at office hour.
• 2/20 (M): President's Day--no class.
• 2/22 (W): Assignment 4 due at 11:59 pm.
• 2/24 (F): No office hour.
• 3/1 (W): Assignment 5 discussion at special office hour at 5 pm.
• 3/3 (W): Seminar on Understanding the role of "rattling" guest atoms on the thermal properties of intermetallic clathrates by Prof. Matt Beaman (CalPoly San Luis Obispo) at 2 pm in SSL 202.
• 3/3 (F): Special office hour to meet with Prof. Matt Beekman.
• 3/3 (F): Assignment 5 due at 11:59 pm.
• 3/6 (M): Remote-only class on Zoom due to American Physical Society March meeting.
• 3/13 (M)-3/17 (F): Spring Recess--no class.
• 3/22 (W): Assignment 6 discussion at special office hour at 4 pm.
• 3/24 (F): Assignment 6 due at 11:59 pm -- extended, new due date is Mar. 27 (M).
• 3/27 (M): Assignment 6 due at 11:59 pm.
• 3/27 (M)-3/31 (F): UCLA-IPAM workshop on Increasing the Length, Time, and Accuracy of Materials Modeling Using Exascale Computing in the New Mathematics for the Exascale: Applications to Materials Science program.
• 3/31 (F): No office hour.
• 4/7 (F): Assignment 7, part 1 discussion at office hour.
• 4/14 (F): Physics happy hour at 3 pm in the ACB courtyard.
• 4/14 (F): Assignment 7, part 2 discussion at office hour.
• 4/14 (F): Please discuss your final-project topic with me by this date.
• 4/17 (M): Please create your account at IBM Quantum, which will be used in quantum-computing hands-on classes, and familiarize yourself with the Quantum Composer and Quantum Lab.
• 4/21 (F): See a UCLA-IPAM program on Mathematical and Computational Challenges in Quantum Computing.
• 4/21 (F): Assignment 7, part 3 discussion at office hour.
• 4/21 (F): Assignment 7 due at 11:59 pm.
• 4/26 (W), 4/28 (F): Final-project presentations.
• 5/10 (W): Final-project report due.

Class Schedule

• 1/9 (M): Course information & logistics; Math quiz
• 1/11 (W): Introduction
• 1/13 (F): Assignment 1 discussion -- computing and math preparation
• 1/18 (W): Monte Carlo (MC) basics: notes and slides
• 1/20 (F): Assignment 2, part 1 discussion -- hands-on MC
• 1/23 (M): Assignment 2, part 2 discussion -- nonuniform random number generation by coordinate transformation
• 1/25 (W): Metropolis MC algorithm
• 1/27 (F): MC simulation of spins: notes and slides
• 1/30 (M): Assignment 3 discussion
• 2/1 (W): Metropolis MC simulation Q&A
• 2/3 (F): Fluctuation-dissipation theorem; unitary time propagation; linear response; cf. advanced Monte Carlo algorithms
• 2/6 (M): Numerical integration and Gaussian quadratures; recurisive formula for Legendre polynomials; Numerical Recipes, Sec. 4.5; fast multipole method
• 2/8 (W): Molecular dynamics (MD) basics; slides; Michael Levitt's Nobel lecture in 2013
• 2/10 (F): MD technical details; Lennard-Jones Q&A
• 2/13 (M): Assignment 4 (MD), part I discussion -- Liouville's theorem
• 2/15 (W): Assignment 4 (MD), part II discussion -- velocity autocorrelation; nucleation theory
• 2/17 (F): Assignment 4 (MD), part III discussion -- split-operator formalism; MD simulation Q&A
• 2/22 (W): Quantum dynamics (QD) basics: split-operator and spectral methods; slides
• 2/24 (F): Assignment 5 (QD), part I discussion -- split-operator method; lecture on spectral method
• 2/27 (M): Assignment 5 (QD), part II discussion -- spectral-method programming
• 3/1 (W): Assignment 5 (QD), part III discussion -- quantum tunneling
• 3/3 (F): Spectral method and fast Fourier transform (FFT); note on unitary time-propagators; quantum Fourier transform
• 3/6 (M): Iterative energy minimization for quantum molecular dynamics; Numerical Recipes, Sec. 10.6 on the conjugate-gradient method; see CSCI 699: Extreme-scale Quantum Simulations
• 3/8 (W): Tight binding (TB) model of electronic structures; slides
• 3/10 (F): Computing TB Hamiltonian elements by projection; assignment 6 discussion; energy band
• 3/20 (M): Newton method for root finding; slides
• 3/22 (W): O(N) Fermi-operator expansions; eigensystems: note and slides
• 3/24 (F): Singular value decomposition (SVD) and density matrix (notes on SVD and polar decomposition; slides; Numerical Recipes, Sec. 2.6); Lanczos method for eigensystems (slides and supplementary notes); Cholesky decomposition (notes and Numerical Recipes, Sec. 2.9)
• 3/27 (M): No regular class; please watch a video recording of the lecture, Quantum materials dynamics at the nexus of exascale computing, artificial intelligence, and quantum computing , once posted
• 3/29 (W): Final project discussion; see notes on final projects and Whitesides' group: writing a paper, G. M. Whitesides, Adv. Mater. 16, 1375 (2004)
• 3/31 (F): Monte Carlo simulation of stochastic processes; slides
• 4/3 (M): Assignment 7, part I (stochastic simulation) discussion
• 4/5 (W): Option price; Viterbi algorithm
• 4/7 (F): Quantum Monte Carlo simulation; slides
• 4/10 (M): Assignment 7, part II (QMC) discussion
• 4/12 (W): Kinetic Monte Carlo (KMC) simulation; motivating slides
• 4/14 (F): KMC algorithm and electron-transfer simulation
• 4/17 (M): Assignment 7, part III (KMC) discussion
• 4/19 (W): KMC theory and transition state theory; suppl. 1: Liouville equation; suppl. 2: master equation; suppl. 3: transition state theory; suppl. 4: kinetic Monte Carlo simulation
• 4/21 (F): Quantum dynamics simulations on quantum computers: slides; qubits and quantum circuits
• 4/24 (M): Transverse-field Ising model: lecture note; Qiskit code; Phys 516 summary (where to go from here)
• 4/26 (W): Final-project presentation, part I; see all-star roster
• 4/28 (F): Final-project presentation, part II