Yin, XiSandor, Joshua2025-09-1820252025-05-082025Sandor, Joshua. 2025. The Discrete Bootstrap for Quantum Thermodynamics. Doctoral Dissertation, Harvard University Graduate School of Arts and Sciences.32002593https://dash.harvard.edu/handle/1/42719471A novel bootstrap method is exemplified by lattice theories and quantum mechanics. Positivity of expectation values combined with sets of non-trivial constraint equations and semidefinite optimization rigorously and precisely bound correlation functions. Starting with the example of a one-dimensional integral, the technique is built upon to extract limit cycles in a two-dimensional classical dynamical system and spin correlation functions in the Statistical Ising Model. Further positivity constraints and simplifications arising in a large rank limit are implemented to bound the energy expectation value as a function of temperature in Matrix Quantum Mechanics. Along the way, the S-matrix of Chern-Simons-matter theory is computed as an example of computational simplification at large gauge group rank.application/pdfenBootstrapQuantumThermodynamicsTheoretical physicsQuantum physicsThermodynamicsThesis or Dissertation2025-09-180000-0002-8672-9091