TY - JOUR
TI - Topics in classical and quantum integrability
DO - https://doi.org/doi:10.7282/t3-y3j4-vp24
PY - 2019
AB - This Thesis is an amalgamation of research I conducted as a physics graduate student at Rutgers University. Each chapter stands independently of the others with its own introduction and set of references, though Chapters 4 and 5 treat the same subject and may be read in succession. The chapters are presented roughly in reverse chronological order, so that the first chapters are my most recent work.
The common threads of this research program are the statistical and dynamical properties of many body systems, both in and out of equilibrium. Save for Chapter 6, the works are strongly associated with physical models called integrable, whose Hamiltonians have a comparatively large number of conservation laws with respect to generic models. Using numerical and analytical techniques, we shall explore the effects of integrability on a diverse set of phenomena including far-from-equilibrium steady states in Chapter 2, heat conductivity in Chapter 3, and Hamiltonian level statistics in Chapters 4-5. We also characterize these phenomena for systems that are not quite integrable, but are in certain ways close to integrable.
The chapters in this Thesis are based on the following works:
J. A. Scaramazza, P. Smacchia, and E. A. Yuzbashyan, Consequences of integrability breaking in quench dynamics of pairing Hamiltonians, Accepted by Phys. Rev. B Jan. 2019.
J. L. Lebowitz and J. A. Scaramazza, Ballistic Transport in the classical Toda chain with harmonic pinning, arXiv:1801.07153 (2018).
A. Dhar, A. Kundu, J. L. Lebowitz and J. A. Scaramazza, Transport properties of the classical Toda chain: effect of a pinning potential, arXiv:1812.11770 (2018). Submitted to J. Stat. Phys. Jan. 2019.
E. A. Yuzbashyan, B. S. Shastry and J. A. Scaramazza, Rotationally invariant ensembles of integrable matrices, Phys. Rev. E 93, 052114 (2016).
J. A. Scaramazza, B. S. Shastry and E. A. Yuzbashyan, Integrable matrix theory: Level statistics, Phys. Rev. E 94, 032106 (2016).
J. L. Lebowitz and J. A. Scaramazza, A note on Lee-Yang zeros in the negative half-plane, J. Phys.: Condens. Matter 28, 414004 (2016).
KW - Condensed matter physics
KW - Physics and Astronomy
LA - English
ER -