An assortment of three stories

Microscopic origin of thermodynamic entropy in isolated systems: The quantum entropy is usually defined using von Neumann's formula, which measures lack of information and vanishes for pure states. In contrast, we obtain a formula for the entropy of a pure state as it is measured from thermodynamic experiments, solely from the self-entanglement of the wave function, and find strong numerical evidence that the two are in agreement for nonintegrable systems, both for energy eigenstates and for states that are obtained at long times under the evolution of more general initial conditions. This is an extension of Boltzmann's hypothesis for classical systems, relating microscopic motion to thermodynamics [1].

Fine structures in the spectrum of the open-boundary Heisenberg XXZ chain at large anisotropies: At large anisotropies, the spectrum of the Heisenberg XXZ spin chain separates into `bands' with energies largely determined by the number of domain walls. The band structure is richer with open boundary conditions: there are more bands and the bands develop intricate fine structures. We characterize and explain these structures and substructures in the open-boundary chain. The fine structures are explained using degenerate perturbation theory. We also present some dynamical consequences of these sub-band structures, through explicit time evolution of the wavefunction from initial states motivated by the fine structure analysis [2].

Hysteresis in a fully-connected XY spin glass: We study the avalanches along the magnetization hysteresis curve of a long-range interacting spinglass with continuous XY symmetry. We numerically identify sudden jumps of magnetization in the T = 0 configurations of spins as the external field is increased. Jumps are initiated by the softest mode of an inverse susceptibility matrix, that becomes unstable and leads to an avalanche. We analyze the statistics of these events, and nd that the density of jumps is scale-free, similarly as in the Ising spin-glass (Sherrington-Kirkpatrick) that were studied previously, however with the absence of a clear powerlaw, thus displaying a novel type of `self-organized criticality' [3].

References:

1. Deutsch, J. M., Haibin Li, and Auditya Sharma, ``Microscopic origin of thermodynamic entropy in isolated systems.'' Physical Review E 87 (2013), 042135.

2. Auditya Sharma, and Masudul Haque, ``Fine structures in the spectrum of the open-boundary Heisenberg XXZ chain at large anisotropies.'' arXiv preprint arXiv:1309.1471 (2013).

3. Auditya Sharma, Alexei Andreanov, and Markus uller. In preparation.