Dynamical Quantum Phase Transitions, Scrambling and Quantum Simulations of Many-Body Neutrino Systems

Abstract

This dissertation covers three main topics: dynamical quantum phase transitions, the far-from-equilibrium phenomenon of quantum information scrambling, and quantum simulations on both trapped ion and superconducting qubit devices, all in the context of many-body neutrino systems.For the dynamical quantum phase transitions study in the first chapter, the analysis of Loschmidt echos within dense neutrino systems yields insight into a system's initial state requirements needed to achieve a dynamical quantum phase transition (DQPT). Focus is paid to Loschmidt echo crossing distributions, which confirm the presence of two distinct classes of DQPTs in two-flavor neutrino systems. Further analysis reveals a nontrivial dependence on the coupling angle distributions chosen for the two-body interaction term. The results establish two distinct classes of DQPT's in two flavor neutrino systems, verfied via robust statistics. Scrambling as diagnosed by the Out-of-Time-Ordered Correlator (OTOC) has been demonstrated in the Sachdev-Ye-Kitaev model, Transverse Field Ising Model, the transverse axial next nearest neighbor Ising model among many others. However they have yet to be characterized in many-body neutrino systems. Such systems are often modeled as all-to-all connected random-Heisenberg spin chains. In the second chapter, this work demonstrates numerical evidence for scrambling's occurrence in two-flavor many-body neutrino systems. The results demonstrate dynamical quantum phase transitions (DQPTs) potential role as a witness for scrambling in many- body neutrino systems. We see what appears to be discreet modes of scrambling times corresponding to a system's first DQPT occurrence. We attempt to formulate an analytical argument resting on the concept of weak measurement schemes to explain how the DQPTs can serve as a witness for OTOCs in families of random-coupled two-flavor many-body neutrino systems in the forward scattering limit. In the last chapter, quantum circuits for three flavor many body neutrino systems are constructed, for both qubit and qutrit devices. The qubit-based circuits are run on super- conducting qubit devices with heavy-hex connectivity and trapped ion devices with all-to-all connectivity, demonstrating the one of the first quantum simulations of three flavor neutrino systems on two level devices. This work demonstrates a proof of principle for simulating three-flavor neutrino systems on two-level devices, the performance of the qubit circuits on each device, and calculation of physical observables off of the device.