Disorder driven transitions in non-equilibrium quantum systems

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.

Chemical Reaction Dynamics of the Liquid/Vapor Interface Studied by Mass Spectrometry

This thesis presents investigations of chemical reactions occurring at the liquid/vapor interface studied using novel sampling methodologies coupled with detection by mass spectrometry. Chapters 2 and 3 utilize the recently developed technique of field-induced droplet ionization mass spectrometry (FIDI-MS), in which the application of a strong electric field to a pendant microliter droplet results in the ejection of highly charged progeny droplets from the liquid surface. In Chapter 2, this method is employed to study the base-catalyzed dissociation of a surfactant molecule at the liquid/vapor interface upon uptake of ammonia from the gas phase. This process is observed to occur without significant modulation of the bulk solution pH, suggesting a transient increase in surface pH following the uptake of gaseous ammonia. Chapter 3 presents real-time studies of the oxidation of the model tropospheric organic compound glycolaldehyde by photodissociation of iron (III) oxalate complexes. The oxidation products of glycolaldehyde formed in this process are identified, and experiments in a deoxygenated environment identify the role of oxygen in the oxidation pathway and in the regeneration of iron (III) following photo-initiated reduction. Chapter 4 explores alternative methods for the study of heterogeneous reaction processes by mass spectrometric sampling from liquid surfaces. Bursting bubble ionization (BBI) and interfacial sampling with an acoustic transducer (ISAT) generate nanoliter droplets from a liquid surface that can be sampled via the atmospheric pressure interface of a mass spectrometer. Experiments on the oxidation of oleic acid by ozone using ISAT are also presented. Chapters 5 and 6 detail mechanistic studies and applications of free-radical-initiated peptide sequencing (FRIPS), a technique employing gas-phase free radical chemistry to the sequencing of peptides and proteins by mass spectrometry. Chapter 5 presents experimental and theoretical studies on the anomalous mechanism of dissociation observed in the presence of serine and threonine residues in peptides. Chapter 6 demonstrates the combination of FRIPS with ion mobility-mass spectrometry (IM-MS) for the separation of isomeric peptides.