Quantum Transport and Integrability of the Anderson Model for a Quantum Dot with Multiple Leads

We show that an Anderson Hamiltonian describing a quantum dot connected to multiple leads is integrable. A general expression for the non-linear conductance is obtained by combining the Bethe ansatz exact solution with Landauer-B\"uttiker theory. In the Kondo regime, a closed form expression is given for the matrix conductance at zero temperature and when all the leads are close to the symmetric point. A bias-induced splitting of the Kondo resonance is possible for three or more leads. Specifically, for $N$ leads, with each at a different chemical potential, there can be $N-1$ Kondo peaks in the conductance.Comment: 5 pages, 2 figure

Exact solution at integrable coupling of a model for the Josephson effect between small metallic grains

A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Further, a connection with perturbed conformal field theory is made.Comment: 12 pages, latex, no figure

Data-driven Methodologies and Applications in Urban Mobility

The world is urbanizing at an unprecedented rate where urbanization goes from 39% in 1980 to 58% in 2019 (World Bank, 2019). This poses more and more transportation demand and pressure on the already at or over-capacity old transport infrastructure, especially in urban areas. Along the same timeline, more data generated as a byproduct of daily activity are being collected via the advancement of the internet of things, and computers are getting more and more powerful. These are shown by the statistics such as 90% of the world’s data is generated within the last two years and IBM’s computer is now processing at the speed of 120,000 GPS points per second. Thus, this dissertation discusses the challenges and opportunities arising from the growing demand for urban mobility, particularly in cities with outdated infrastructure, and how to capitalize on the unprecedented growth in data in solving these problems by ways of data-driven transportation-specific methodologies. The dissertation identifies three primary challenges and/or opportunities, which are (1) optimally locating dynamic wireless charging to promote the adoption of electric vehicles, (2) predicting dynamic traffic state using an enormously large dataset of taxi trips, and (3) improving the ride-hailing system with carpooling, smart dispatching, and preemptive repositioning. The dissertation presents potential solutions/methodologies that have become available only recently thanks to the extraordinary growth of data and computers with explosive power, and these methodologies are (1) bi-level optimization planning frameworks for locating dynamic wireless charging facilities, (2) Traffic Graph Convolutional Network for dynamic urban traffic state estimation, and (3) Graph Matching and Reinforcement Learning for the operation and management of mixed autonomous electric taxi fleets. These methodologies are then carefully calibrated, methodically scrutinized under various performance metrics and procedures, and validated with previous research and ground truth data, which is gathered directly from the real world. In order to bridge the gap between scientific discoveries and practical applications, the three methodologies are applied to the case study of (1) Montgomery County, MD, (2) the City of New York, and (3) the City of Chicago and from which, real-world implementation are suggested. This dissertation’s contribution via the provided methodologies, along with the continual increase in data, have the potential to significantly benefit urban mobility and work toward a sustainable transportation system

Exact results for a tunnel-coupled pair of trapped Bose-Einstein condensates

A model describing coherent quantum tunneling between two trapped Bose-Einstein condensates is shown to admit an exact solution. The spectrum is obtained by the algebraic Bethe ansatz. An asymptotic analysis of the Bethe ansatz equations leads us to explicit expressions for the energies of the ground and first excited states in the limit of {\it weak} tunneling and all energies for {\it strong} tunneling. The results are used to extract the asymptotic limits of the quantum fluctuations of the boson number difference between the two Bose-Einstein condensates and to characterize the degree of coherence in the system.Comment: 5 pages, RevTex, No figure

Valence Bond Entanglement and Fluctuations in Random Singlet Phases

The ground state of the uniform antiferromagnetic spin-1/2 Heisenberg chain can be viewed as a strongly fluctuating liquid of valence bonds, while in disordered chains these bonds lock into random singlet states on long length scales. We show that this phenomenon can be studied numerically, even in the case of weak disorder, by calculating the mean value of the number of valence bonds leaving a block of $L$ contiguous spins (the valence-bond entanglement entropy) as well as the fluctuations in this number. These fluctuations show a clear crossover from a small $L$ regime, in which they behave similar to those of the uniform model, to a large $L$ regime in which they saturate in a way consistent with the formation of a random singlet state on long length scales. A scaling analysis of these fluctuations is used to study the dependence on disorder strength of the length scale characterizing the crossover between these two regimes. Results are obtained for a class of models which include, in addition to the spin-1/2 Heisenberg chain, the uniform and disordered critical 1D transverse-field Ising model and chains of interacting non-Abelian anyons.Comment: 8 pages, 6 figure

The first 40 million years of circumstellar disk evolution: the signature of terrestrial planet formation

We characterize the first 40 Myr of evolution of circumstellar disks through a unified study of the infrared properties of members of young clusters and associations with ages from 2 Myr up to ~ 40 Myr: NGC 1333, NGC 1960, NGC 2232, NGC 2244, NGC 2362, NGC 2547, IC 348, IC 2395, IC 4665, Chamaeleon I, Orion OB1a and OB1b, Taurus, the \b{eta} Pictoris Moving Group, \r{ho} Ophiuchi, and the associations of Argus, Carina, Columba, Scorpius-Centaurus, and Tucana-Horologium. Our work features: 1.) a filtering technique to flag noisy backgrounds, 2.) a method based on the probability distribution of deflections, P(D), to obtain statistically valid photometry for faint sources, and 3.) use of the evolutionary trend of transitional disks to constrain the overall behavior of bright disks. We find that the fraction of disks three or more times brighter than the stellar photospheres at 24 {\mu}m decays relatively slowly initially and then much more rapidly by ~ 10 Myr. However, there is a continuing component until ~ 35 Myr, probably due primarily to massive clouds of debris generated in giant impacts during the oligarchic/chaotic growth phases of terrestrial planets. If the contribution from primordial disks is excluded, the evolution of the incidence of these oligarchic/chaotic debris disks can be described empirically by a log-normal function with the peak at 12 - 20 Myr, including ~ 13 % of the original population, and with a post-peak mean duration of 10 - 20 Myr.Comment: accepted for publication, the Astrophysical Journal (2017

Dynamics of glass phases in the two-dimensional gauge glass model

Large-scale simulations have been performed on the current-driven two-dimensional XY gauge glass model with resistively-shunted-junction dynamics. It is observed that the linear resistivity at low temperatures tends to zero, providing strong evidence of glass transition at finite temperature. Dynamic scaling analysis demonstrates that perfect collapses of current-voltage data can be achieved with the glass transition temperature $T_{g}=0.22$, the correlation length critical exponent $\nu =1.8$, and the dynamic critical exponent $z=2.0$. A genuine continuous depinning transition is found at zero temperature. For creeping at low temperatures, critical exponents are evaluated and a non-Arrhenius creep motion is observed in the glass phase.Comment: 10 pages, 6 figure