Oscillator potential for the four-dimensional Hall effect

We suggest the exactly solvable model of oscillator on the four-dimensional sphere interacting with the SU(2) Yang monopole. We show, that the properties of the model essentially depend on the monopole charge.Comment: 4 page

Privacy in the Age of Autonomous Vehicles

To prepare for the age of the intelligent, highly connected, and autonomous vehicle, a new approach to concepts of granting consent, managing privacy, and dealing with the need to interact quickly and meaningfully is needed. Additionally, in an environment where personal data is rapidly shared with a multitude of independent parties, there exists a need to reduce the information asymmetry that currently exists between the user and data collecting entities. This Article rethinks the traditional notice and consent model in the context of real-time communication between vehicles or vehicles and infrastructure or vehicles and other surroundings and proposes a re-engineering of current privacy concepts to prepare for a rapidly approaching digital future. In this future, multiple independent actors such as vehicles or other machines may seek personal information at a rate that makes the traditional informed consent model untenable. This Article proposes a two-step approach: As an attempt to meet and balance user needs for a seamless experience while preserving their rights to privacy, the first step is a less static consent paradigm able to better support personal data in systems which use machine based real-time communication and automation. In addition, the article proposes a radical re-thinking of the current privacy protection system by sharing the vision of “Privacy as a Service” as a second step, which is an independently managed method of granular technical privacy control that can better protect individual privacy while at the same time facilitating high-frequency communication in a machine-to-machine environment

Quantum Hall Effect on the Flag Manifold F_2

The Landau problem on the flag manifold ${\bf F}_2 = SU(3)/U(1)\times U(1)$ is analyzed from an algebraic point of view. The involved magnetic background is induced by two U(1) abelian connections. In quantizing the theory, we show that the wavefunctions, of a non-relativistic particle living on ${\bf F}_2$, are the SU(3) Wigner ${\cal D}$-functions satisfying two constraints. Using the ${\bf F}_2$ algebraic and geometrical structures, we derive the Landau Hamiltonian as well as its energy levels. The Lowest Landau level (LLL) wavefunctions coincide with the coherent states for the mixed SU(3) representations. We discuss the quantum Hall effect for a filling factor $\nu =1$. where the obtained particle density is constant and finite for a strong magnetic field. In this limit, we also show that the system behaves like an incompressible fluid. We study the semi-classical properties of the system confined in LLL. These will be used to discuss the edge excitations and construct the corresponding Wess-Zumino-Witten action.Comment: 23 pages, two sections and references added, misprints corrected, version to appear in IJMP

Theory of Four-dimensional Fractional Quantum Hall States

We propose a pseudo-potential Hamiltonian for the Zhang-Hu's generalized fractional quantum Hall states to be the exact and unique ground states. Analogously to Laughlin's quasi-hole (quasi-particle), the excitations in the generalized fractional quantum Hall states are extended objects. They are vortex-like excitations with fractional charges $+(-)1/m^3$ in the total configuration space CP$^3$. The density correlation function of the Zhang-Hu states indicates that they are incompressible liquid.Comment: 4 page

Casimir effect between moving branes

We consider a supersymmetric model with a single matter supermultiplet in a five-dimensional space-time with orbifold compactification along the fifth dimension. The boundary conditions on the two orbifold planes are chosen in such a way that supersymmetry remains unbroken on the boundaries. We calculate the vacuum energy-momentum tensor in a configuration in which the boundary branes are moving with constant velocity. The results show that the contribution from fermions cancels that of bosons only in the static limit, but in general a velocity-dependent Casimir energy arises between the branes. We relate this effect to the particle production due to the branes motion and finally we discuss some cosmological consequences.Comment: 14 pages, LaTeX. Final version with new references included, to be published in Nucl. Phys.

Quantum Oscillator on \DC P^n in a constant magnetic field

We construct the quantum oscillator interacting with a constant magnetic field on complex projective spaces \DC P^N, as well as on their non-compact counterparts, i. e. the $N-$dimensional Lobachewski spaces ${\cal L}_N$. We find the spectrum of this system and the complete basis of wavefunctions. Surprisingly, the inclusion of a magnetic field does not yield any qualitative change in the energy spectrum. For $N>1$ the magnetic field does not break the superintegrability of the system, whereas for N=1 it preserves the exact solvability of the system. We extend this results to the cones constructed over \DC P^N and ${\cal L}_N$, and perform the (Kustaanheimo-Stiefel) transformation of these systems to the three-dimensional Coulomb-like systems.Comment: 9 pages, 1 figur

Essays on Trade and Imperfectly Competitive Markets

This dissertation is a collection of three essays on markets with imperfect competition, with implications for international economics. The first essay presents an analytic solution framework applicable to a wide variety of general equilibrium international trade models, including those of Krugman (1980), Eaton and Kortum (2002), Anderson and van Wincoop (2003), and Melitz (2003), in multi-location cases. For asymptotically power-law trade costs and in the large-space limit, it is shown that there are parameter thresholds where the qualitative behavior of the model economy changes. In the case of the Krugman (1980) model, the relevant parameter is closely related to the elasticity of substitution between different varieties of goods. The geographic reach of economic shocks changes fundamentally when the elasticity crosses a critical threshold: below this point shocks are felt even at long distances, while above it they remain local. The value of the threshold depends on the approximate dimensionality of the spatial configuration. This work bridges the gap between empirical work on international and intranational trade, which frequently uses data sets involving large numbers of locations, and the theoretical literature, which has analytically examined solutions to the relevant models with realistic trade costs only for the case of very few locations. The second essay, coauthored with Glen Weyl, extends the incidence-based framework for the analysis of perfectly competitive markets to imperfect competition. We show how, just as under perfect competition, a wide range of comparative statics and policy analyses turn on simple properties of incidence, particularly the rate at which unit taxes are passed through to consumer prices. We derive local and global incidence properties, the division of surplus among deadweight loss, consumer surplus and profits and show how these are linked to one another under a range of imperfectly competitive environments. We then show how incidence functions as a simplifying analytic and pedagogic device, an empirical sufficient statistic and a key structural parameter in both classic and recently popular topics in industrial economics including platforms, concession auctions, mergers, entry, price discrimination, product design, supply chains and advertising. The third essay, coauthored with Gita Gopinath and Oleg Itskhoki, studies pricing of durable goods by producers with market power. The durable nature of these products makes their pricing differ from that of nondurables, since consumer demand depends not only on prices today but also on their expectation of future prices. When firms cannot commit to future prices, pass-through of cost shocks into prices is incomplete and the adjustment is gradual. This is the case even when prices are fully flexible and in environments where non-durable pricing would generate complete pass-through. Prices are also sensitive to demand shocks and mark-ups are pro-cyclical, in contrast to the case of cost shocks when mark-ups are countercyclical. We present these results for the case of a monopolist, for oligopolistic competition and for monopolistic competition.Economic