Topological degeneracy and pairing in a one-dimensional gas of spinless Fermions

We revisit the low energy physics of one dimensional spinless fermion liquids, showing that with sufficiently strong interactions the conventional Luttinger liquid can give way to a strong pairing phase. While the density fluctuations in both phases are described by a gapless Luttinger liquid, single fermion excitations are gapped only in the strong pairing phase. Smooth spatial Interfaces between the two phases lead to topological degeneracies in the ground state and low energy phonon spectrum. Using a concrete microscopic model, with both single particle and pair hopping, we show that the strong pairing state is established through emergence of a new low energy fermionic mode. We characterize the two phases with numerical calculations using the density matrix renormalization group. In particular we find enhancement of the central charge from $c=1$ in the two Luttinger liquid phases to $c=3/2$ at the critical point, which gives direct evidence for an emergent critical Majorana mode. Finally, we confirm the existence of topological degeneracies in the low energy phonon spectrum, associated with spatial interfaces between the two phases

Russian A2/AD in the Eastern Mediterranean A Growing Risk

Much has been written about the challenges posed by the Chinese adoption of what the U.S. military calls “A2/AD” (antiaccess/area-denial) in the western Pacific. Accordingly, the Pacific remains a key focus area for the U.S. Navy and Air Force, and more recently the Army, with the Navy promising to put 60 percent of its forces in that theater as part of the “Pacific pivot.” Yet as focus remains on the Pacific, the rest of the world is not standing still. This is exemplified in the eastern Mediterranean, where the Russians have begun laying the seeds to create an A2/AD zone in the region against the United States and its allies. If fully realized, an A2/AD envelope would put Western access to the Suez Canal, the Black Sea, and the resource-rich eastern Mediterranean at the mercy of an increasingly aggressive Russian regime

CONTRACTING IN THE PHARMACEUTICAL INDUSTRY: PREDICTING PAYMENTS IN STRATEGIC ALLIANCES

ABSTRACT This paper empirically analyzes how circumstances affect the creation of strategic alliances in the pharmaceutical industry, and the form these alliances take. The models introduced in this paper use the cost of capital and monitoring costs to predict the timing of the deal, which in turn allows the prediction of the deal type. The deal type is then used to predict payment types used in the deal. Deals are characterized by five payment types; upfront, royalty, milestone, equity, and research payments. Deals are also characterized by one of five deal types; co-development, license, acquisition, outsource, and asset purchase. Each of these is a response to a specific contracting problem such as cost of acquiring capital and asymmetric information. The payment types used in pharmaceutical alliances are chosen to efficiently produce monitoring or purchase assets in the face of asymmetric information and to maximize firm profits

Fate of the one-dimensional Ising quantum critical point coupled to a gapless boson

The problem of a quantum Ising degree of freedom coupled to a gapless bosonic mode appears naturally in many one dimensional systems, yet surprisingly little is known how such a coupling affects the Ising quantum critical point. We investigate the fate of the critical point in a regime, where the weak coupling renormalization group (RG) indicates a flow toward strong coupling. Using a renormalization group analysis and numerical density matrix renormalization group (DMRG) calculations we show that, depending on the ratio of velocities of the gapless bosonic mode and the Ising critical fluctuations, the transition may remain continuous or become fluctuation-driven first order. The two regimes are separated by a tri-critical point of a novel type.Comment: 8 pages, 8 figures; published versio

Rule 10b-5 and Reasonable Reliance: Why Courts Should Abandon Focus on Non-Reliance Clauses

In a typical privately negotiated merger or acquisition, the parties involved will be engaged in months of negotiations prior to the closing of their deal. Over the course of such, many projections, agreements, documents, oral representations and warranties (hereinafter “information”) will undoubtedly be exchanged by both sides. In the final purchase agreement, a seller typically lists detailed representations and warranties about its business, and includes a proviso that the buyer is not relying on any other information. Inclusion of this “non-reliance clause” (hereinafter “NRC”) is intended to restrict a buyer’s ability to bring a fraud claim under Rule 10b-5