Rules, Standards, and the Internal Point of View

Large scale structure and cosmolog

Rules and similarity - a false dichotomy

Unless restricted to explicitly held, sharable beliefs that control and justify a person’s behavior, the notion of a rule has little value as an explanatory concept. Similarity-based processing is a general characteristic of the mind-world interface where internal processes (including explicitly represented rules) act on the external world. The distinction between rules and similarity is therefore misconceived

Exact relations for thermodynamics of heavy quarks

We derive finite-temperature sum rules for excesses in internal energy and in (volume-integrated) pressure arising due to presence of heavy quarks in SU(N) gluon plasma. In the limit of zero temperature our formulae reduce to the Michael-Rothe sum rules. The excesses in energy and pressure of the gluon plasma are related to expectation values of certain gluon condensates, and, simultaneously, to the heavy quark potential. The sum rules lead to a known relation between the internal energy and the potential, and to a new expression for the excess in the pressure. The pressure appears in the free energy as a generalized force associated with variations of the spatial size of the heavy-quark system. We find that the excess in gluonic pressure around a heavy quarkonium is always negative. Finally, we derive an exact equation of state that provides a relationship between the gluonic energy and pressure of heavy quarks.Comment: 7 page

Crises and Tax

How can law best mitigate harm from crises like storms, epidemics, and financial meltdowns? This Article uses the law and economics framework of property rules and liability rules to analyze crisis responses across multiple areas of law, focusing particularly on the ways the Internal Revenue Service (IRS) battled the 2008–09 financial crisis. Remarkably, the IRS’s responses to that crisis cost more than Congress’s higher-profile bank bailouts. Despite their costs, many of the IRS’s responses were underinclusive, causing preventable layoffs and foreclosures. This Article explains these failures and demonstrates that the optimal response to crises is to shift from harsh property rules to compensatory liability rules, temporarily. Arranging such a shift in advance further mitigates harm when crises arrive. This analysis also provides new insights for the broader literature on property rules and liability rules. For example, arranging in advance for temporary moves to liability rules during crises can avoid windfalls, allow speedier relief, and encourage flexible private contracts. These lessons have practical applications in areas as far afield as how constitutional law and patent law respond to epidemics

Alternative Dispute Resolution in Patent Controversies

Mr. Balmer relates how ADR allows attorneys to tailor rules to resolve disputes in light of, e.g., party relationships and internal dynamics. He notes that, for life to go on, having resolution is itself an important goal

Recursion Relations in pp-adic Mellin Space

In this work, we formulate a set of rules for writing down $p$-adic Mellin amplitudes at tree-level. The rules lead to closed-form expressions for Mellin amplitudes for arbitrary scalar bulk diagrams. The prescription is recursive in nature, with two different physical interpretations: one as a recursion on the number of internal lines in the diagram, and the other as reminiscent of on-shell BCFW recursion for flat-space amplitudes, especially when viewed in auxiliary momentum space. The prescriptions are proven in full generality, and their close connection with Feynman rules for real Mellin amplitudes is explained. We also show that the integrands in the Mellin-Barnes representation of both real and $p$-adic Mellin amplitudes, the so-called pre-amplitudes, can be constructed according to virtually identical rules, and that these pre-amplitudes themselves may be re-expressed as products of particular Mellin amplitudes with complexified conformal dimensions.Comment: 45 pages + appendices, several figure

Interface electronic states and boundary conditions for envelope functions

The envelope-function method with generalized boundary conditions is applied to the description of localized and resonant interface states. A complete set of phenomenological conditions which restrict the form of connection rules for envelope functions is derived using the Hermiticity and symmetry requirements. Empirical coefficients in the connection rules play role of material parameters which characterize an internal structure of every particular heterointerface. As an illustration we present the derivation of the most general connection rules for the one-band effective mass and 4-band Kane models. The conditions for the existence of Tamm-like localized interface states are established. It is shown that a nontrivial form of the connection rules can also result in the formation of resonant states. The most transparent manifestation of such states is the resonant tunneling through a single-barrier heterostructure.Comment: RevTeX4, 11 pages, 5 eps figures, submitted to Phys.Rev.

Firms’ Financial Choices and Thin Capitalization Rules under Corporate Tax Competition

Thin capitalization rules have become an important element in the corporate tax systems of developed countries. This paper sets up a model where national and multinational firms choose tax-efficient financial structures and countries compete for multinational firms through statutory tax rates and thin capitalization rules that limit the tax-deductibility of internal debt flows. In a symmetric tax competition equilibrium each country chooses inefficiently low tax rates and inefficiently lax thin capitalization rules. We show that a coordinated tightening of thin capitalization rules benefits both countries, even though it intensifies competition via tax rates. When countries differ in size, the smaller country not only chooses the lower tax rate but also the more lenient thin capitalization rule.thin capitalization, capital structure, tax competition

Quantum Energies of Interfaces

We present a method for computing the one-loop, renormalized quantum energies of symmetrical interfaces of arbitrary dimension and codimension using elementary scattering data. Internal consistency requires finite-energy sum rules relating phase shifts to bound state energies.Comment: 8 pages, 1 figure, minor changes, Phys. Rev. Lett., in prin