Logarithmic terms in entanglement entropies of 2D quantum critical points and Shannon entropies of spin chains

Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the "Shannon entropy" of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient $\pm 0.25$. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on replica or R\'enyi index resulting from flows to different boundary conditions at the entanglement cut.Comment: 4 pages and 4 page appendix, 4 figure

Fixed versus Flexible: Lessons from EMS Order Flow

This paper addresses the puzzle of regime-dependent volatility in foreign exchange. We extend the literature in two ways. First, our microstructural model provides a qualitatively new explanation for the puzzle. Second, we test implications of our model using Europe's recent shift to rigidly fixed rates (EMS to EMU). In the model, shocks to order flow induce volatility under flexible rates because they have portfolio-balance effects on price, whereas under fixed rates the same shocks do not have portfolio-balance effects. These effects arise in one regime and not the other because the elasticity of speculative demand for foreign exchange is (endogenously) regime-dependent: low elasticity under flexible rates magnifies portfolio-balance effects; under credibly fixed rates, elasticity of speculative demand is infinite, eliminating portfolio-balance effects. New data on FF/DM transactions show that order flow had persistent effects on the exchange rate before EMU parities were announced. After announcement, determination of the FF/DM rate was decoupled from order flow, as predicted by the model.

Optimal Estimation of Several Linear Parameters in the Presence of Lorentzian Thermal Noise

In a previous article we developed an approach to the optimal (minimum variance, unbiased) statistical estimation technique for the equilibrium displacement of a damped, harmonic oscillator in the presence of thermal noise. Here, we expand that work to include the optimal estimation of several linear parameters from a continuous time series. We show that working in the basis of the thermal driving force both simplifies the calculations and provides additional insight to why various approximate (not optimal) estimation techniques perform as they do. To illustrate this point, we compare the variance in the optimal estimator that we derive for thermal noise with those of two approximate methods which, like the optimal estimator, suppress the contribution to the variance that would come from the irrelevant, resonant motion of the oscillator. We discuss how these methods fare when the dominant noise process is either white displacement noise or noise with power spectral density that is inversely proportional to the frequency ($1/f$ noise). We also construct, in the basis of the driving force, an estimator that performs well for a mixture of white noise and thermal noise. To find the optimal multi-parameter estimators for thermal noise, we derive and illustrate a generalization of traditional matrix methods for parameter estimation that can accommodate continuous data. We discuss how this approach may help refine the design of experiments as they allow an exact, quantitative comparison of the precision of estimated parameters under various data acquisition and data analysis strategies.Comment: 16 pages, 10 figures. Accepted for publication in Classical and Quantum Gravit

Time-evolving a matrix product state with long-ranged interactions

We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions are necessary to simulate not just many physical interactions but also higher-dimensional problems with short-ranged interactions. Since our method overcomes the restriction to short-ranged Hamiltonians of most existing methods, it proves particularly useful for studying the dynamics of both power-law interacting one-dimensional systems, such as Coulombic and dipolar systems, and quasi two-dimensional systems, such as strips or cylinders. First, we benchmark the method by verifying a long-standing theoretical prediction for the dynamical correlation functions of the Haldane-Shastry model. Second, we simulate the time evolution of an expanding cloud of particles in the two-dimensional Bose-Hubbard model, a subject of several recent experiments.Comment: 5 pages + 3 pages appendices, 4 figure

Snake venom toxins, unlike smaller antagonists, appear to stabilize a resting state conformation of the nicotinic acetylcholine receptor

AbstractPrevious studies have shown that the pattern and degree of 3-(trifluoromethyl)-3-(m-[125I]iodophenyl)diazirine ([125I]TID) photoincorporation into the nicotinic acetylcholine receptor (nAChR) can be used as a sensitive measure of nAChR conformation. Upon desensitization by prolonged exposure to agonists, certain drugs and detergents, or reconstitution into desensitizing lipids, the levels of [125I]TID incorporation into the subunits of the nAChR are dramatically reduced. In this study, we characterized the effects of the snake venom proteins α-bungarotoxin and α-cobrotoxin, as well as the smaller antagonists tubocurarine and gallamine, on [125I]TID incorporation into the subunits of both partially-purified nAChR in native lipids, or affinity-purified nAChR reconstituted into different combinations of lipids. Unlike all other compounds previously tested, α-bungarotoxin and α-cobrotoxin reproducibly increased the level of [125I]TID incorporation into all four subunits of nAChR reconstituted into dioleoylphosphatidylcholine, dioleoylphosphatidic acid and cholesterol. Gallamine had little or no effect on [125I]TID incorporation at any concentration tested (0.1 μM—5 mM). Tubocurarine had no effect on [125I]TID incorporation at low concentrations, but at higher concentrations reduced the level of [125I]TID labeling. The snake venom proteins may shift the population of nAChR, which exists as a mixture of resting state and desensitized conformations, entirely to the resting state. However, the binding of the snake venom toxins does not appear sufficient to induce the resting state conformation in nAChR which have been desensitized by other means, such as solubilization in desensitizing detergents or reconstitution in desensitizing lipids

Environmental Governance by Contract: The Growing Role of Supply Chain Contracting

Corporate net zero climate commitments and environmental, social, and governance (ESG) policies have the potential to bypass barriers to international, national, and subnational government action on climate change and other environmental issues. This Article presents the results of a new empirical study that demonstrates the remarkably widespread use of environmental supply chain contracting requirements. The study finds that roughly 80% of the ten largest firms in seven global sectors include environmental requirements in supply chain contracting, a substantial increase over the 50% reported by a comparable study fifteen years ago. The Article concludes that the prevalence of environmental supply chain requirements, the types of contract requirements, and the motivations of the contracting parties signal new ways to fill important gaps in public governance

Recent Cases

Courts Split on the Necessity of Separate Authorization for a Covert Entry Under Title III of the Omnibus Crime Control and Safe Streets Act of 1968 Daniel Paul Smith Title III of the Omnibus Crime Control and Safe Streets Act of 1968,\u27 which regulates the use of electronic surveillance, was designed to protect the privacy of wire and oral communications, and to delineate on a uniform basis the circumstances and conditions under which the interception of wire and oral communications may be authorized. \u27 In general, communications may be intercepted only by law enforcement officers, who are engaged in the investigation of a certain type of crime, and who have obtained a court order based upon probable cause that authorizes the use of electronic surveillance. Although certain details of the particular interception must be specified in the court order, the statute does not expressly require that the judge who authorizes the use of electronic surveillance also authorize covert entries that may be required to place the electronic listening devices Until recently the federal courts apparently had assumed that an order authorizing the use of electronic surveillance implicitly authorized a surreptitious entry by law enforcement officials to install the necessary device. In United States v. Ford, however, the District of Columbia Circuit became the first federal court of appeals to reject this assumption, holding that absent express judicial authorization, a trespassory entry incident to the placement of an electronic listening device is an invasion of privacy that violates the fourth amendment. =============== ================= =========== Custodial Suspect\u27s Admissions After Assertion and Subsequent Waiver of Right to Counsel Are Not Per Se Excluded in Absence of Coercion R. Michael Moore The holding in this case carries the trend toward reinterpretation of Miranda to an undesirable extreme. Although the rejection of the per se rule will diminish the number of reversals of factually correct convictions, relegating the protection of the right to counsel to the same analysis employed in right to silence cases operates an injustice on criminal suspects. The request for an attorney should trigger greater protection because every effort should be made to insure that the suspect exercises his judgment intelligently. Despite the Supreme Court\u27s retrenchment from the Miranda assumption that all custodial interrogations are inherently coercive, coercion remains a problem, especially where a suspect is confused or unable to exercise his rights intelligently. Thus implementation of a strict waiver test is necessary to secure a suspect\u27s rights in the absence of the per se rule