Long Live the Lie Bill!

What successful defamation plaintiffs typically desire and doctrinally deserve is to have their reputations restored. Presently, however, a plaintiff who has established that she was defamed by the defendant is entitled only to an award of damages, which does nothing to restore reputation. This Note proposes that in addition to a damages award, courts-- if they are to take seriously their obligation to compensate the plaintiff-- should order the defendant to retract the defamatory statement. Contrary to the prevailing view, this Note argues that the proposed retraction order does not jeopardize the First Amendment guarantee of free expression

Dark matter as integration constant in Horava-Lifshitz gravity

In the non-relativistic theory of gravitation recently proposed by Horava, the Hamiltonian constraint is not a local equation satisfied at each spatial point but an equation integrated over a whole space. The global Hamiltonian constraint is less restrictive than its local version, and allows a richer set of solutions than in general relativity. We show that a component which behaves like pressureless dust emerges as an "integration constant" of dynamical equations and momentum constraint equations. Consequently, classical solutions to the infrared limit of Horava-Lifshitz gravity can mimic general relativity plus cold dark matter.Comment: 16 pages; (non-)conservation equation for "dark matter" added (v2); note added to comment on some recent preprints (v3); version accepted for publication in PRD (v4

Adiabatic quantum computation and quantum phase transitions

We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass gap becomes small, suggesting that the system passes near a quantum phase transition. Such a large scaling of entanglement suggests that the effective connectivity of the system diverges as the number of qubits goes to infinity and that this algorithm cannot be efficiently simulated by classical means. On the other hand, entanglement in Grover's algorithm is bounded by a constant.Comment: 5 pages, 4 figures, accepted for publication in PR

Bigravity and Lorentz-violating Massive Gravity

Bigravity is a natural arena where a non-linear theory of massive gravity can be formulated. If the interaction between the metrics $f$ and $g$ is non-derivative, spherically symmetric exact solutions can be found. At large distances from the origin, these are generically Lorentz-breaking bi-flat solutions (provided that the corresponding vacuum energies are adjusted appropriately). The spectrum of linearized perturbations around such backgrounds contains a massless as well as a massive graviton, with {\em two} physical polarizations each. There are no propagating vectors or scalars, and the theory is ghost free (as happens with certain massive gravities with explicit breaking of Lorentz invariance). At the linearized level, corrections to GR are proportional to the square of the graviton mass, and so there is no vDVZ discontinuity. Surprisingly, the solution of linear theory for a static spherically symmetric source does {\em not} agree with the linearization of any of the known exact solutions. The latter coincide with the standard Schwarzschild-(A)dS solutions of General Relativity, with no corrections at all. Another interesting class of solutions is obtained where $f$ and $g$ are proportional to each other. The case of bi-de Sitter solutions is analyzed in some detail.Comment: 25 pages. v3 Typos corrected, references added. v4 Introduction extende

Simple proof of equivalence between adiabatic quantum computation and the circuit model

We prove the equivalence between adiabatic quantum computation and quantum computation in the circuit model. An explicit adiabatic computation procedure is given that generates a ground state from which the answer can be extracted. The amount of time needed is evaluated by computing the gap. We show that the procedure is computationally efficient.Comment: 5 pages, 2 figures. v2: improved gap estimates and added some more detail

Spontaneous Lorentz Breaking and Massive Gravity

We study a theory where the presence of an extra spin-two field coupled to gravity gives rise to a phase with spontaneously broken Lorentz symmetry. In this phase gravity is massive, and the Weak Equivalence Principle is respected. The newtonian potentials are in general modified, but we identify an non-perturbative symmetry that protects them. The gravitational waves sector has a rich phenomenology: sources emit a combination of massless and massive gravitons that propagate with distinct velocities and also oscillate. Since their velocities differ from the speed of light, the time of flight difference between gravitons and photons from a common source could be measured.Comment: 4 page

An updated biostratigraphy for the late Aragonian and Vallesian of the Vallès-Penedès Basin (Catalonia)

The Vallès-Penedès Basin (Catalonia, Spain) is a classical area for the study of the Miocene land mammal faunas and includes one of the densest and most continuous records in Eurasia. Furthermore, it is the type area for the Vallesian European land mammal age. After decades of study a huge amount of bio- and magnetostratigraphic data have been collected, allowing an unprecedented dating accuracy. Here we provide an updated local biostratigraphy for the late Aragonian, Vallesian and Turolian of the Vallès-Penedès Basin. This new biostratigraphic scheme is almost exclusively based on fossil rodents, which are the most abundant and one of the best known mammal orders in the area. Our proposal represents a significant refinement compared to previous attempts and provides a formal diagnosis and description of each zone, as well as clear definition of boundaries and a reference locality and section. The chronology of zone boundaries and main bioevents is based on detailed magnetostratigraphic data. The defined biozones allow for the correlation of the sites without associated magnetostratigraphical data. Finally, the correlation of the Vallès-Penedès local zones with other detailed local biostratigraphies, such as those of the Calatayud-Montalbán and Teruel basins (east-central Spain) is discussed. The sequence and chronology of the main bioevents is roughly comparable, although the rodent succession and the structure of the assemblage show important differences between these areas

Universality of Entanglement and Quantum Computation Complexity

We study the universality of scaling of entanglement in Shor's factoring algorithm and in adiabatic quantum algorithms across a quantum phase transition for both the NP-complete Exact Cover problem as well as the Grover's problem. The analytic result for Shor's algorithm shows a linear scaling of the entropy in terms of the number of qubits, therefore difficulting the possibility of an efficient classical simulation protocol. A similar result is obtained numerically for the quantum adiabatic evolution Exact Cover algorithm, which also shows universality of the quantum phase transition the system evolves nearby. On the other hand, entanglement in Grover's adiabatic algorithm remains a bounded quantity even at the critical point. A classification of scaling of entanglement appears as a natural grading of the computational complexity of simulating quantum phase transitions.Comment: 30 pages, 17 figures, accepted for publication in PR