Characterization of some causality conditions through the continuity of the Lorentzian distance

A classical result in Lorentzian geometry states that a strongly causal spacetime is globally hyperbolic if and only if the Lorentzian distance is finite valued for every metric choice in the conformal class. It is proved here that a non-total imprisoning spacetime is globally hyperbolic if and only if for every metric choice in the conformal class the Lorentzian distance is continuous. Moreover, it is proved that a non-total imprisoning spacetime is causally simple if and only if for every metric choice in the conformal class the Lorentzian distance is continuous wherever it vanishes. Finally, a strongly causal spacetime is causally continuous if and only if there is at least one metric in the conformal class such that the Lorentzian distance is continuous wherever it vanishes.     

The Generalized Canonical Ensemble and Its Universal Equivalence with the Microcanonical Ensemble

This paper shows for a general class of statistical mechanical models that when the microcanonical and canonical ensembles are nonequivalent on a subset of values of the energy, there often exists a generalized canonical ensemble that satisfies a strong form of equivalence with the microcanonical ensemble that we call universal equivalence. The generalized canonical ensemble that we consider is obtained from the standard canonical ensemble by adding an exponential factor involving a continuous function g of the Hamiltonian. For example, if the microcanonical entropy is C², then universal equivalence of ensembles holds with g taken from a class of quadratic functions, giving rise to a generalized canonical ensemble known in the literature as the Gaussian ensemble. This use of functions g to obtain ensemble equivalence is a counterpart to the use of penalty functions and augmented Lagrangians in global optimization. linebreak Generalizing the paper by Ellis et al. [J. Stat. Phys. 101:999–1064 (2000)], we analyze the equivalence of the microcanonical and generalized canonical ensembles both at the level of equilibrium macrostates and at the thermodynamic level. A neat but not quite precise statement of one of our main results is that the microcanonical and generalized canonical ensembles are equivalent at the level of equilibrium macrostates if and only if they are equivalent at the thermodynamic level, which is the case if and only if the generalized microcanonical entropy s–g is concave. This generalizes the work of Ellis et al., who basically proved that the microcanonical and canonical ensembles are equivalent at the level of equilibrium macrostates if and only if they are equivalent at the thermodynamic level, which is the case if and only if the microcanonical entropy s is concave.     

A regularity theorem for solutions of the spherically symmetric Vlasov-Einstein system

We show that if a solution of the spherically symmetric Vlasov-Einstein system develops a singularity at all then the first singularity has to appear at the center of symmetry. The main tool is an estimate which shows that a solution is global if all the matter remains away from the center of symmetry.Research supported in part by NSF DMS 9101517     

Impossibility of perturbative restoration of F type spontaneously broken supersymmetry

We prove that higher order corrections cannot restore supersymmetry if it is spontaneously broken at the tree level by an F type mechanism even if not all terms consistent with the symmetries have been included.     

A New Qualitative Prediction of the Parton Model for High-Energy Hadron Collisions

Inclusive single jet production in hadron collisions is considered. It is shown that the QCD parton model predicts a nonmonotonic dependence of the inclusive cross section on the fraction of the energy deposited in the jet registered, if it is normalized on the same cross section measured at another collision energy. Specifically, if the cross section is normalized by the one measured at a higher collision energy, it possesses a minimum which depends on jet rapidity. This prediction can be tested at the Fermilab Tevatron, at the CERN LHC, and at the Very Large Hadron Collider under discussion.     

Threshold anomaly in non-central forces

The behaviour of the threshold anomaly for non-central potentials, which account for collective excitations in heavy-ion collisions, is investigated. It is shown that the non-central potentials should exhibit an energy dependence at energies in the vicinity of the Coulomb barrier. This energy dependence is, however, different from that of the elastic optical potential, occurring at lower energies. It if further shown that there are corrections to the traditional collective model such that, if the transition potential is expressed as the derivative of the optical potential, the corresponding deformation length will be complex and energy-dependent. Simple model calculations are presented.     

Do multineutrons really exist?

It is argued, that nuclear multineutrons, if they exist at all, are rather heavy nuclei, which contain at least 100 neutrons.     

Classicality of the primordial perturbations

We show that during inflation, a quantum fluctuation becomes classical at all orders if it becomes classical at first order. Implications are discussed.     

Replacing energy by von Neumann entropy in quantum phase transitions

We propose that quantum phase transitions are generally accompanied by non-analyticities of the von Neumann (entanglement) entropy. In particular, the entropy is non-analytic at the Anderson transition, where it exhibits unusual fractal scaling. We also examine two dissipative quantum systems of considerable interest to the study of decoherence and find that non-analyticities occur if and only if the system undergoes a quantum phase transition.     

A simplified basis for Bell–Kochen–Specker theorems

We show that a reduced form of the structural requirements for deterministic hidden variables used in Bell–Kochen–Specker theorems is already sufficient for the no-go results. Those requirements are captured by the following principle: an observable takes a spectral value x if and only if the spectral projector associated with x takes the value 1. We show that the “only if” part of this condition suffices. The proof identifies an important structural feature behind the no-go results; namely, if at least one projector is assigned the value 1 in any resolution of the identity, then at most one is.     

A Rigidity Property of Asymptotically Simple Spacetimes Arising from Conformally Flat Data

Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through the critical sets where null infinity touches spatial infinity if and only if the initial data coincides with Schwarzschild data.     

Bose-Einstein condensation of incommensurate solid 4He

It is pointed out that the simulation computation of energy performed so far cannot be used to decide if the ground state of solid 4He has the number of lattice sites equal to the number of atoms (commensurate state) or if it is different (incommensurate state). The best variational wave function, a shadow wave function, gives an incommensurate state, but the equilibrium concentration of vacancies remains to be determined. We have computed the one-body density matrix in solid 4He for the incommensurate state by means of an exact ground state projector method in which incommensurability occurs spontaneously. We find a vacancy induced Bose-Einstein condensation of about 0.23 atoms per vacancy at a pressure of 54 bar. This means that bulk solid 4He is supersolid at low enough temperature if the exact ground state is incommensurate.     

No anomalous fluctuations exist in stable equilibrium systems

A general theorem is rigorously proved for the case, when an observable is a sum of linearly independent terms: the dispersion of a global observable is normal if and only if all partial dispersions of its terms are normal, and it is anomalous if and only if at least one of the partial dispersions is anomalous. This theorem, in particular, rules out the possibility that in a stable system with Bose–Einstein condensate some fluctuations of either condensed or non-condensed particles could be anomalous. The conclusion is valid for arbitrary systems, whether uniform or non-uniform, interacting weakly or strongly. The origin of fictitious fluctuation anomalies, arising in some calculations, is elucidated.     

Use of quantum dots as a switch for single-electron transfer free from cotunneling

Based on symmetry constraint that leads to the appearance of nodes in the wave functions of 3-electron systems at regular triangle configurations, it was found that, if the parameters of confinement are skillfully chosen and if a magnetic field is tuned around the first critical point of the single-triplet transition, a 2-electron quantum dot can be used as a switch for single-electron transport free from cotunneling.     

Measuring the Higgs boson self-coupling at the Large Hadron Collider

Inclusive standard model Higgs boson pair production and subsequent decay to same-sign dileptons via weak gauge W+/- bosons at the CERN Large Hadron Collider (LHC) has the capability to determine the Higgs boson self-coupling, lambda. The large top quark mass limit is found not to be a good approximation for the signal if one wishes to utilize differential distributions in the analysis. We find that it should be possible at the LHC with design luminosity to establish that the standard model Higgs boson has a nonzero self-coupling and that lambda/lambda(SM) can be restricted to a range of 0-3.7 at 95% confidence level if its mass is between 150 and 200 GeV.     

Effect Algebras Are Not Adequate Models for Quantum Mechanics

We show that an effect algebra E possess an order-determining set of states if and only if E is semiclassical; that is, E is essentially a classical effect algebra. We also show that if E possesses at least one state, then E admits hidden variables in the sense that E is homomorphic to an MV-algebra that reproduces the states of E. Both of these results indicate that we cannot distinguish between a quantum mechanical effect algebra and a classical one. Hereditary properties of sharpness and coexistence are discussed and the existence of {0,1} and dispersion-free states are considered. We then discuss a stronger structure called a sequential effect algebra (SEA) that we believe overcomes some of the inadequacies of an effect algebra. We show that a SEA is semiclassical if and only if it possesses an order-determining set of dispersion-free states.     

Modular almost orthogonal quantum logics

Almost orthogonal quantum logics, i.e., atomic orthomodular lattices in which to every atom there exist only finitely many nonorthogonal atoms, are studied. It is shown that an almost orthogonal quantum logic is modular if and only if it has the exchange property if and only if it can be embedded into a direct product of finite modular quantum logics. The class of almost orthogonal modular OMLs is the largest subclass of the class of atomic modular OMLs in which the conditions commutator-finite and block-finite are equivalent. A finite faithful valuation on an almost orthogonal quantum logicL exists if and only ifL is modular and the set of all atoms ofL is at most countable.     

Internal electron diffraction from atomically ordered subsurface nanostructures in metals

We demonstrate that a part of interface at a subsurface nanocavity in Cu(110) can efficiently induce electron scattering back to the surface even if it is inclined with respect to the surface, if the condition for electron diffraction is fulfilled. This backscattering induces oscillations of electron local density of states at the surface versus electron energy. In agreement with our model calculations, the diffraction is assigned to a specific atomic structure at the interface, and is found to be significantly enhanced by focussing of electron waves for propagation along the [110] direction.     

The potential profile in LEED theory

The effect of variations in the inner potential at a crystal surface on low-energy electron diffraction (LEED) is investigated. It is shown in particular that surface structural determination using LEED is sensitive to the local value of the inner potential if energies roughly below 100 eV are used. It is however not sensitive to scattering effects at potential steps, except if intensities near beam emergences are considered, in which case LEED is shown to be a suitable tool for examining these potential steps.