Asymptotic neutrality of large ions

It is proved that a nucleus of chargeZ can bind at mostZ+O(Z ^a) electrons, witha=47/56.Partially supported by a NSF grant at Princeton UniversitySupported by a Sloan Foundation Dissertation Fellowship at Princeton University     

Large-N collective field theory of electrons around a large-Z nucleus

The large-N collective field formalism developed by Jevicki and Sakita is applied to the many electron system around a large-Z nucleus. It is shown that the well known energy level of the hydrogenlike atom can be reproduced as the excitation spectrum of the charge density vibration. The structure of atomic electron system with short-range repulsive interaction is investigated within the high-density approximation.     

Asymptotic neutrality of diatomic molecules

We use the no-binding theorem of Thomas-Fermi theory to prove that a large diatomic molecule is almost neutral. That is to say, that if the total nuclear charge isZ then the numberN of electrons required for the diatomic molecule to be stable satisfies . In contrast to the atomic case the emphasis here is on the lower bound onN. Our analysis will imply a new bound on the size of the molecule. These results are proved in the Born-Oppenheimer approximation. We also give bounds onN which hold for allZ by a very elementary method, not assuming the Born-Oppenheimer approximation.Work supported by a Danish Research Academy fellowship and U.S. National Science Foundation grant PHY-85-15288-A03Adress from September 1989: Department of Mathematics, The University of Michigan, Ann Arbor, Michigan 48109 USA     

Quantum field theories around a large-Z nucleus: metastable states in supercritical phase

We show that new metastable charge-neutral excitations exist in the supercritical phase of QED around a hypothetical large-Z nucleus. They are the vibration modes of the electron cloud induced around the external charge, and therefore do not have their counterpart in the normal phase. To uncover their properties we utilize our bosonized formulation of QED with proper care of renormal-ordering. In this framework the states can be described as small fluctuations on the solitonic ground state. Their energy levels and the widths are estimated by using the WKB approximation. Some of them are found to be very narrow, of the order of 1–10 keV, and have energies around ～1.6 MeV. The nature of the states is clarified and their quantum numbers are determined:J ^PC =O^+? and 1⁺⁺. Possible relevance of these states to the anomalous peak structure found in heavy ion collision experiments is briefly discussed and a new coincidence experiment is proposed to test this picture.     

Charge neutrality condition for solid surfaces

The charge neutrality condition for the plane contact of the two media is derived, using the technique of the surface Green functions. For illustration, a simple semiinfinite one-dimensional Sommerfeld model with a-function is discussed.     

Enforced electrical neutrality of the color-flavor locked phase

We demonstrate that quark matter in the color-flavor locked phase of QCD is rigorously electrically neutral, despite the unequal quark masses, and even in the presence of an electron chemical potential. As long as the strange quark mass and the electron chemical potential do not preclude the color-flavor locked phase, quark matter is automatically neutral. No electrons are required and none are admitted.     

Approximate Disentanglement

We construct a quantum machine which, by using an asymmetric cloner, disentangles an entangled state and nearly retains it. The attainable maximum value of the scaling parameter for disentangling is identical to that obtained in previous works. The fidelity of the output residual entangled state with respect to the input entangled state is state-dependent. The result shows that it is possible to deal with disentanglement and broadcasting entanglement in a single unitary evolution.     

The charge neutrality point in covalent semiconductor surfaces

The electronic surface density of states in the entire energy spectrum is studied for a covalent semiconductor. A one-dimensional model has been firstly analyzed. The results are generalized for the (111)-surface, and it is shown that when an abrupt potential is placed between ions, the only surface band should be half occupied, in agreement with Shockley. However, this no longer holds for a more general situation.     

Magnetoresistance measurements of graphene at the charge neutrality point

We report on transport measurements of the insulating state that forms at the charge neutrality point of graphene in a magnetic field. Using both conventional two-terminal measurements, sensitive to bulk and edge conductance, and Corbino measurements, sensitive only to the bulk conductance, we observed a vanishing conductance with increasing magnetic fields. By examining the resistance changes of this insulating state with varying perpendicular and in-plane fields, we probe the spin-active components of the excitations in total fields of up to 45?T. Our results indicate that the ν=0 quantum Hall state in single layer graphene is not spin-polarized.     

Approximate Bayesian Inference

This is the Editorial article summarizing the scope of the Special Issue: Approximate Bayesian Inference.     

Approximate Noether symmetries

We present a theory of approximate Noether symmetries, based on the concept of approximate infinitesimal point transformations. The theory is applied to the first-order perturbations of the orbit equations corresponding to Kepler's law and Hooke's law. The effect of the perturbations on the orbits are then discussed.     

Approximate Bogomol'nyi-Prasad-Sommerfield states

We consider dimensionally reduced three-dimensional supersymmetric Yang-Mills-Chern-Simons theory. Although the N=1 supersymmetry of this theory does not allow local massive Bogomol'nyi-Prasad-Sommerfield (BPS) states, we find approximate BPS states which have nonzero masses that are almost independent of the Yang-Mills coupling constant and which are a reflection of the massless BPS states of the underlying N=1 super-Yang-Mills theory. The masses of these states at large Yang-Mills coupling are exactly at the n-particle continuum thresholds. This leads to a relation between their masses at zero and large Yang-Mills coupling.     

Approximate Hidden Variables

The usual definition of (non-contextual) hidden variables is found to be too restrictive, in the sense that, according to it, even some classical systems do not admit hidden variables. A more general concept is introduced and the term approximate hidden variables is used for it. This new concept avoids the aforementioned problems, since all classical systems admit approximate hidden variables. Standard quantum systems do not admit approximate hidden variables, unless the corresponding Hilbert space is 2-dimensional. However, an appropriate non-standard quantum system, which arises by focussing on momentum and position and neglecting the remaining observables, admits approximate hidden variables. Systems associated with JBW-algebras (resp. von Neumann algebras) and satisfying some mild conditions admit approximate hidden variables iff they are classical, that is, iff the corresponding JBW-algebra (resp. von Neumann algebra) is associative (resp. commutative).     

Approximate sine-Gordon solitons

We look at the recently proposed scheme of approximating a sine-Gordon soliton by an expression derived from two dimensional instantons. We point out that the scheme of Sutcliffe in which he uses two dimensional instantons can be generalised to higher dimensions and that these generalisations produce even better approximations than the original approximation. We also comment on generalisations to other models.     

Approximate weinberg mixing

We present a model of the weak interactions in which a custodial symmetry that is not an invariance of the starting Lagrangian emerges in the effective low-energy sector of the theory. This symmetry maintains the relationM _w=M _z cos _w to all orders in the Higgs self-couplings to any required degree of accuracy, while leaving the quark mass spectrum completely unconstrained. The model is a local left-right symmetric chiral flavor gauge theory of the electroweak interactions in which the symmetry is spontaneously broken by fundamental Higgs fields which transform the same way under the chiral group as fermion Dirac and Majorana masses.