Classical anomalies and local version of the atiyah-singer theorem

We give a split-point derivation of the m = 0 axial anomaly in an external Euclidean Riemann metric. We discuss two new anomalous currents which lead to the Euler-density and the Hirzebruch L density.     

High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continuous variables

We experimentally demonstrate continuous-variable quantum teleportation beyond the no-cloning limit. We teleport a coherent state and achieve the fidelity of 0.70 +/- 0.02 that surpasses the no-cloning limit of 2/3. Surpassing the limit is necessary to transfer the nonclassicality of an input quantum state. By using our high-fidelity teleporter, we demonstrate entanglement swapping, namely, teleportation of quantum entanglement, as an example of transfer of nonclassicality.     

Scattering-phase theorem

We derive two mathematical relations between quantitative phase images of thin slices of inhomogeneous media and the scattering parameters of the bulk, i.e., scattering mean free path, l(s), and anisotropy factor, g. The l(s) turns out to be inversely proportional to the spatial variance of the phase shift, and g is related to the variance of the phase gradient. These formulas, referred collectively to as the scattering-phase theorem, allow for extracting l(s) and g in a spatially resolved manner and across an entire tissue section, that is, mapping large cross sections of tissues in terms of l(s) and g.     

Classical tunneling

A classical representation of an extended body over barriers of height greater than the energy of the incident body is shown to have many features in common with quantum tunneling as the center-of-mass literally goes through the barrier. It is even classically possible to penetrate any finite barrier with a body of arbitrarily low energy if the body is sufficiently long. A distribution of body lengths around the de Broglie wavelength leads to reasonable agreement with the quantum transmission coefficient.     

Brillouin's theorem and the Hellmann-Feynman theorem for Hartree-Fock wave functions

It is shown that there is an intimate relation between the Hellmann-Feynman theorem and Brillouin's theorem. A more general form of Brillouin's theorem is provided, which applies to excited states of arbitrary symmetry and multiplicity. This new form leads to a simple proof of the Hellmann-Feynman theorem. This theorem is valid when all the orbitals that occur in the wave function are determined by a complete, and not a partial, variational procedure. Arguing in the opposite direction it is shown that the complete satisfaction of the generalized Brillouin's theorem provides an alternative scheme for obtaining the Hartree-Fock orbitals.     

The Kochen-Specker theorem and Bell's theorem: An algebraic approach

In this paper we present a systematic formulation of some recent results concerning the algebraic demonstration of the two major no-hidden-variables theorems for N spin-1/2 particles. We derive explicitly the GHZ states involved and their associated eigenvalues. These eigenvalues turn out to be undefined for N=, this fact providing a new proof showing that the nonlocality argument breaks down in the limit of a truly infinite number of particles.     

Ann-dimensional Borg-Levinson theorem

We show that the potentialq is uniquely determined by the spectrum, and boundary values of the normal derivatives of the eigenfunctions of the Schrödinger operator –+q with Dirichlet boundary conditions on a bounded domain in ⁿ . This and related results can be viewed as a direct generalization of the theorem in the title, which states that the spectrum and the norming constants determine the potential in the one dimensional case.Supported by NSF grant DMS-8602033Supported by NSF grant DMS-8600797Supported by NSF grant DMS-8601118 and an Alfred P. Sloan Research Fellowship     

Generalized Kochen-Specker theorem

A generalized Kochen-Specker theorem is proved. It is shown that there exist sets of n projection operators, representing n yes-no questions about a quantum system, such that none of the 2 possible answers is compatible with sum rules imposed by quantum mechanics. Namely, if a subset of commuting projection operators sums up to a matrix having only even or only odd eigenvalues, the number of yes answers ought to he even or odd, respectively. This requirement may lead to contradictions. An example is provided, involving nine projection operators in a 4-dimensional space.Dedicated to Professor Max Jammer on the occasion of his 80th birthday.I am grateful to N. D. Mermin for patiently explaining to me that ref. 11 was a Kochen-Specker argument, not one about locality, as I had wrongly thought. This work was supported by the Gerard Swope Fund, and the Fund for Encouragement of Research.     

Ferromagnetic Lieb-Mattis theorem

We prove ferromagnetic ordering of energy levels for XXX Heisenberg chains with spins of arbitrary magnitude, thus extending our previous result for the spin-1/2 chain. Ferromagnetic ordering means that the minimum energies in the invariant subspaces of fixed total spin are monotone decreasing as a function of the total spin. This result provides a ferromagnetic analogue of the well-known theorem by Lieb and Mattis about ordering of energy levels in antiferromagnetic and ferrimagnetic systems on bipartite graphs.     

Generalized no-broadcasting theorem

We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with "superquantum" correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.     

Random Classical Fidelity

We introduce a random perturbed version of the classical fidelity and we show that it converges with the same rate of decay of correlations, but not uniformly in the noise. This makes the classical fidelity unstable in the zero-noise limit.     

Proper-Time Classical Electrodynamics

We construct a generalization of Maxwell's equations associated with the proper-time of the source which accounts for radiation reaction without any assumptions concerning the nature of the source. The theory leads to a new invariance group, related to the Lorentz group, which leaves the proper-time of the source fixed for all observers.     

Classical Schwinger terms

Schwinger terms must be present in equal time ground state Poisson brackets among currents unless the latter are stationary in that state.Supported in part by U.S.A.E.C. Contract AT(45-1)1388 B.Supported in part by U.S.A.F. OAR under OSR Grant 70-1864.     

Classical relativistic particles

The concept of Lorentz-invariant classical elementary particle is made precise and it is found that there are exactly two families: (0) the well-known free point-particles distinguished only by their masses and (+) a family with eight-dimensional phase space whose members are distinguished either by their mass or their positive spin.     

Classical superstring mechanics

We describe the classical mechanics of the superstring in both hamiltonian and lagrangian formulations, including massless external fields. The formulation is a modification of that of Green and Schwarz that allows supersymmetric Lorentz covariant quantization.