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Self-interactions and interaction with the environment tend to push quantum systems toward states of maximal entanglement. This is a definition of decoherence. We argue that these maximally entangled states fall into the well-defined classes that can be uniquely described by the values of certain entanglement invariants. After discussing these ideas we present examples of maximally entangled states for a number of generic systems, construct compact states in the most entangled classes for tripartite systems, and suggest how they may be constructed for other $n$-partite systems. We study random walks through the space of entanglement classes to see how decoherence might work in practice., Comment: 35 pages, 7 figures, 15 tables

For any choice of initial state and weak assumptions about the Hamiltonian, large isolated quantum systems undergoing Schrodinger evolution spend most of their time in macroscopic superposition states. The result follows from von Neumann's 1929 Quantum Ergodic Theorem. As a specific example, we consider a box containing a solid ball and some gas molecules. Regardless of the initial state, the system will evolve into a quantum superposition of states with the ball in macroscopically different positions. Thus, despite their seeming fragility, macroscopic superposition states are ubiquitous consequences of quantum evolution. We discuss the connection to many worlds quantum mechanics., Comment: version to appear in Foundations of Physics

We develop a new iterative method for finding approximate solutions for spherical bounces associated with the decay of the false vacuum in scalar field theories. The method works for any generic potential in any number of dimensions, contains Coleman's thin-wall approximation as its first iteration, and greatly improves its accuracy by including higher order terms., Comment: 23 pages, 4 figures

We suggest a structure for the vacuum comprised of a network of tightly knotted/linked flux tubes formed in a QCD-like cosmological phase transition and show that such a network can drive cosmological inflation. As the network can be topologically stable only in three space dimensions, this scenario provides a dynamical explanation for the existence of exactly three large spatial dimensions in our Universe., Comment: 5 pages

We propose covariant and non-abelian generalizations of the magnetic helicity and Beltrami equation. The gauge invariance, variational principle, conserved current, energy-momentum tensor and choice of boundary conditions elucidate the subject. In particular, we prove that any extremal of the Yang-Mills action functional $\tfrac{1}{4}\int_\Omega\tr{F_{\mu\nu}F^{\mu\nu}}\,d^4x$ subject to the local constraint $\epsilon^{\mu\nu\alpha\beta}\tr{F_{\mu\nu}F_{\alpha\beta}}=0$ satisfies the covariant non-abelian Beltrami equation., Comment: 22 pages

The next generation of large scale surveys will not only measure cosmological parameters within the framework of General Relativity, but will also allow for precision tests of the framework itself. At the order of linear perturbations, departures from the growth in the LCDM model can be quantified in terms of two functions of time and Fourier number k. We argue that in local theories of gravity, in the quasi-static approximation, these functions must be ratios of polynomials in k, with the numerator of one function being equal to the denominator of the other. Moreover, the polynomials are even and of second degree in practically all viable models considered today. This means that, without significant loss of generality, one can use data to constraint only five functions of a single variable, instead of two functions of two variables. Furthermore, since the five functions are expected to be slowly varying, one can fit them to data in a non-parametric way with the aid of an explicit smoothness prior. We discuss practical application of this parametrization to forecasts and fits., Comment: 9 pages, v2: matching the published version

We model the observed $J^{++}$ mesonic mass spectrum in terms of energies for tightly knotted and linked chromoelectric QCD flux tubes. The data is fit with one and two parameter models. We predict a possible new state at approximately 1190 MeV and a plethora of new states above 1690 MeV., Comment: 30 pages, 17 figures, 7 tables

We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly so that two randomly chosen particles are unlikely to be directly entangled with each other -- the reduced density matrix describing any pair is likely to be separable., Comment: 5 pages, 3 figures, revtex. arXiv admin note: text overlap with arXiv:0908.1265

We provide a classification of entangled states that uses new discrete entanglement invariants. The invariants are defined by algebraic properties of linear maps associated with the states. We prove a theorem on a correspondence between the invariants and sets of equivalent classes of entangled states. The new method works for an arbitrary finite number of finite-dimensional state subspaces. As an application of the method, we considered a large selection of cases of three subspaces of various dimensions. We also obtain an entanglement classification of four qubits, where we find 27 fundamental sets of classes., Comment: published version

We discuss physical systems with topologies more complicated than simple gaussian linking. Our examples of these higher topologies are in non-relativistic quantum mechanics and in QCD., Comment: 6 pages, 5 figures

We propose new algebraic invariants that distinguish and classify entangled states. Considering qubits as well as higher spin systems, we obtained complete entanglement classifications for cases that were either unsolved or only conjectured in the literature., Comment: published version

The typical scalar field theory has a cosmological constant problem. We propose a generic mechanism by which this problem is avoided at tree level by embedding the theory into a larger theory. The metric and the scalar field coupling constants in the original theory do not need to be fine-tuned, while the extra scalar field parameters and the metric associated with the extended theory are fine-tuned dynamically. Hence, no fine-tuning of parameters in the full Lagrangian is needed for the vacuum energy in the new physical system to vanish at tree level. The cosmological constant problem can be solved if the method can be extended to quantum loops., Comment: published version

For an infinitesimal deformation of a Riemannian manifold, we prove that the scalar, vector, and tensor modes in decompositions of perturbations of the metric tensor, the scalar curvature, the Ricci tensor, and the Einstein tensor decouple if and only if the manifold is Einstein. Four-dimensional space-time satisfying the condition of the theorem is homogeneous and isotropic. Cosmological applications are discussed., Comment: 7 pages

Few physical systems with topologies more complicated than simple gaussian linking have been explored in detail. Here we focus on examples with higher topologies in non-relativistic quantum mechanics and in QCD., Comment: Presented by TWK at "Knots and soft-matter physics", YITP, Kyoto, August, 2008

Gaussian linking of superconducting loops containing Josephson junctions with enclosed magnetic fields give rise to interference shifts in the phase that modulates the current carried through the loop, proportional to the magnitude of the enclosed flux. We generalize these results to higher order linking of a superconducting loop with several magnetic solenoids, and show there may be interference shifts proportional to the product of two or more fluxes., Comment: 8 pages, 2 figures

We show that the linking of a semiclassical path of a charged particle with a knotted magnetic solenoid results in the Aharonov-Bohm effect. The phase shift in the wave function is proportional to the flux intersecting a certain connected and orientable surface bounded by the knot (a Seifert surface of the knot)., Comment: 9 pages, 7 figures

The entanglement entropy in a quantum field theory between two regions of space has been shown in simple cases to be proportional to the volume of the hypersurface separating the regions. We prove that this is true for a free scalar field in an arbitrary geometry with purely spatial curvature and obtain a complete asymptotic expansion for the entropy., Comment: published version

It is well known that for a field theory with the Chern-Simons action, expectation values of Wilson line operators are topological invariants. The standard result is expressed in terms of the Gaussian linkings of closed curves defining the operators. We show how judicious choice of Wilson lines leads to higher order topological linkings.

Gaussian linking of a semiclassical path of a charged particle with a magnetic flux tube is responsible for the Aharonov-Bohm effect, where one observes interference proportional to the magnitude of the enclosed flux. We construct quantum mechanical wave functions where semiclassical paths can have second order linking to two magnetic flux tubes, and show there is interference proportional to the product of the two fluxes., Comment: 7 pages, 4 figures

In classical mechanics, an action is defined only modulo additive terms which do not modify the equations of motion; in certain cases, these terms are topological quantities. We construct an infinite sequence of higher order topological actions and argue that they play a role in quantum mechanics, and hence can be accessed experimentally., Comment: 7 pages

We extend previous work showing that violation of the null energy condition implies instability in a broad class of models, including gauge theories with scalar and fermionic matter as well as any perfect fluid. Simple examples are given to illustrate these results. The role of causality in our results is discussed. Finally, we extend the fluid results to more general systems in thermal equilibrium. When applied to the dark energy, our results imply that w is unlikely to be less than -1., Comment: 11 pages, 5 figures, Revtex

Attempts to derive the Born rule, either in the Many Worlds or Copenhagen interpretation, are unsatisfactory for systems with only a finite number of degrees of freedom. In the case of Many Worlds this is a serious problem, since its goal is to account for apparent collapse phenomena, including the Born rule for probabilities, assuming only unitary evolution of the wavefunction. For finite number of degrees of freedom, observers on the vast majority of branches would not deduce the Born rule. However, discreteness of the quantum state space, even if extremely tiny, may restore the validity of the usual arguments., Comment: 5 pages, revtex, 1 figure. Revised version, to appear in Physics Letters B. (Small clarifcation, references added.)

We provide exact solutions to the Einstein equations when the Universe contains vacuum energy plus a uniform arrangements of magnetic fields, strings, or domain walls. Such a universe has planar symmetry, i. e., it is homogeneous but, not isotropic. Further exact solutions are obtained when dust is included and approximate solutions are found for $w\not=0$ matter. These cosmologies also have planar symmetry. These results may eventually be used to explain some features in the WMAP data. The magnetic field case is the easiest to motivate and has the highest possibility of yielding reliable constraints on observational cosmology., Comment: 42 pages, 24 figures, 3 tables

We show that Lorentzian (traversable) wormholes and time machines with semi-classical spacetimes are unstable due to their violation of the null energy condition (NEC). Semi-classicality of the energy-momentum tensor in a given quantum state (required for semi-classicality of the spacetime) implies localization of its wavefunction in phase space, leading to evolution according to the classical equations of motion. Previous results related to violation of the NEC then require that the configuration is unstable to small perturbations., Comment: 3 pages, 1 figure, revtex

We show that violation of the null energy condition implies instability in a broad class of models, including classical gauge theories with scalar and fermionic matter as well as any perfect fluid. When applied to the dark energy, our results imply that $w = p / \rho$ is unlikely to be less than -1., Comment: 5 pages, 1 figure, revtex, presentation improved, minor changes

Systems of tightly knotted, linked, or braided flux tubes will have a universal mass-energy spectrum if the flux is quantized. We focus on a model of glueballs as knotted QCD flux tubes., Comment: 5 pages, 1 table, 1 figure

For uniform arrangements of magnetic fields, strings, or domain walls (together with the cosmological constant and non-relativistic matter), exact solutions to the Einstein equations are shown to lead to a universe with ellipsoidal expansion. We argue the results can be used to explain some features in the WMAP data. The magnetic field case is the easiest to motivate and has the highest possibility of yielding reliable constraints on observational cosmology., Comment: 5 pages, 1 figure

We argue that a systems of tightly knotted, linked, or braided flux tubes will have a universal mass-energy spectrum, since the length of fixed radius flux tubes depend only on the topology of the configuration. We motivate the discussion with plasma physics examples, then concentrate on the model of glueballs as knotted QCD flux tubes. Other applications will also be discussed., Comment: 10 pages, 1 table, 4 figures

It has been proposed that propagation of cosmic rays at extreme-energy may be sensitive to Lorentz-violating metric fluctuations (``foam''). We investigate the changes in interaction thresholds for cosmic-rays and gamma-rays interacting on the CMB and IR backgrounds, for a class of stochastic models of spacetime foam. The strength of the foam is characterized by the factor (E/M_P)^a, where ``a'' is a phenomenological suppression parameter. We find that there exists a critical value of ``a'' (dependent on the particular reaction), below which the threshold energy can only be lowered, and above which the threshold energy may be raised, but at most by a factor of two. Thus, it does not appear possible in this class of models to extend cosmic-ray spectra significantly beyond their classical absorption energies. However, the lower thresholds resulting from foam may have signatures in the cosmic-ray spectrum. We also find that cosmic-ray energies cannot exceed the fundamental Planck scale, and so set a lower bound of 10^8 TeV on the context of this model for the scale of gravity. Finally, we comment in the apparent non-conservation of particle energy-momentum, and speculate on its re-emergence as dark energy in the foamy vacuum., Comment: 27 pages, 13 figures. Author added (Buniy), appendix added, and new section added, corrections made. To appear in Astroparticle Physics

For a universe containing cosmological constant together with uniform arrangements of magnetic fields, strings, or domain walls, exact solutions to the Einstein equations are shown to lead to a universe with ellipsoidal expansion. The magnetic field case is the easiest to motivate and has the highest possibility of finding application in observational cosmology., Comment: 9 pages, 1 table, 2 figures; minor changes; to appear in JCAP

We show how the existence of non-trivial finite-energy time-dependent classical lumps is restricted by a generalized virial theorem. For simple model Lagrangians, bounds on energies follow., Comment: 4 pages, 1 figure; substantial changes

We consider an eight-dimensional local octonionic theory with the seven-sphere playing the role of the gauge group. Duality conditions for two- and four-forms in eight dimensions are related. Dual fields--octonionic instantons--solve an 8D generalization of the Yang-Mills equation. Modifying the ADHM construction of 4D instantons, we find general $k$-instanton 8D solutions which depends on $16k-7$ effective parameters.

We model the observed glueball mass spectrum in terms of energies for tightly knotted and linked QCD flux tubes. The data is fit well with one parameter. We predict additional glueball masses., Comment: 11 pages, 3 figures, 1 table; minor changes, comments added, typos corrected

Skew density matrices can be diagonalized to yield probability interpretation. The power-counting prediction of perturbative QCD is found consistent with recent CEBAF data on $F_2(Q^2)/F_1(Q^2)$, Comment: 4 pages, Presented May 23, 2000 by John Ralston. Published in the Proceedings of the 7th International Conference on Intersections of Particle and Nuclear Physics, (May 22-28, 2000 Quebec City), Edited by Z. Parseh and W. Marciano, (AIP Conference Proceedings Number 549.)

A new picture is given of generalized parton distributions probed in experiments in which the probe scale $Q^{2}$ and the momentum transfer $\DD^{2}$ are well separated. Application of this picture to the $Q^{2}$ dependence of the form factors $F_{1}, F_{2}$ shows that gauge invariant quark orbital angular momentum can be measured and indeed {\it localized} in the transverse profile of the proton. A previous prediction that $\sqrt{Q^{2}}F_{2}(Q^{2})/F_{1}(Q^{2}) \sim const. $ is generalized to GPD language. This prediction appears to have been confirmed by recent CEBAF data., Comment: 6 pages, 1 figure. To appear in DIS 2001, 9th International Workshop on Deep Inelastic Scattering, Bologna, 27 April - 1 May, 2001

Radio Cherenkov emission underlines detection of high energy particles via a signal growing like the particle-energy-squared. Cosmic ray-induced electromagnetic showers are a primary application. While many studies have treated the phenomenon approximately, none have attempted to incorporate all the physical scales involved in problems with time- or spatially- evolving charges. We find it is possible to decompose the calculated fields into the product of a form factor, characterizing a moving charge distribution, multiplying a general integral which depends on the charge evolution. In circumstances of interest for cosmic ray physics, the resulting expressions can be evaluated explicitely in terms of a few parameters obtainable from shower codes. The classic issues of Frauhofer and Fresnel zones play a crucial role in the coherence., Comment: 25 pages, 10 figures