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Despite its amazing quantitative successes and contributions to revolutionary technologies, physics currently faces many unsolved mysteries ranging from the meaning of quantum mechanics to the nature of the dark energy that will determine the future of the Universe. It is clearly prohibitive for the general reader, and even the best informed physicists, to follow the vast number of technical papers published in the thousands of specialized journals. For this reason, we have asked the leading experts across many of the most important areas of physics to summarise their global assessment of some of the most important issues. In lieu of an extremely long abstract summarising the contents, we invite the reader to look at the section headings and their authors, and then to indulge in a feast of stimulating topics spanning the current frontiers of fundamental physics from The Future of Physics by William D Phillips and What characterises topological effects in physics? by Gerard t Hooft through the contributions of the widest imaginable range of world leaders in their respective areas. This paper is presented as a preface to exciting developments by senior and young scientists in the years that lie ahead, and a complement to the less authoritative popular accounts by journalists., Comment: 54 pages, 13 figures

Intriguing symmetries are uncovered regarding magic squares of size 3 and 4, and associative magic squares of size 5. In analogy with the travelling salesman problem, the distributions of the total topological distances of the paths travelled by passing through all the vertices (matrix elements) only once and spanning all elements of the matrix are analyzed. Symmetries are found to characterise the distributions of the total topological distances in these instances. These results open the question of whether these symmetries are found in higher order magic squares as well., Comment: 11 pages, 5 figures

ATP synthase's intrinsic molecular electrostatic potential (MESP) adds constructively to, and hence reinforces, the chemiosmotic voltage. This ATP synthase voltage represents a new free energy term that appears to have been overlooked. This term is at least roughly equal in order of magnitude and opposite in sign to the energy needed to be dissipated as a Maxwell's demon (Landauer principle)., Comment: 4 pages, 3 figures, 1 table

Linus Pauling contributions span structural biology, chemistry in its broadest definition, quantum mechanical theory, valence bond theory, and even nuclear physics. A principal tool developed and used by Pauling is Xray, and electron, diffraction. One possible extension of the Pauling oeuvre could be the marriage of crystallography and quantum mechanics. Such an effort dates back to the sixties and has now flourished into an entire subfield termed quantum crystallography. Quantum crystallography could be achieved through the application of Clinton equations to yield N-representable density matrices consistent with experimental data. The implementation of the Clinton equations is qualitatively different for small and for large systems. For a small system, quantum mechanics is extracted from Xray data while for a large system, the quantum mechanics is injected into the system. In both cases, Nrepresentability is imposed by the use of the Clinton equations., Comment: 20 pages, 3 figures

Consider a projector matrix P, representing the first order reduced density matrix in a basis of orthonormal atom-centric basis functions. A mathematical question arises, and that is, how to break P into its natural component kernel projector matrices, while preserving N-representability of P. The answer relies upon 2- projector triple products, P'jPP'j. The triple product solutions, applicable within the quantum crystallography of large molecules, are determined by a new form of the Clinton equations, which - in their original form - have long been used to ensure N-representability of density matrices consistent with X-ray diffraction scattering factors.

Experiments by Chretien and co-workers suggest that mitochondria are 10oC hotter than their surroundings. Steady-state theoretical estimates place this difference at a maximum of 10^-5 oC. This million-fold disagreement may be called the hot mitochondrion paradox. It is suggested that every proton translocated via ATP synthase sparks a picosecond temperature-difference spike of the order of magnitude measured by Chretien et al. Time-averaging of these spikes recovers the theoretical value. Further, a temporal and spatial superposition of the fluorescence intensity of a very large number of molecular thermometer molecules in the sample can give the appearance of a steady signal. The inner mitochondrial membrane appears to be flanked by temperature differences fluctuating in time and along the membrane s surface, with hot and cold spots as ultrashort temperature spikes.

'Oriented external electric fields (OEEFs)' have been shown to have great potential in being able to provide unprecedented control of chemical reactions, catalysis and selectivity with applications ranging from H2 storage to molecular machines. We report a theoretical study of the atomic origins of molecular changes due to OEEFs; understanding the characteristics of OEEF-induced couplings between atomic and molecular properties is an important step toward comprehensive understanding of the effects of strong external fields on molecular structure, stability, and reactivity. We focus on the atomic and molecular (bond) properties of a set of homo- (H2, N2, O2, F2, and Cl2) and hetero-diatomic (HF, HCl, CO, and NO) molecules under intense external electric fields in the context of quantum theory of atoms in molecules (QTAIM). It is shown that atomic properties (atomic charges and energies, and localization index) correlate linearly with the field strengths, but molecular properties (bond length, electron density at bond critical point, bond length, and electron delocalization index) exhibit non-linear responses to the imposed fields. In particular, the changes in the electron density distribution alter the shapes and locations of the zero-flux surfaces, atomic volumes, atomic electron population, and localization/delocalization indices. At the molecular level, the topography and topology of the molecular electrostatic potential undergo dramatic changes. The external fields also perturb the covalent-polar-ionic characteristic of the studied chemical bonds, hallmarking the impact of electric fields on the stability and reactivity of chemical compounds. The findings are well-rationalized within the framework of the quantum theory of atoms in molecules and form a coherent conceptual understanding of these effects in prototypical molecules such as diatomics.

The sources behind numerous key diffuse interstellar bands (DIBs) remain elusive, and thus evidence is presented here that a family of seven anionic hydrogen atomic clusters (H(-)2n+1, n = 1 to 7) are pertinent contributors. Configuration interaction calculations show hat these charge-induced dipole clusters are stable at temperatures characteristic of the interstellar medium, and emerge from the most abundant element in the Universe. The clusters' spectra yield 25 absorption optical lines that align with observed DIBs to within the computational uncertainties. The absorption bands are due to excitations from the ground states of the clusters to metastable states., Comment: 20 pages in total including 3 figures, 3 tables, and Supporting Information