Statistical mechanics and dynamics of solvable models with long-range interactions

It has recently been suggested that the presence of a plenitude of light axions, an Axiverse, is evidence for the extra dimensions of string theory. We discuss the observational consequences of these axions on astrophysical black holes through the Penrose superradiance process. When an axion Compton wavelength is comparable to the size of a black hole, the axion binds to the black hole ``nucleus'' forming a gravitational atom in the sky. The occupation number of superradiant atomic levels, fed by the energy and angular momentum of the black hole, grows exponentially. The black hole spins down and an axion Bose-Einstein condensate cloud forms around it. When the attractive axion self-interactions become stronger than the gravitational binding energy, the axion cloud collapses, a phenomenon known in condensed matter physics as ``bosenova''. The existence of axions is first diagnosed by gaps in the mass vs spin plot of astrophysical black holes. For young black holes the allowed values of spin are quantized, giving rise to ``Regge trajectories'' inside the gap region. The axion cloud can also be observed directly either through precision mapping of the near-horizon geometry or through gravitational waves coming from the bosenova explosion, as well as axion transitions and annihilations in the gravitational atom. Our estimates suggest that these signals are detectable in upcoming experiments, such as Advanced LIGO, AGIS, and LISA. Current black hole spin measurements imply an upper bound on the QCD axion decay constant of $2\ifmmode\times\else\texttimes\fi{}{10}^{17}\text{ }\text{ }\mathrm{GeV}$, while Advanced LIGO can detect signals from a QCD axion cloud with a decay constant as low as the GUT scale. We finally discuss the possibility of observing the $\ensuremath{\gamma}$-rays associated with the bosenova explosion and, perhaps, the radio waves from axion-to-photon conversion for the QCD axion.

Exploring the String Axiverse with Precision Black Hole Physics

CONTENTS Introduction Chapter I. Hamiltonian theory of systems of hydrodynamic type § 1. General properties of Poisson brackets § 2. Hamiltonian formalism of systems of hydrodynamic type and Riemannian geometry § 3. Generalizations: differential-geometric Poisson brackets of higher orders, differential-geometric Poisson brackets on a lattice, and the Yang-Baxter equation § 4. Riemann invariants and the Hamiltonian formalism of diagonal systems of hydrodynamic type. Novikov's conjecture. Tsarev's theorem. The generalized hodograph method Chapter II. Equations of hydrodynamics of soliton lattices § 5. The Bogolyubov-Whitham averaging method for field-theoretic systems and soliton lattices. The results of Whitham and Hayes for Lagrangian systems § 6. The Whitham equations of hydrodynamics of weakly deformed soliton lattices for Hamiltonian field-theoretic systems. The principle of conservation of the Hamiltonian structure under averaging § 7. Modulations of soliton lattices of completely integrable evolutionary systems. Krichever's method. The analytic solution of the Gurevich-Pitaevskii problem on the dispersive analogue of a shock wave § 8. Evolution of the oscillatory zone in the KdV theory. Multi-valued functions in the hydrodynamics of soliton lattices. Numerical studies § 9. Influence of small viscosity on the evolution of the oscillatory zone References

/pdf/hydrodynamics-of-weakly-deformed-soliton-lattices-49f7qjte8e.pdf

Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory

A model of copper-oxygen bonding and antibonding bands with the most general two-body interactions allowable by symmetry is considered. The model has a continuous transition as a function of hole density x and temperature T to a phase in which a current circulates in each unit cell. This phase preserves the translational symmetry of the lattice while breaking time-reversal invariance and fourfold rotational symmetry. The product of time reversal and fourfold rotation is preserved. The circulating current phase terminates at a critical point at x=${\mathrm{x}}_{\mathrm{c}}$, T=0. In the quantum critical region about this point the logarithm of the frequency of the current fluctuations scales with their momentum. The microscopic basis for the marginal Fermi-liquid phenemenology and the observed long-wavelength transport anomalies near x=${\mathrm{x}}_{\mathrm{c}}$ are derived from such fluctuations. The symmetry of the current fluctuations is such that the associated magnetic field fluctuations are absent at oxygen sites and have the correct form to explain the anomalous copper nuclear relaxation rate. Crossovers to the Fermi-liquid phase on either side of ${\mathrm{x}}_{\mathrm{c}}$ and the role of disorder are briefly considered. The current fluctuations promote superconductive instability with a propensity towards ``D-wave'' symmetry or ``extended S-wave''symmetry depending on details of the band structure. Several experiments are proposed to test the theory.

行雄小幡

Papers

Soviet Physics JETP

J. von Neumann: Mathematical Foundations of Quantum Mechanics (translated by R. T. Beyer), Princeton University Press, 1955. 472 pages, $6.00.

Nuclear magnetic relaxation in transition metals

行雄 小幡

Papers

Soviet Physics JETP

J. von Neumann: Mathematical Foundations of Quantum Mechanics (translated by R. T. Beyer), Princeton University Press, 1955. 472 pages, $6.00.

Nuclear magnetic relaxation in transition metals

行雄小幡