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Parisi G.,University of Rome La Sapienza | Zamponi F.,Laboratoire Of Physique Theorique
Reviews of Modern Physics | Year: 2010

Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest as they are related to important problems in information theory, such as digitalization of signals, error correcting codes, and optimization problems. In three dimensions the densest packing of identical hard spheres has been proven to be the fcc lattice, and it is conjectured that the closest packing is ordered (a regular lattice, e.g., a crystal) in low enough dimension. Still, amorphous packings have attracted much interest because for polydisperse colloids and granular materials the crystalline state is not obtained in experiments for kinetic reasons. A theory of amorphous packings, and more generally glassy states, of hard spheres is reviewed here, that is based on the replica method: this theory gives predictions on the structure and thermodynamics of these states. In dimensions between two and six these predictions can be successfully compared with numerical simulations. The limit of large dimension is also discussed where an exact solution is possible. Some of the results presented here were published, but others are original: in particular, an improved discussion of the large dimension limit and new results on the correlation function and the contact force distribution in three dimensions. The main assumptions that are beyond the theory presented are clarified and, in particular, the relation between static computation and the dynamical procedures used to construct amorphous packings. There remain many weak points in the theory that should be better investigated. © 2010 The American Physical Society.

Prolhac S.,Laboratoire Of Physique Theorique | Prolhac S.,CNRS Laboratory for Theoretical Physics
Journal of Physics A: Mathematical and Theoretical | Year: 2015

The fluctuations of the current for the one-dimensional totally asymmetric exclusion process with L sites are studied in the relaxation regime of times T ∼ L3/2. Using Bethe ansatz for the periodic system with an evolution conditioned on special initial and final states, the Fourier transform of the probability distribution of the fluctuations is calculated exactly in the thermodynamic limit L → ∞ with finite density of particles. It is found to be equal to a sum over discrete realizations of a scalar field in a linear potential with coupling constant equal to the rescaled time T/L3/2. © 2015 IOP Publishing Ltd.

Schulgin W.,Solvay Group | Troost J.,Laboratoire Of Physique Theorique
Journal of High Energy Physics | Year: 2014

The quantum theory of a massless spin two particle is strongly constrained by diffeomorphism invariance, which is in turn implied by unitarity. We explicitly exhibit the space-time diffeomorphism algebra of string theory, realizing it in terms of world sheet vertex operators. Viewing diffeomorphisms as field redefinitions in the two-dimensional conformal field theory renders the calculation of their algebra straightforward. Next, we generalize the analysis to combinations of space-time anti-symmetric tensor gauge transformations and diffeomorphisms. We also point out a left-right split of the algebra combined with a twist that reproduces the C-bracket of double field theory. We further compare our derivation to an analysis in terms of marginal deformations as well as vertex operator algebras. © 2014 The Author(s).

Loebbert F.,Niels Bohr Institute | Loebbert F.,Laboratoire Of Physique Theorique | Loebbert F.,Max Planck Institute For Gravitationsphysik
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2012

It is well known that integrable charges for short-range (e.g. nearest-neighbor) spin chains with periodic boundary conditions can be recursively generated by a so-called boost operator. In the past, this iterative construction has been generalized to periodic long-range spin chains as they appear in the context of the gauge/gravity correspondence. Here we introduce recursion relations for open long-range spin chain charges converting a short-range into a long-range integrable model. © 2012 American Physical Society.

Gao X.,CNRS Astroparticle and Cosmology Lab | Gao X.,Laboratoire Of Physique Theorique | Gao X.,University Pierre and Marie Curie | Kobayashi T.,Kyoto University | And 2 more authors.
Physical Review Letters | Year: 2011

We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in the most general single-field inflation model with second-order field equations. It is shown that the most general cubic action for the tensor perturbation hij is composed only of two contributions, one with two spacial derivatives and the other with one time derivative on each hij. The former is essentially identical to the cubic term that appears in Einstein gravity and predicts a squeezed shape, while the latter newly appears in the presence of the kinetic coupling to the Einstein tensor and predicts an equilateral shape. Thus, only two shapes appear in the graviton bispectrum of the most general single-field inflation model, which could open a new clue to the identification of inflationary gravitational waves in observations of cosmic microwave background anisotropies as well as direct detection experiments. © 2011 American Physical Society.

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