String fragmentation in supercooled confinement and implications for dark matter

A strongly-coupled sector can feature a supercooled confinement transition in the early universe. We point out that, when fundamental quanta of the strong sector are swept into expanding bubbles of the confined phase, the distance between them is large compared to the confinement scale. We suggest a modelling of the subsequent dynamics and find that the flux linking the fundamental quanta deforms and stretches towards the wall, producing an enhanced number of composite states upon string fragmentation. The composite states are highly boosted in the plasma frame, which leads to additional particle production through the subsequent deep inelastic scattering. We study the consequences for the abundance and energetics of particles in the universe and for bubble-wall Lorentz factors. This opens several new avenues of investigation, which we begin to explore here, showing that the composite dark matter relic density is affected by many orders of magnitude

Supercool composite Dark Matter beyond 100 TeV

Dark Matter could be a composite state of a confining sector with an approximate scale symmetry. We consider the case where the associated pseudo-Goldstone boson, the dilaton, mediates its interactions with the Standard Model. When the confining phase transition in the early universe is supercooled, its dynamics allows for Dark Matter masses up to 106 TeV. We derive the precise parameter space compatible with all experimental constraints, finding that this scenario can be tested partly by telescopes and entirely by gravitational waves

Scattering theory for lattice operators in dimension d≥3d\geq 3

This paper analyzes the scattering theory for periodic tight-binding Hamiltonians perturbed by a finite range impurity. The classical energy gradient flow is used to construct a conjugate (or dilation) operator to the unperturbed Hamiltonian. For dimension $d\geq 3$ the wave operator is given by an explicit formula in terms of this dilation operator, the free resolvent and the perturbation. From this formula the scattering and time delay operators can be read off. Using the index theorem approach, a Levinson theorem is proved which also holds in presence of embedded eigenvalues and threshold singularities.Comment: Minor errors and misprints corrected; new result on absense of embedded eigenvalues for potential scattering; to appear in RM

Random Dirac operators with time-reversal symmetry

Quasi-one-dimensional stochastic Dirac operators with an odd number of channels, time reversal symmetry but otherwise efficiently coupled randomness are shown to have one conducting channel and absolutely continuous spectrum of multiplicity two. This follows by adapting the criteria of Guivarch-Raugi and Goldsheid-Margulis to the analysis of random products of matrices in the group SO$^*(2L)$, and then a version of Kotani theory for these operators. Absence of singular spectrum can be shown by adapting an argument of Jaksic-Last if the potential contains random Dirac peaks with absolutely continuous distribution.Comment: parts of introduction made more precise, corrections as follow-up on referee report

Spectrum and diffusion for a class of tight-binding models on hypercubes

We propose a class of exactly solvable anisotropic tight-binding models on an infinite-dimensional hypercube. The energy spectrum is analytically computed and is shown to be fractal and/or absolutely continuous according to the value hopping parameters. In both cases, the spectral and diffusion exponents are derived. The main result is that, even if the spectrum is absolutely continuous, the diffusion exponent for the wave packet may be anything between 0 and 1 depending upon the class of models.Comment: 5 pages Late

The scaling limit of the critical one-dimensional random Schrodinger operator

We consider two models of one-dimensional discrete random Schrodinger operators (H_n \psi)_l ={\psi}_{l-1}+{\psi}_{l +1}+v_l {\psi}_l, {\psi}_0={\psi}_{n+1}=0 in the cases v_k=\sigma {\omega}_k/\sqrt{n} and v_k=\sigma {\omega}_k/ \sqrt{k}. Here {\omega}_k are independent random variables with mean 0 and variance 1. We show that the eigenvectors are delocalized and the transfer matrix evolution has a scaling limit given by a stochastic differential equation. In both cases, eigenvalues near a fixed bulk energy E have a point process limit. We give bounds on the eigenvalue repulsion, large gap probability, identify the limiting intensity and provide a central limit theorem. In the second model, the limiting processes are the same as the point processes obtained as the bulk scaling limits of the beta-ensembles of random matrix theory. In the first model, the eigenvalue repulsion is much stronger.Comment: 36 pages, 2 figure

Upper bounds on wavepacket spreading for random Jacobi matrices

A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds on the diffusion exponents for random polymer models, coinciding with the lower bounds obtained in a prior work. The second application is an elementary argument (not using multiscale analysis or the Aizenman-Molchanov method) showing that under the condition of uniformly positive Lyapunov exponents, the moments of the position operator grow at most logarithmically in time.Comment: final version, to appear in CM

Quantum Return Probability for Substitution Potentials

We propose an effective exponent ruling the algebraic decay of the average quantum return probability for discrete Schrodinger operators. We compute it for some non-periodic substitution potentials with different degrees of randomness, and do not find a complete qualitative agreement with the spectral type of the substitution sequences themselves, i.e., more random the sequence smaller such exponent.Comment: Latex, 13 pages, 6 figures; to be published in Journal of Physics

Investigation of quantum transport by means of O(N) real-space methods

Quantum transport for different systems is investigated by developing the Kubo formula on a basis of orthogonal polynomials. Results on quantum Hall systems are presented with particular attention to metal insulator transitions and new universalities. Other potential applications of the present method for RKKY mesoscopic interaction and insight for large scale computational problems, are given.Comment: 7 pages, 8 figure

Interacting fermions in self-similar potentials

We consider interacting spinless fermions in one dimension embedded in self-similar quasiperiodic potentials. We examine generalizations of the Fibonacci potential known as precious mean potentials. Using a bosonization technique and a renormalization group analysis, we study the low-energy physics of the system. We show that it undergoes a metal-insulator transition for any filling factor, with a critical interaction that strongly depends on the position of the Fermi level in the Fourier spectrum of the potential. For some positions of the Fermi level the metal-insulator transition occurs at the non interacting point. The repulsive side is an insulator with a gapped spectrum whereas in the attractive side the spectrum is gapless and the properties of the system are described by a Luttinger liquid. We compute the transport properties and give the characteristic exponents associated to the frequency and temperature dependence of the conductivity.Comment: 18 pages, 10 EPS figure