Quantum gravity on the black hole horizon

We study scattering on the black hole horizon in a partial wave basis, with an impact parameter of the order of the Schwarzschild radius or less. This resembles the strong gravity regime where quantum gravitational effects appear. The scattering is governed by an infinite number of virtual gravitons exchanged on the horizon. Remarkably, they can all be summed non-perturbatively in ħ and γ ∼ MPl/MBH. These results generalise those obtained from studying gravitational backreaction. Unlike in the eikonal calculations in flat space, the relevant centre of mass energy of the collisions is not necessarily Planckian; instead it is easily satisfied, s » γ2$$ {M}_{\mathrm{Pl}}^2 $$ M Pl 2 , for semi-classical black holes. The calculation lends further support to the scattering matrix approach to quantum black holes, and is a second-quantised generalisation of the same.

Black holes, quantum chaos, and the Riemann hypothesis

Quantum gravity is expected to gauge all global symmetries of effective theories, in the ultraviolet. Inspired by this expectation, we explore the consequences of gauging CPT as a quantum boundary condition in phase space. We find that it provides for a natural semiclassical regularisation and discretisation of the continuous spectrum of a quantum Hamiltonian related to the Dilation operator. We observe that the said spectrum is in correspondence with the zeros of the Riemann zeta and Dirichlet beta functions. Following ideas of Berry and Keating, this may help the pursuit of the Riemann hypothesis. It strengthens the proposal that this quantum Hamiltonian captures the near horizon dynamics of the scattering matrix of the Schwarzschild black hole, given the rich chaotic spectrum upon discretisation. It also explains why the spectrum appears to be erratic despite the unitarity of the scattering matrix.

Phonons transmission through atomic interface connecting two semi-infinite 2D lattices with different meshes

A calculation of the phonon contribution to the coherent transport between two-dimensional (2D) lattices is presented in this paper. The model structure is obtained by the juxtaposition of semi-infinites square ([Formula: see text] and triangular ([Formula: see text] leads, which thus define the nanojunction [Formula: see text]/[Formula: see text] and its inverse [Formula: see text]/[Formula: see text]. We determine, numerically and by simulation, the 2D interface observables for different values of masses and elastic coupling in the nanojunction zone. The local dynamics and atomic nanojunction response to the microscopic changes, in the interfacial domain, are subjects to our investigation. The theoretical formalism based on the matching technique is applied to describe the lattice dynamics and the evanescent phonon modes, in the two studied 2D interfaces. We mainly analyze the vibration spectra, the coherent phonon transmission/reflection and the phononic transmittance through the interface, as elements of a Landauer–Büttiker type scattering matrix. The obtained results show that the nanojunction domain is an effective phonon splitter and suggest that its characteristics may be controlled by varying its nanometric parameters. The observed fluctuations are due to the coherent coupling between continuum modes and the phonons’ discrete states induced by the connected atomic sites.