Universal and non-universal amplitude ratios for scaling corrections on Ising strips

We consider strips of Ising spins at criticality. For strips of width $N$ sites, subdominant (additive) finite-size corrections to scaling are assumed to be of the form $a_k/N^k$ for the free energy, and $b_k/N^k$ for inverse correlation length, with integer values of $k$. We investigate the set $\{a_k,b_k\}$ ($k \geq 2$) by exact evaluation and numerical transfer-matrix diagonalization techniques, and their changes upon varying anisotropy of couplings, spin quantum number $S$, and (finite) interaction range, in all cases for both periodic (PBC) and free (FBC) boundary conditions across the strip. We find that the coefficient ratios $b_k/a_k$ remain constant upon varying coupling anisotropy for $S=1/2$ and first-neighbor couplings, for both PBC and FBC (albeit at distinct values in either case). Such universal behavior is not maintained upon changes in $S$ or interaction range.Comment: 9 pages, 4 figures; published versio

Near-horizon modes and self-adjoint extensions of the Schroedinger operator

We investigate the dynamics of scalar fields in the near-horizon exterior region of a Schwarzschild black hole. We show that low-energy modes are typically long-living and might be considered as being confined near the black hole horizon. Such dynamics are effectively governed by a Schroedinger operator with infinitely many self-adjoint extensions parameterized by $U(1)$, a situation closely resembling the case of an ordinary free particle moving on a semiaxis. Even though these different self-adjoint extensions lead to equivalent scattering and thermal processes, a comparison with a simplified model suggests a physical prescription to chose the pertinent self-adjoint extensions. However, since all extensions are in principle physically equivalent, they might be considered in equal footing for statistical analyses of near-horizon modes around black holes. Analogous results hold for any non-extremal, spherically symmetric, asymptotically flat black hole.Comment: 10 pages, 1 fig, contribution submitted to the volume "Classical and Quantum Physics: Geometry, Dynamics and Control. (60 Years Alberto Ibort Fest)" Springer (2018

Localization in the Rindler Wedge

One of the striking features of QED is that charged particles create a coherent cloud of photons. The resultant coherent state vectors of photons generate a non-trivial representation of the localized algebra of observables that do not support a representation of the Lorentz group: Lorentz symmetry is spontaneously broken. We show in particular that Lorentz boost generators diverge in this representation, a result shown also in [1] (See also [2]). Localization of observables, for example in the Rindler wedge, uses Poincar\'e invariance in an essential way [3]. Hence in the presence of charged fields, the photon observables cannot be localized in the Rindler wedge. These observations may have a bearing on the black hole information loss paradox, as the physics in the exterior of the black hole has points of resemblance to that in the Rindler wedge.Comment: 11 page