Related papers: Boundary conditions and the entropy bound
We derive the first positivity bounds for low-energy Effective Field Theories (EFTs) that are not invariant under Lorentz boosts. "Positivity bounds" are the low-energy manifestation of certain fundamental properties in the UV -- to date…
We study the spectrum of the Helmholtz equation in a two-dimensional infinite waveguide, containing a weak heterogeneity localized at an internal point, and obeying Dirichlet boundary conditions at its border. We prove that, when the…
The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables can not be predicted simultaneously. In quantum information theory, this principle can be…
We consider whether L = limsup_{n to infty} n ||T^{n+1}-T^n|| < infty implies that the operator T is power bounded. We show that this is so if L<1/e, but it does not necessarily hold if L=1/e. As part of our methods, we improve a result of…
We study the spectrum of the Laplacian on the hemisphere with Robin boundary conditions. It is found that the eigenvalues fall into small clusters around the Neumann spectrum, and satisfy a Szeg\H{o} type limit theorem. Sharp upper and…
We show that a surface term should be added to the Einstein-Hilbert action in order to properly describe quantum transitions occurring around a black hole. The introduction of this boundary term has been advocated by Teitelboim and…
The aim of the present dissertation is to analyze the meaning of the entropy bounds of the holographic sector once tested for statistical ensembles of particles, in order to deeper investigate the nature of these constraints and their…
Simple arguments related to the entropy of black holes strongly constrain the spectrum of the area operator for a Schwarzschild black hole in loop quantum gravity. In particular, this spectrum is fixed completely by the assumption that the…
The various entropy bounds that exist in the literature suggest that spacetime is fundamentally discrete, and hint at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered,…
We show that the relative entropy between the reduced density matrix of the vacuum state in some region $A$ and that of an excited state created by a unitary operator localized at a small distance $\ell$ of a boundary point $p$ is…
Let $B$ be a spatial region of width $2R$ and $\Phi$ a Klein-Gordon wave packet localized in $B$ at time zero. We show the inequality $S \leq 2\pi R E$; here, $S$ is the entropy of $\Phi$ contained in a region $B$, and $E$ is the energy…
We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any…
A simple argument shows that negative energy cannot be isolated far away from positive energy in a conformal field theory and strongly constrains its possible dispersal. This is also required by consistency with the Bekenstein bound written…
Several arguments suggest that the entropy density at high energy density $\rho$ should be given by the expression $s=K\sqrt{\rho/G}$, where $K$ is a constant of order unity. On the other hand the covariant entropy bound requires that the…
We consider how the energy can be stored in the boundary of spacetime, in particular in a spherical bubble that can be made by a quantum gravitational process. Our calculation is performed within the framework of classical Einstein gravity…
Boundary conditions in confined geometries and measurement interactions in quantum mechanics share a common structural role: both select a preferred basis by determining which states are compatible with the imposed constraint. This paper…
We analyze how a short distance boundary condition for the Schrodinger equation must change as a function of the boundary radius by imposing the physical requirement of phase shift independence on the boundary condition. The resulting…
We calculate the energy of the state closest to threshold for two and three identical, spinless particles confined to a cubic spatial volume with periodic boundary conditions and with zero total momentum in the finite-volume frame. The…
The thermodynamic properties of the XXZ spin chain with integrable open boundary conditions at the gaped region (i.e., the anisotropic parameter $\eta$ being a real number) are investigated.It is shown that the contribution of the…
We consider weak solutions of the inhomogeneous non-cutoff Boltzmann equation in a bounded domain with any of the usual physical boundary conditions: in-flow, bounce-back, specular-reflection and diffuse-reflection. When the mass, energy…