相关论文: Quantum hamiltonians and prime numbers

The study investigates the gravitational scattering amplitude between two Schwarzschild black holes in a two to two interaction, focusing on the Second Post-Minkowskian correction (2 PM). Analyzing contributions from box and cross-box…

Inspired by the recent conjecture that black holes are condensates of gravitons, we investigate a simple model for the black hole degrees of freedom that is consistent both from the point of view of Quantum mechanics and of General…

Motivated by the known mathematical and physical problems arising from the current mathematical formalization of the physical spatio-temporal continuum, as a substantial technical clarification of our earlier attempt, the aim in this paper…

We study first order fluctuations of a relativistic membrane in the curved background of a black hole. The zeroth-order solution corresponds to a spherical membrane tightly covering the event horizon. We obtain a massive Klein-Gordon…

In this Letter we set up a suggestive number theory interpretation of a quantum ladder system made of N coupled chains of spin 1/2. Using the hard-core boson representation and a leg-Hamiltonian made of a magnetic field and a hopping term,…

Here we discuss the two dimensional quantum electrodynamics in curved space-time, especially in the background of some black holes. We first show the existence of some new quantum mechanical solution which has interesting properties. Then…

Primordial black holes (PBHs), if they exist, may collide with and be captured by neutron stars. We adopt a relativistic point-mass approximation to study this capture, the subsequent confinement of the PBH of mass $m$ inside the neutron…

Transmission probabilities of the scattering problem with a position dependent mass are studied. After sketching the basis of the theory, within the context of the Schr\"{o}dinger equation for spatially varying effective mass, the simplest…

This paper is devoted to the study of the statistical mechanics of trapped gravitons obtained by 'trapping' a spherical gravitational wave in a box. As a consequence, a discrete spectrum dependent on the Legendre index $\ell$ similar to the…

Here, we present a review about the quantization of spherically-symmetric spacetimes adopting loop quantum gravity techniques. Several models that have been studied so far share similar properties: the resolution of the classical…

This review describes quantum systems of bosonic particles moving on a lattice. These models are relevant in statistical physics, and have natural ties with probability theory. The general setting is recalled and the main questions about…

The simplest possible equation for Hawking radiation, and other black hole radiated power is derived in terms of black hole density. Black hole density also leads to the simplest possible model of a gas of elementary constituents confined…

Analog models of black holes have unequivocally proven to be extremely beneficial in providing critical information regarding black hole spectroscopy, superradiance, quantum phenomena and most importantly Hawking radiation and black hole…

We study the Frobenius problem for certain k-tuplets, which include prime k-tuplets, in particular prime triplets and prime quadruplets. Moreover, we analyze some properties of the numerical semigroups associated with these tuplets.

It is known how to choose initial data for Einstein's equations describing an arbitrary number of black holes at a moment of time symmetry. This idea has been used to give insight into the cosmological averaging problem. We study the local…

We analyze terms subleading to Rutherford in the $S$-matrix between black hole and probes of successively high energies. We show that by an appropriate choice of the probe one can read off the quantum state of the black hole from the…

The Hawking effect can be rederived in terms of two-point functions and in such a way that it makes it possible to estimate, within the conventional semiclassical theory, the contribution of ultrashort distances to the Planckian spectrum.…

The possibility that primordial black holes (PBHs) are the dark matter (or a fraction thereof) has attracted much attention recently. Their spatial clustering is a fundamental property which determines, among others, whether current…

The primordial black hole (PBH) abundance evaluated by the conventional Press-Schechter (PS) probability distribution is shown to be equivalent to the high-peak limit of a special point-like peak statistics via unphysical dimensionality…

The entropy of the Reissner-N\"{o}rdstrom black hole is studied within the context of a brane-world scenario. Such a black hole is a solution of the Einstein field equations on the brane, possessing a tidal charge which is a reflection of…