相关论文: Quantum hamiltonians and prime numbers

Black holes are inevitable mathematical outcome of spacetime-energy coupling in general relativity. Currently these objects are of vital importance for understanding numerous phenomena in astrophysics and cosmology. However, neither theory…

[Remark: Much more natural and important models are studied in arXiv:1405.2083. Furthermore, the physical picture given there is much more complete.] The quantum N-portrait -- black holes pictured as Bose-Einstein condensates -- is studied…

We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data…

Two effectively one-dimensional parallel coupled Bose-Einstein condensates in the presence of external potentials are studied. The system is modelled by linearly coupled Gross-Pitaevskii equations. In particular, the interactions of…

Some basic features of black-hole statistical mechanics are investigated, assuming that black holes respect the principles of quantum mechanics. Care is needed in defining an entropy S_bh corresponding to the number of microstates of a…

We describe some studies related to the frequency of prime values of integer polynomials.

We study odd-parity perturbations about static and spherically symmetric black hole solutions with a linearly time-dependent scalar field in higher-order scalar-tensor theories. In particular, we consider stealth Schwarzschild and stealth…

We discuss the problem of the quantization and dynamic evolution of a scalar free field in the interior of a Schwarzschild black hole. A unitary approach to the dynamics of the quantized field is proposed: a time-dependent Hamiltonian…

We investigate the formation of primordial black holes in curvaton models of inflation, where the curvature perturbation is not only generated by the inflaton but also by a light scalar field (the curvaton) that decays after inflation.…

We experimentally study cosmological particle production in a two-dimensional Bose-Einstein condensate, whose density excitations map to an analog cosmology. The expansion of spacetime is realized with tunable interactions. The particle…

The study of hyperbolic binary black hole encounters yields an effective probe of the strong field regime of black holes, thus providing an additional channel to test General Relativity. We study the scattering of two black holes in…

The density density correlation function is computed for the Bogoliubov pseudoparticles created in a Bose-Einstein condensate undergoing a black hole flow. On the basis of the gravitational analogy, the method used relies only on quantum…

The theory of quadratic forms and class numbers has connections to many classical problems in number theory. Recently, class numbers have appeared in the study of black holes in string theory. We describe this connection and raise questions…

The Schinzel Hypothesis is a celebrated conjecture in number theory linking polynomial values and prime numbers. In the same vein we investigate the common divisors of values $P_1(n),\ldots, P_s(n)$ of several polynomials. We deduce this…

We investigate numerically simulated collisions between experimentally realistic Bose-Einstein condensate wavepackets, within a regime where highly populated scattering haloes are formed. The theoretical basis for this work is the truncated…

The linear alpha-prime corrections and the field redefinition ambiguities are studied for half-BPS singular backgrounds representing a wrapped fundamental string. It is showed that there exist schemes in which the inclusion of all the…

We observe spontaneous Hawking radiation, stimulated by quantum vacuum fluctuations, emanating from an analogue black hole in an atomic Bose-Einstein condensate. Correlations are observed between the Hawking particles outside the black hole…

We study polytopes associated to factorisations of prime powers. These polytopes have explicit descriptions either in terms of their vertices or as intersections of closed halfspaces associated to their facets. We give formulae for their…

By applying Rosen's quantization approach to the historical Oppenheimer and Snyder gravitational collapse and by setting the constraints for the formation of the Schwarzschild black hole (SBH), in a previous paper [1] two of the Authors (CC…

Quantum aspects of black holes represent an important testing ground for a theory of quantum gravity. The recent success of string theory in reproducing the Bekenstein-Hawking black hole entropy formula provides a link between general…