Quantum hamiltonians and prime numbers

Abstract

A short review of Schroedinger hamiltonians for which the spectral problem has been related in the literature to the distribution of the prime numbers is presented here. We notice a possible connection between prime numbers and centrifugal inversions in black holes and suggest that this remarkable link could be directly studied within trapped Bose-Einstein condensates. In addition, when referring to the factorizing operators of Pitkanen and Castro and collaborators, we perform a mathematical extension allowing a more standard supersymmetric approach

10 pages, 2 figures, accepted as a Brief Review at MPLA

References in corpus (4)

• Bose-Einstein Condensation in a Surface Micro Trap
• Gravitational lensing in spherically symmetric static spacetimes with centrifugal force reversal
• Symmetry of the Riemann Operator
• (De)Localization in the Prime Schrodinger Operator

Cited by in corpus (15)

• Physics of the Riemann Hypothesis
• H = x p with interaction and the Riemann zeros
• Quantum mechanical potentials related to the prime numbers and Riemann zeros
• Nearest neighbor spacing distribution of prime numbers and quantum chaos
• Will a physicist prove the Riemann Hypothesis?
• A quantum mechanical model of the Riemann zeros
• Heat-kernel expansion on non compact domains and a generalised zeta-function regularisation procedure
• The Riemann zeros and the cyclic Renormalization Group
• Riemann zeta zeros and prime number spectra in quantum field theory
• Hilbert-Pólya Conjecture, Zeta-Functions and Bosonic Quantum Field Theories
• On the Quantum Reconstruction of the Riemann zeros
• Wigner quantization of some one-dimensional Hamiltonians
• Polymeric quantum mechanics and the zeros of the Riemann zeta function
• Functional equations for regularized zeta-functions and diffusion processes
• Equivalence between the zero distributions of the Riemann zeta function and a two-dimensional Ising model with randomly distributed competing interactions