Quasi Kepler's third law for quantum many-body systems

Abstract

The Kepler's third law is a relation between the period and the energy of two classical particles interacting via a gravitational potential. Recent works showed that this law could be extended, at least approximately, to classical three-body systems, or even many-body classical systems. So, a classical quasi Kepler's third law seems to exist. In this paper, approximate analytical solutions are computed for quantum self-gravitating particles with different masses. The results give strong indications in favor of the existence of a quasi Kepler's third law for such systems. The relevance of the proposal is checked with accurate numerical data for the ground state of self-gravitating identical bosons and with numerical estimations for systems with identical particles plus a different one. Connections between the quantum and classical systems are discussed.

arXiv commentSome explanations and references added. To appear in Eur. J. Phys. Plus

References in corpus (15)

• More than six hundreds new families of Newtonian periodic planar collisionless three-body orbits
• The 1223 new periodic orbits of planar three-body problem with unequal mass and zero angular momentum
• Collisionless periodic orbits in the free-fall three-body problem
• Relativistic N-boson systems bound by pair potentials V(r_{ij}) = g(r_{ij}^2)
• The quantum N-body problem and the auxiliary field method
• Topological Dependence of Kepler's Third Law for Collisionless Periodic Three-Body Orbits with Vanishing Angular Momentum and Equal Masses
• Numerical tests of the envelope theory for few-boson systems
• Improvement of the envelope theory with the dominantly orbital state method
• Kepler's third law of n-body periodic orbits in a Newtonian gravitation field
• Periodic three-body orbits in the Coulomb potential
• Tests of the Envelope Theory in One Dimension
• Quantum support to BoHua Sun's conjecture
• Envelope Theory for Systems with Different Particles
• A conjecture on Kepler's third law of n-body periodic orbits
• Potential envelope theory and the local energy theorem

Cited by in corpus (5)

• Improvement of the Envelope Theory for Systems with Different Particles
• The envelope theory as a pedagogical tool
• Compact equations for the envelope theory
• Accuracy Tests of the Envelope Theory
• Some specific solutions to the translation-invariant $N$-body harmonic oscillator Hamiltonian