Quantum Scarring from TGD Point of View

Abstract

Quantum scarring (QS) and its many-body counterpart MBQS are very interesting challenges for TGD. Eigenstate thermalization hypothesis (ETH) states the time development of energy eigenstate to a superposition of large number of eigenstates with the same energy gives rise to thermalization. In MBQS the thermalization is however very slow for most states and there are states for which it it does not occur at all and the system returns to the original state periodically. Integrable systems for which the energies of the states are rational multiples of a finite number of "fundamentals" have this property. MBQS in the case considered occurs for an array containing ground state atoms and their Rydberg counterparts. In TGD framework one can consider the possibility that instead of Rydberg atoms one has pseudo Rydberg atoms having non-standard value h_eff =nh₀ of Planck constant such that h_eff =mh is true (also fractional effective principal quantum number is possible and could serve as a test for the proposal). In this framework the exchange force between valence electrons would be scaled by factor (h_eff /h)² and promote localization in turn forcing the periodic orbits. Even if this effect is not involved in the case considered, it could make possible to have dark variant of MBQS at higher temperatures.