Long-Range Correlations in Classical and Quantum Systems

Xi Li, SongJJ, XingYZ +1 more

Using the classical quantization way in a two dimensional integrable system and quantized energies periodic orbits correspondence relationship, the long range correlation among the quantum lavels has been discussed in detail. Making use of Berry Tabor trace formula, the quantization conditions of the action of the periodic orbits in two dimensional integrable systems have been obtained. Furthermore, considering the periodicity conditions for the periodic orbits on reasonable torus, the correspondence relations between quantum levels and classical periodic orbits in the two dimensional uncoupled oscillators have been established. It is also shown that there exist the long range correlations among these quantum levels which correspond to the group of the classical periodic orbits with same topology M (M 1,M 2) . To concert state the new points, an example has been given.

Hermann Haken

Paweł Cieśliński, Wiesław Laskowski

Long-range interacting quantum systems exhibit interesting phenomena beyond the nearest-neighbours regime. Such interactions can reach further separated particles and change the behaviour of many-body correlations. Here, we analyse their structure in the antiferromagnetic long-range interaction transverse field Ising model with power-law interactions decaying as $1/r^α$. We examine the spatial behaviour of basis-independent total multipartite correlations, called sector lengths $S_k$, of its ground state in the vicinity of critical points for different interaction exponents $α$ and fixed system size. These correlation functions were shown to indicate entanglement and the existence of local realistic models, allowing us to make claims about the Bell nonlocality and entanglement in the system. We further investigate them in the context of non-stabiliserness, often referred to as quantum magic, which holds information on their classical simulability and usefulness for quantum computation. We evaluate R{é}nyi stabiliser entropy near and outside the criticality and show that cumulative magic, up to the critical point, increases with $α$ for all of the examined system sizes. Our results provide new insights into the interplay between the long-range interactions, observable non-classical phenomena and their classical simulability.

Guido Bellomo, A. P. Majtey, Angel Ricardo Plastino +1 more

Samuel Fernández-Lorenzo, Jacob Dunningham, Diego Porras

The Heisenberg scaling is typically associated with nonclassicality and entanglement. In this work, however, we discuss how classical long-range correlations between lattice sites in many-body systems may lead to a $1/N$ scaling in precision with the number of probes in the context of quantum optical dissipative systems. In particular, we show that networks of coupled single qubit lasers can be mapped onto a classical $XY$ model, and a Heisenberg scaling with the number of sites appears when estimating the amplitude and phase of a weak periodic driving field.

Charles Radin