Systems and Subsystems, Multiple Particles

P. Céspedes, Federico Holik, A. P. Majtey

While the concept of entanglement for distinguishable particles is well established, defining entanglement and nonlocality in systems of indistinguishable particles, which require the use of the (anti)symmetrization postulate, remains challenging, and multiple approaches have been proposed to address this issue. In this work we study the problem of detecting genuine tripartite entanglement among systems of indistinguishable bosons. A genuine entangled state is one that cannot be separable under any bipartition, where separability in the indistinguishable regime is defined by the existence of single-particle properties within each subsystem, without the possibility of knowing which property belongs to which subsystem. We use an algorithm that allows us to search for these single-particle properties and consequently rank states according to their degree of separability. In particular, we introduce a state of indistinguishable bosons with properties analogous to those of the standard Greenberger-Horne-Zeilinger state.

Russell K. Hobbie, Bradley John Roth

Guoxin Yang

On October 21, 2020, the invention “A multi-level and multi-dimensional dynamic system motion model construction and simulation method” was accepted by the State Intellectual Property Office of China. Through the construction and simulation of the motion model of a multi-level and multi-dimensional dynamic system, the motion trajectory of the motion factors in each dynamic system is nested and substituted into the next dynamic subsystem to establish the motion trajectory of the motion factors in its dynamic subsystem. Until the dynamic trajectory model of the motion factors in the minimum dynamic subsystem is obtained, the motion model of a multi-level and multi-dimensional dynamic system is constructed, which reveals the motion law that can unify the microscopic particles and all the motion factors in the macroscopic universe. Multiple dynamic systems are entangled systems. If the entanglement properties are obtained not by ``absolutely simultaneous'' measurements of the entangled particles, it just proves that there is no non-local hyper-distance action.

Walter E Thirring

Eugen Fick, Günter Sauermann

Quntao Zhuang, Biao Wu

A large class of isolated quantum systems in a pure state can equilibrate and serve as a heat bath. We show that, once equilibrium is reached, any of its subsystems, which are much smaller than the isolated system, can be thermalized such that the subsystem is governed by the Gibbs distribution. Within this theoretical framework, the celebrated superposition principle of quantum mechanics leads to a prediction of a thermalized subsystem with multiple temperatures when the isolated system is in a superposition state of energy eigenstates of multiple distinct energy scales. This multiple-temperature state is at equilibrium, completely different from a non-equilibrium state that has multiple temperatures at different parts. Feasible experimental schemes, in particular with ultra-cold atoms, to verify this prediction are discussed.