Related papers: From Short-Range to Mean-Field Models in Quantum L…
The typical bound on parameter estimation, known as the standard quantum limit (SQL), can be surpassed by exploiting quantum resources such as entanglement. To estimate the magnetic probe field, we propose a quantum sensor based on a…
The fact that mean field theory is appropriate to describe an Ising model with long-range interactions has been already shown by Cannas and Tamarit. Although not explicited in our Letter, we have used periodic boundary conditions in all our…
In this paper we discuss in detail the nonlinear equations of the mean--field approximation and their connection to the exact many--body Schr\"odinger equation. Then we analyze the mean--field approach and the nonlinear dynamics of a…
Bi-local mean field theory is applied to one dimensional quantum liquid with long range $1/r^2$ interaction, which has exact ground state wave function. We obtain a mean field solution and an effective action which expresses a long range…
Understanding the emergence of novel collective behaviors in strongly interacting systems lies at the heart of quantum many-body physics. Valuable insight comes from examining how few-body correlations manifest in many-body systems,…
Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. Here, we prove that the entire physics of any other quantum many-body system is replicated in certain simple, "universal" spin-lattice models. We…
Ensemble inequivalence has been observed in several systems. In particular it has been recently shown that negative specific heat can arise in the microcanonical ensemble in the thermodynamic limit for systems with long-range interactions.…
In all local low-dimensional models, scaling at critical points deviates from mean field behavior -- with one possible exception. This exceptional model with ``ordinary" behavior is an inherently non-equilibrium model studied some time ago…
The Random Batch Method proposed in our previous work [Jin et al., J. Comput. Phys., 400(1), 2020] is not only a numerical method for interacting particle systems and its mean-field limit, but also can be viewed as a model of particle…
In quantum systems with a classical limit, advanced semiclassical methods provide the crucial link between phase-space structures, reflecting the distinction between chaotic, mixed or integrable classical dynamics, and the corresponding…
Discrete systems with long-range interactions are considered. Continuous medium models as continuous limit of discrete chain system are defined. Long-range interactions of chain elements that give the fractional equations for the medium…
Driven-dissipative quantum many-body systems have attracted increasing interest in recent years as they lead to novel classes of quantum many-body phenomena. In particular, mean-field calculations predict limit cycle phases, slow…
When spatial correlations are short-range, the physics of strongly correlated systems is controlled by local quantum fluctuations. In those regimes, Dynamical Mean-Field Theory can be viewed as a `compass' which provides guidance on the…
This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that…
The non-equilibrium response of a quantum many-body system defines its fundamental transport properties and how initially localized quantum information spreads. However, for long-range-interacting quantum systems little is known. We address…
Interacting particle systems are known for their ability to generate large-scale self-organized structures from simple local interaction rules between each agent and its neighbors. In addition to studying their emergent behavior, a main…
We shall present a new strategy for handling mean field limits of quantum mechanical systems. The new method is simple and effective. It is simple, because it translates the idea behind the mean field description of a many particle quantum…
One- to three-dimensional hypercubic lattices half-filled with localized particles interacting via the long-range Coulomb potential are investigated numerically. The temperature dependences of specific heat, mean staggered occupation, and…
We investigate the canonical equilibrium of systems with long-range forces in competition. These forces create a modulation in the interaction potential and modulated phases appear at the system scale. The structure of these phases…
Interactions between quantum particles, such as electrons, are the source of important effects, ranging from superconductivity, to the formation of molecular bonds, or the stability of elementary compounds at high-energies. In this article,…