Superradiant phase transition in complex networks

Abstract

In this work we consider a superradiant phase transition problem for the Dicke-Ising model, which generalizes the Dicke and Ising models for annealed complex networks presuming spin-spin interaction. The model accounts the interaction between a spin (two-level) system and external classical (magnetic) and quantized (transverse) fields. We examine regular, random, and scale-free network structures characterized by the delta-function, random (Poisson), and power-law exponent degree distributions, respectively. To describe paramagnetic (PM) - ferromagnetic (FM) and superradiant (SR) phase transitions we introduce two order parameters: the total weighted spin z-component and the normalized transverse field amplitude, which correspond to the spontaneous magnetization in z and x directions, respectively. Due to the interplay between the spin interaction and the finite size effects in the networks we first elucidate novel features of the SR state in the presence of the PM-FM phase transition. We reveal that the critical temperature of the SR phase transition grows monotonically from some certain value that corresponds to the critical number of nodes. For the scale-free networks we find that this critical temperature rises with the degree exponent increase accompanied both by establishing spontaneous magnetization in a quantum transverse field and vanishing of the collective spin component in z direction. In addition, we establish the conditions for the network parameters to obtain a quantum phase transition in the spin system when the critical temperature approaches zero. The fundamental features, which involve critical values of the classical and quantum field parameters, are discussed for the occurrence of the superradiance phase in this limit.

References in corpus (34)

• Statistical mechanics of complex networks
• Critical phenomena in complex networks
• Community detection in networks: A user guide
• Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems
• Bose-Einstein condensation in complex networks
• Chaos and the Quantum Phase Transition in the Dicke Model
• Natural and artificial atoms for quantum computation
• Modeling echo chambers and polarization dynamics in social networks
• Ising Model on Networks with an Arbitrary Distribution of Connections
• Ferromagnetic ordering in graphs with arbitrary degree distribution
• Ferromagnetic Phase Transition in Barabasi-Albert Networks
• Mean field solution of the Ising model on a Barabasi-Albert network
• Bose condensation of cavity polaritons beyond the linear regime: the thermal equilibrium of a model microcavity
• Dicke Superradiance in Solids
• Phase transitions in social impact models of opinion formation
• Photon localization and Dicke superradiance in atomic gases
• Quantifying echo chamber effects in information spreading over political communication networks
• Generation and controllable switching of superradiant and subradiant states in a 10-qubit superconducting circuit
• Some remarks on 'superradiant' phase transitions in light-matter systems
• Super-radiant phase transition in superconducting circuit in thermal equilibrium
• Supercondutor-Insulator Transition on Annealed Complex Networks
• Phase transitions in an Ising chain interacting with a single mode cavity field
• First-order super-radiant phase transitions in a multi-qubit--cavity system
• Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks
• Theory of Bose-Einstein condensation and superfluidity of two-dimensional polaritons in an in-plane harmonic potential
• "Social Laser": Action Amplification by Stimulated Emission of Social Energy
• Statistical properties of the quantum internet
• Critical behavior of the Ising model in annealed scale-free networks
• Enhancement of Tc in the Superconductor-Insulator Phase Transition on Scale-Free Networks
• Revealing and exploiting hierarchical material structure through complex atomic networks
• Strongly localized polaritons in an array of trapped two-level atoms interacting with a light field
• Polariton Condensation and Lasing
• Lasing and high temperature phase transitions in atomic systems with dressed state polaritons
• A Long-Range Ising Model of a Barabási-Albert Network

Cited by in corpus (2)

• Open systems, quantum probability and logic for quantum-like modeling in biology, cognition, and decision making
• Continuous Dissipative Phase Transitions without Symmetry Breaking