The critical dynamics of the O(n)-symmetric relaxational models with either nonconserved (model A) or conserved order parameter (model B) are studied below the transition temperature. As a consequence of Goldstone's theorem, the transverse modes are massless, implying infrared divergences in the theory along the entire coexistence curve. These Goldstone singularities can be treated within the field-theoretical formulation of the dynamical renormalization group by using the generalized regularization scheme as introduced by Amit and Goldschmidt, which has already been applied on the statics of the ${\mathrm{\ensuremath{\varphi}}}^{4}$ model below ${\mathit{T}}_{\mathit{c}}$ by Lawrie. We extend the formalism in several respects: (i) we generalize it to dynamical phenomena, (ii) taking advantage of the fact that the theory is exactly treatable in the coexistence limit, we do not use the \ensuremath{\epsilon} expansion; (iii) the flow equations are solved numerically, thus allowing for a detailed description of the crossover from the critical isotropic Heisenberg fixed point to the infrared-stable coexistence fixed point. We calculate the static susceptibilities as well as the dynamical correlation functions for models A and B within the complete crossover region, identifying the asymptotic coexistence anomalies and also a pronounced intermediate minimum of the effective critical exponents. Furthermore, the longitudinal dynamical correlation function ${\mathit{G}}_{\mathit{L}}$ (q,\ensuremath{\omega}) displays an anomalous line shape.The critical dynamics of the O(n)-symmetric relaxational models with either nonconserved (model A) or conserved order parameter (model B) are studied below the transition temperature. As a consequence of Goldstone's theorem, the transverse modes are massless, implying infrared divergences in the theory along the entire coexistence curve. These Goldstone singularities can be treated within the field-theoretical formulation of the dynamical renormalization group by using the generalized regularization scheme as introduced by Amit and Goldschmidt, which has already been applied on the statics of the ${\mathrm{\ensuremath{\varphi}}}^{4}$ model below ${\mathit{T}}_{\mathit{c}}$ by Lawrie. We extend the formalism in several respects: (i) we generalize it to dynamical phenomena, (ii) taking advantage of the fact that the theory is exactly treatable in the coexistence limit, we do not use the \ensuremath{\epsilon} expansion; (iii) the flow equations are solved numerically, thus allowing for a detailed description of the crossover from the critical isotropic Heisenberg fixed point to the infrared-stable coexistence fixed point. We calculate the static susceptibilities as well as the dynamical correlation functions for models A and B within the complete crossover region, identifying the asymptotic coexistence anomalies and also a pronounced intermediate minimum of the effective critical exponents. Furthermore, the longitudinal dynamical correlation function ${\mathit{G}}_{\mathit{L}}$(q,\ensuremath{\omega}) displays an anomalous line shape.

Physical review. B, Condensed matterAug 1, 199236 citations

Lindblad dissipative dynamics in the presence of phase coexistence

Andrea Kazemi Nava, Michele Fabrizio

We investigate the dissipative dynamics yielded by the Lindblad equation within the coexistence region around a first-order phase transition. In particular, we consider an exactly solvable, fully connected quantum Ising model with $n$ -spin exchange ( $n>2$ )---the prototype of quantum first-order phase transitions---and several variants of the Lindblad equations. We show that physically sound results, including exotic nonequilibrium phenomena such as the Mpemba effect, can be obtained only when the Lindblad equation involves jump operators defined for each of the coexisting phases, whether stable or metastable.We investigate the dissipative dynamics yielded by the Lindblad equation within the coexistence region around a first-order phase transition. In particular, we consider an exactly solvable, fully connected quantum Ising model with $n$-spin exchange ($n>2$)---the prototype of quantum first-order phase transitions---and several variants of the Lindblad equations. We show that physically sound results, including exotic nonequilibrium phenomena such as the Mpemba effect, can be obtained only when the Lindblad equation involves jump operators defined for each of the coexisting phases, whether stable or metastable.

arXiv:1905.12029Physical review. B./Physical review. BSep 3, 2019100 citations

Groups as dynamical models

E. C. G. Sudarshan

Foundations of PhysicsApr 1, 19950 citations

Relational Coexistence Theory (TCR): Foundational Ontology for Quantum and Cosmological Phenomena

Pietro Curatola

Abstract The ”Teoria della Coesistenza Relazionale” (TCR, Relational Coexistence Theory) proposes an ontological framework in which spacetime R is not the primary level of reality, but emerges from a more fundamental relational domain R′. Within this perspective, quantum and cosmological phenomena commonly treated as independent such as entanglement, decoherence, cosmic expansion, and the arrow of time are reinterpreted as different manifestations of the same underlying relational dynamics. The present work is devoted to the definition of the ontological assumptions and axiomatic structure of the TCR. In particular, it introduces the concepts of relational coexistence and emergence as the foundational elements from which physical phenomena in spacetime are derived. The aim of this study is not to provide an empirical validation of the framework, but to establish its internal coherence, conceptual consistency, and explanatory scope at the level of fundamental ontology. This work does not aim at providing a complete physical model or immediate empirical validation, but at establishing a coherent ontological and axiomatic framework within the scope of foundational physics.Abstract The ”Teoria della Coesistenza Relazionale” (TCR, Relational Coexistence Theory) proposes an ontological framework in which spacetime R is not the primary level of reality, but emerges from a more fundamental relational domain R′. Within this perspective, quantum and cosmological phenomena commonly treated as independent such as entanglement, decoherence, cosmic expansion, and the arrow of time are reinterpreted as different manifestations of the same underlying relational dynamics. The present work is devoted to the definition of the ontological assumptions and axiomatic structure of the TCR. In particular, it introduces the concepts of relational coexistence and emergence as the foundational elements from which physical phenomena in spacetime are derived. The aim of this study is not to provide an empirical validation of the framework, but to establish its internal coherence, conceptual consistency, and explanatory scope at the level of fundamental ontology. This work does not aim at providing a complete physical model or immediate empirical validation, but at establishing a coherent ontological and axiomatic framework within the scope of foundational physics.

Mar 2, 20260 citations

From Classical Stochastic to Monitored Quantum Dynamics: Dynamical Phase Coexistence in East Circuit Models

Marcel Cech, Johan du Buisson, Cecilia De Fazio +2 more

Kinetically constrained models have been widely studied in the context of glass formers and non-equilibrium statistical mechanics. Although their simple local rules often result in structureless static properties, their dynamics exhibit intricate emergent phenomena. In this work, we investigate monitored quantum circuit models that interpolate between classical stochastic and unitary quantum dynamics. For any finite measurement strength, the measurement records provide an experimentally accessible probe of the emergence of dynamical phases. By interpreting space-time resolved records as microstates of a fictitious 1+1D spin system, we employ thermodynamic concepts that allow us to investigate the dynamical coexistence between an active and inactive phase. We combine insights from classical stochastic dynamics and numerical simulations of monitored quantum dynamics to investigate different signatures of this dynamical phase coexistence as the measurement strength is varied. Our results shed light on the persistence of dynamical phase coexistence in the quantum regime, offering insights into future experimental studies of complex many-body dynamics in quantum simulators.Kinetically constrained models have been widely studied in the context of glass formers and non-equilibrium statistical mechanics. Although their simple local rules often result in structureless static properties, their dynamics exhibit intricate emergent phenomena. In this work, we investigate monitored quantum circuit models that interpolate between classical stochastic and unitary quantum dynamics. For any finite measurement strength, the measurement records provide an experimentally accessible probe of the emergence of dynamical phases. By interpreting space-time resolved records as microstates of a fictitious 1+1D spin system, we employ thermodynamic concepts that allow us to investigate the dynamical coexistence between an active and inactive phase. We combine insights from classical stochastic dynamics and numerical simulations of monitored quantum dynamics to investigate different signatures of this dynamical phase coexistence as the measurement strength is varied. Our results shed light on the persistence of dynamical phase coexistence in the quantum regime, offering insights into future experimental studies of complex many-body dynamics in quantum simulators.

quant-pharXiv:2603.18227Mar 20, 20260 citations

{\mathit{T}}_{\mathit{c}}

by Lawrie. We extend the formalism in several respects: (i) we generalize it to dynamical phenomena, (ii) taking advantage of the fact that the theory is exactly treatable in the coexistence limit, we do not use the \ensuremath{\epsilon} expansion; (iii) the flow equations are solved numerically, thus allowing for a detailed description of the crossover from the critical isotropic Heisenberg fixed point to the infrared-stable coexistence fixed point. We calculate the static susceptibilities as well as the dynamical correlation functions for models A and B within the complete crossover region, identifying the asymptotic coexistence anomalies and also a pronounced intermediate minimum of the effective critical exponents. Furthermore, the longitudinal dynamical correlation function

{\mathit{G}}_{\mathit{L}}

(q,\ensuremath{\omega}) displays an anomalous line shape.

n

-spin exchange (

n>2

)---the prototype of quantum first-order phase transitions---and several variants of the Lindblad equations. We show that physically sound results, including exotic nonequilibrium phenomena such as the Mpemba effect, can be obtained only when the Lindblad equation involves jump operators defined for each of the coexisting phases, whether stable or metastable.