scholarly journals Dynamical Phase Transitions for Flows on Finite Graphs

2020 ◽  
Vol 181 (6) ◽  
pp. 2353-2371
Author(s):  
Davide Gabrielli ◽  
D. R. Michiel Renger
Keyword(s):  
Large Deviation ◽  
Time Window ◽  
Scaling Limit ◽  
Sufficient Conditions ◽  
Finite Graph ◽  
Dynamical Phase Transition ◽  
Dynamical Phase ◽  
Hydrodynamic Scaling ◽  
Deviation Rate ◽  
Dynamical Phase Transitions

AbstractWe study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate functional of the average flow is given by a variational formulation involving paths of the density and flow. We give sufficient conditions under which the large deviations of a given time averaged flow is determined by paths that are constant in time. We then consider a class of models on a discrete ring for which it is possible to show that a better strategy is obtained producing a time-dependent path. This phenomenon, called a dynamical phase transition, is known to occur for some particle systems in the hydrodynamic scaling limit, which is thus extended to the setting of a finite graph.

DYNAMICAL PHASE TRANSITIONS ON COMB LATTICES

1992 ◽  
Vol 06 (29) ◽  
pp. 1887-1891
Author(s):  
D. CASSI ◽  
S. REGINA
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Critical Point ◽  
Critical Exponents ◽  
Analytical Techniques ◽  
Spectral Dimension ◽  
Dynamical Phase Transition ◽  
Dynamical Phase ◽  
Dynamical Phase Transitions ◽  
Bethe Lattices

We study by analytical techniques the dynamical phase transition between recursive and transient regime induced on comb lattices by a topological bias. The critical exponents are expressed as functions of the intrinsic dimensions of these structures. In particular we show that, unlike what happens on Bethe lattices, it takes in general two different exponents to characterize the approach to the critical point from the recursive phase and from the transient one. These exponents depend respectively on the connectivity and on the spectral dimension.

scholarly journals Probing dynamical phase transitions with a superconducting quantum simulator

2020 ◽  
Vol 6 (25) ◽  
pp. eaba4935
Author(s):  
Kai Xu ◽  
Zheng-Hang Sun ◽  
Wuxin Liu ◽  
Yu-Ran Zhang ◽  
Hekang Li ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Quantum Limit ◽  
Single Shot ◽  
Many Body ◽  
Dynamical Phase Transition ◽  
Dynamical Phase ◽  
Dynamical Phase Transitions ◽  
Quantum Simulator ◽  
Many Body Systems ◽  
Loschmidt Echo

Nonequilibrium quantum many-body systems, which are difficult to study via classical computation, have attracted wide interest. Quantum simulation can provide insights into these problems. Here, using a programmable quantum simulator with 16 all-to-all connected superconducting qubits, we investigate the dynamical phase transition in the Lipkin-Meshkov-Glick model with a quenched transverse field. Clear signatures of dynamical phase transitions, merging different concepts of dynamical criticality, are observed by measuring the nonequilibrium order parameter, nonlocal correlations, and the Loschmidt echo. Moreover, near the dynamical critical point, we obtain a spin squeezing of −7.0 ± 0.8 dB, showing multipartite entanglement, useful for measurements with precision fivefold beyond the standard quantum limit. On the basis of the capability of entangling qubits simultaneously and the accurate single-shot readout of multiqubit states, this superconducting quantum simulator can be used to study other problems in nonequilibrium quantum many-body systems, such as thermalization, many-body localization, and emergent phenomena in periodically driven systems.

scholarly journals Analytical investigation of self-organized criticality in neural networks

2013 ◽  
Vol 10 (78) ◽  
pp. 20120558 ◽  
Author(s):  
Felix Droste ◽  
Anne-Ly Do ◽  
Thilo Gross
Keyword(s):  
Neural Networks ◽  
Stochastic Dynamics ◽  
Analytical Investigation ◽  
Homeostatic Plasticity ◽  
Dynamical Phase Transition ◽  
Discrete State ◽  
Dynamical Phase ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Activity Dependent

Dynamical criticality has been shown to enhance information processing in dynamical systems, and there is evidence for self-organized criticality in neural networks. A plausible mechanism for such self-organization is activity-dependent synaptic plasticity. Here, we model neurons as discrete-state nodes on an adaptive network following stochastic dynamics. At a threshold connectivity, this system undergoes a dynamical phase transition at which persistent activity sets in. In a low-dimensional representation of the macroscopic dynamics, this corresponds to a transcritical bifurcation. We show analytically that adding activity-dependent rewiring rules, inspired by homeostatic plasticity, leads to the emergence of an attractive steady state at criticality and present numerical evidence for the system's evolution to such a state.

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