Dynamical Field Theory Research Articles

Quantum dynamical field theory for nonequilibrium phase transitions in driven open systems

We develop a quantum dynamical field theory for studying phase transitions in driven open systems coupled to Markovian noise, where non-linear noise effects and fluctuations beyond semiclassical approximations influence the critical behaviour. We systematically compare the diagrammatics, the properties of the renormalization group flow and the structure of the fixed points, of the novel quantum dynamical field theory and of its semi-classical counterpart, which is employed to characterise dynamical criticality in three dimensional driven-dissipative condensates. As an application, we perform the Keldysh Functional Renormalization of a one dimensional driven open Bose gas, where a tailored diffusion Markov noise realises an analog of quantum criticality for driven-dissipative condensation. We find that the associated non-equilibrium quantum phase transition does not map into the critical behaviour of its three dimensional classical driven counterpart.

Dynamical Landau theory of the glass crossover

I introduce a dynamical field theory to describe the glassy behavior in supercooled liquids. The mean-field approximation of the theory predicts a dynamical arrest transition, as in ideal Mode-Coupling-Theory and mean-field discontinuous Spin-Glass Models. Instead {\it beyond} the mean-field approximation the theory predicts that the transition is avoided and transformed into a crossover, as observed in experiments and simulations. To go beyond mean-field a standard perturbative loop expansion is performed at first. Approaching the ideal critical point this expansion is divergent at all orders and I show that the leading divergent term at any given order is the same of a dynamical stochastic equation, called Stochastic-Beta-Relaxation (SBR) in {\it EPL 106, 56003 (2014)}. At variance with the original theory SBR can be studied beyond mean-field directly, without the need to resort to a perturbative expansion. Thus it provides a qualitative and quantitative description of the dynamical crossover. For consistency reasons it is important to establish the connection between the dynamical field theory and SBR beyond perturbation theory. This can be done with the help of a stronger result: the dynamical field theory is {\it exactly} equivalent to a theory with quenched disorder. Qualitatively the non-perturbative mechanism leading to the crossover is therefore the same of SBR. Quantitatively SBR corresponds to make the mean-field approximation once the quenched disorder has been generated.

On the emergent dynamics of fermions in curved spacetime

Relativistic spin-(1/2) particles in curved spacetime are naturally described by Dirac theory, which is a dynamical and Lorentz-invariant field theory. In this work, we propose a non-dynamical fermion theory in 3+1 dimensions dubbed spinor topological field theory, built in terms of a spinor field and a Cartan connection related to de Sitter group. We show that our model gives rise to the Dirac theory in curved spacetime when the local de Sitter gauge invariance of the model breaks down to the Lorentz gauge invariance, providing also a geometric origin to the fermion mass. Finally, we show that other gauge fields and suitable four-fermion interactions can be included in a straightforward way.

Cyclic Solvent Annealing Improves Feature Orientation in Block Copolymer Thin Films

Solvent vapor annealing is a promising, flexible platform for controlling the self-assembly of block copolymer thin films. However, the ability for static solvent annealing alone to provide sufficient bias to generate vertically oriented features is limited. Here, we use dynamical field theory simulations to investigate the morphology dynamics and capacity for pattern selection of a cyclic solvent annealing process. We find that the swell step selectively strains features oriented parallel to the substrate, reducing their stability with respect to disorder, while vertically oriented domains remain stable through the full cycle. This memory effect may be exploited to systematically improve feature orientation with wide operating margins and favorable kinetics compared to static solvent or cyclic thermal annealing. In aggregate, these results suggest a simple, robust method for orienting features in solvent annealed block copolymer films, potentially obviating the need for external fields while minimizing t...

Simultaneous planning and action: neural-dynamic sequencing of elementary behaviors in robot navigation

A technique for simultaneous planning and action based on dynamic field theory is presented. The model builds on previous work on representation of sequential behavior as attractors in dynamic neural fields. Here, we demonstrate how chains of competing attractors can be used to represent dynamic plans towards a goal state. The present work can be seen as an addition to a growing body of work that demonstrates the role of dynamic field theory as a bridge between low-level reactive approaches and high-level symbol processing mechanisms. The architecture is evaluated on a set of planning problems using a simulated e-puck robot, including analysis of the system’s behavior in response to noise and temporary blockages of the planned route. The system makes no explicit distinction between planning and execution phases, allowing continuous adaptation of the planned path. The proposed architecture exploits the dynamic field theory property of stability in relation to noise and changes in the environment. The neural dynamics are also exploited such that stay-or-switch action selection emerges where blockage of a planned path occurs; stay until the transient blockage is removed versus switch to an alternative route to the goal.

A parsimonious computational model of visual target position encoding in the superior colliculus.

The superior colliculus (SC) is a brainstem structure at the crossroad of multiple functional pathways. Several neurophysiological studies suggest that the population of active neurons in the SC encodes the location of a visual target to foveate, pursue or attend to. Although extensive research has been carried out on computational modeling, most of the reported models are often based on complex mechanisms and explain a limited number of experimental results. This suggests that a key aspect may have been overlooked in the design of previous computational models. After a careful study of the literature, we hypothesized that the representation of the whole retinal stimulus (not only its center) might play an important role in the dynamics of SC activity. To test this hypothesis, we designed a model of the SC which is built upon three well-accepted principles: the log-polar representation of the visual field onto the SC, the interplay between a center excitation and a surround inhibition and a simple neuronal dynamics, like the one proposed by the dynamic neural field theory. Results show that the retinotopic organization of the collicular activity conveys an implicit computation that deeply impacts the target selection process.

Non-target stimuli in the visual field influence movement preparation in upper-limb reaching

The present work provides an empirical test of the Dynamic Field Theory of visuospatial cognition. The Dynamic Field Theory is a bi-stable neural network model applied to explain how visual information is integrated during the preparation of reaching responses (Erlhagen and Schöner). The dynamic field theory posits that motor cortices develop peaks of activation for each possible target in the visual field. Targets that are close in space produce neural peaks with overlapping distributions, whereas targets that are far apart produce distinct peaks with non-overlapping distributions. As such, the Dynamic Field Theory predicts reaction times to potential targets that are close in space will be faster than those to targets that are far apart. The present work examined how proximal and distal distractors impact reaction time in an upper-limb reaching task. The results demonstrated that distal distractors result in prolonged reaction times compared to proximal distractors. We suggest that reaction time represents the time required to inhibit neural activity representing the location of the distractor. Thus, prolonged reaction times observed for distal distractors reflect the temporal demands associated with the competition of two non-overlapping distributions of activity in the brain. These findings support the tenets of the Dynamic Field Theory and demonstrate that non-target stimuli in the visual field can influence movement preparation.

Grounding cognitive-level processes in behavior: the view from dynamic systems theory.

Marr's seminal work laid out a program of research by specifying key questions for cognitive science at different levels of analysis. Because dynamic systems theory (DST) focuses on time and interdependence of components, DST research programs come to very different conclusions regarding the nature of cognitive change. We review a specific DST approach to cognitive-level processes: dynamic field theory (DFT). We review research applying DFT to several cognitive-level processes: object permanence, naming hierarchical categories, and inferring intent, that demonstrate the difference in understanding of behavior and cognition that results from a DST perspective. These point to a central challenge for cognitive science research as defined by Marr-emergence. We argue that appreciating emergence raises questions about the utility of computational-level analyses and opens the door to insights concerning the origin of novel forms of behavior and thought (e.g., a new chess strategy). We contend this is one of the most fundamental questions about cognition and behavior.

Different developmental trajectories across feature types support a dynamic field model of visual working memory development.

Research on visual working memory has focused on characterizing the nature of capacity limits as "slots" or "resources" based almost exclusively on adults' performance with little consideration for developmental change. Here we argue that understanding how visual working memory develops can shed new light onto the nature of representations. We present an alternative model, the Dynamic Field Theory (DFT), which can capture effects that have been previously attributed either to "slot" or "resource" explanations. The DFT includes a specific developmental mechanism to account for improvements in both resolution and capacity of visual working memory throughout childhood. Here we show how development in the DFT can account for different capacity estimates across feature types (i.e., color and shape). The current paper tests this account by comparing children's (3, 5, and 7 years of age) performance across different feature types. Results showed that capacity for colors increased faster over development than capacity for shapes. A second experiment confirmed this difference across feature types within subjects, but also showed that the difference can be attenuated by testing memory for less familiar colors. Model simulations demonstrate how developmental changes in connectivity within the model-purportedly arising through experience-can capture differences across feature types.

Learning the Condition of Satisfaction of an Elementary Behavior in Dynamic Field Theory

AbstractIn order to proceed along an action sequence, an autonomous agent has to recognize that the intended final condition of the previous action has been achieved. In previous work, we have shown how a sequence of actions can be generated by an embodied agent using a neural-dynamic architecture for behavioral organization, in which each action has an intention and condition of satisfaction. These components are represented by dynamic neural fields, and are coupled to motors and sensors of the robotic agent.Here,we demonstratehowthemappings between intended actions and their resulting conditions may be learned, rather than pre-wired.We use reward-gated associative learning, in which, over many instances of externally validated goal achievement, the conditions that are expected to result with goal achievement are learned. After learning, the external reward is not needed to recognize that the expected outcome has been achieved. This method was implemented, using dynamic neural fields, and tested on a real-world E-Puck mobile robot and a simulated NAO humanoid robot.

Parsing of action sequences: A neural dynamics approach

AbstractParsing of action sequences is the process of segmenting observed behavior into individual actions. In robotics, this process is critical for imitation learning from observation and for representing an observed behavior in a form that may be communicated to a human. In this paper, we develop a model for action parsing, based on our understanding of principles of grounded cognitive processes, such as perceptual decision making, behavioral organization, and memory formation.We present a neural-dynamic architecture, in which action sequences are parsed using a mathematical and conceptual framework for embodied cognition—the Dynamic Field Theory. In this framework, we introduce a novel mechanism, which allows us to detect and memorize actions that are extended in time and are parametrized by the target object of an action. The core properties of the architecture are demonstrated in a set of simple, proof-of-concept experiments.

Dynamic field theory and equations of motion in cosmology

We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein’s equations in the form of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ/ρ≤1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ/ρ≫1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress–energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein’s equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.

Statistical dynamics of classical systems: a self-consistent field approach.

We develop a self-consistent field theory for particle dynamics by extremizing the functional integral representation of a microscopic Langevin equation with respect to the collective fields. Although our approach is general, here we formulate it in the context of polymer dynamics to highlight satisfying formal analogies with equilibrium self-consistent field theory. An exact treatment of the dynamics of a single chain in a mean force field emerges naturally via a functional Smoluchowski equation, while the time-dependent monomer density and mean force field are determined self-consistently. As a simple initial demonstration of the theory, leaving an application to polymer dynamics for future work, we examine the dynamics of trapped interacting Brownian particles. For binary particle mixtures, we observe the kinetics of phase separation.

Dynamic field theory and executive functions: lending explanation to current theories of development.

Buss and Spencer's monograph is an impressive achievement that is sure to have a lasting impact on the field of child development. The dynamic field theory (DFT) model that forms the heart of this contribution is ambitious in scope, detailed in its implementation, and rigorously tested against data, old and new. As such, the ideas contained in this fine document represent a qualitative advance in our understanding of young children's behavior, and lay a foundation for future research into the developmental origins of executive functioning.

III. DYNAMIC FIELD THEORY

Monographs of the Society for Research in Child DevelopmentVolume 79, Issue 2 p. 26-44 THE EMERGENT EXECUTIVE: A DYNAMIC FIELD THEORY OF THE DEVELOPMENT OF EXECUTIVE FUNCTION III. DYNAMIC FIELD THEORY First published: 12 May 2014 https://doi.org/10.1002/mono.12098Citations: 1Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume79, Issue2June 2014Pages 26-44 RelatedInformation

IV. QUANTITATIVE FITS OF CORE FINDINGS IN THE DCCS LITERATURE

Monographs of the Society for Research in Child DevelopmentVolume 79, Issue 2 p. 45-56 THE EMERGENT EXECUTIVE: A DYNAMIC FIELD THEORY OF THE DEVELOPMENT OF EXECUTIVE FUNCTION IV. QUANTITATIVE FITS OF CORE FINDINGS IN THE DCCS LITERATURE First published: 12 May 2014 https://doi.org/10.1002/mono.12099Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Volume79, Issue2June 2014Pages 45-56 RelatedInformation

What is the simplest model that captures the basic experimental facts of the physics of underdoped cuprates?

I discuss here some well established experimental facts which have been shown to be generic of the pseudogap in underdoped cuprates. Some recent developments on Cellular Dynamic Mean Field Theories of the doped Hubbard model on a square lattice are nowadays allowing one to compute physical properties and k resolved single particle spectra. At high temperatures, recent results present qualitative features which perfectly fit the experimental observations done for more than two decades on the pseudogap in the cuprates. Most various broken symmetry states detected recently at lower temperatures than the pseudogap T*, certainly require more complicated modelling, and are not necessarily generic. I suggest that various perturbations due to the order (or disorder) of chemical dopants, which can hardly be avoided in actual materials, might drive the pseudogap electronic matter into specific ground states which exhibit interesting correlated electronic orders.

Integrating the Behavioral and Neural Dynamics of Response Selection in a Dual-task Paradigm: A Dynamic Neural Field Model of Dux et al. ()

People are typically slower when executing two tasks than when only performing a single task. These dual-task costs are initially robust but are reduced with practice. Dux et al. (2009) explored the neural basis of dual-task costs and learning using fMRI. Inferior frontal junction (IFJ) showed a larger hemodynamic response on dual-task trials compared with single-task trial early in learning. As dual-task costs were eliminated, dual-task hemodynamics in IFJ reduced to single-task levels. Dux and colleagues concluded that the reduction of dual-task costs is accomplished through increased efficiency of information processing in IFJ. We present a dynamic field theory of response selection that addresses two questions regarding these results. First, what mechanism leads to the reduction of dual-task costs and associated changes in hemodynamics? We show that a simple Hebbian learning mechanism is able to capture the quantitative details of learning at both the behavioral and neural levels. Second, is efficiency isolated to cognitive control areas such as IFJ, or is it also evident in sensory motor areas? To investigate this, we restrict Hebbian learning to different parts of the neural model. None of the restricted learning models showed the same reductions in dual-task costs as the unrestricted learning model, suggesting that efficiency is distributed across cognitive control and sensory motor processing systems.

Dynamic neural fields as a step toward cognitive neuromorphic architectures

Dynamic Field Theory (DFT) is an established framework for modeling embodied cognition. In DFT, elementary cognitive functions such as memory formation, formation of grounded representations, attentional processes, decision making, adaptation, and learning emerge from neuronal dynamics. The basic computational element of this framework is a Dynamic Neural Field (DNF). Under constraints on the time-scale of the dynamics, the DNF is computationally equivalent to a soft winner-take-all (WTA) network, which is considered one of the basic computational units in neuronal processing. Recently, it has been shown how a WTA network may be implemented in neuromorphic hardware, such as analog Very Large Scale Integration (VLSI) device. This paper leverages the relationship between DFT and soft WTA networks to systematically revise and integrate established DFT mechanisms that have previously been spread among different architectures. In addition, I also identify some novel computational and architectural mechanisms of DFT which may be implemented in neuromorphic VLSI devices using WTA networks as an intermediate computational layer. These specific mechanisms include the stabilization of working memory, the coupling of sensory systems to motor dynamics, intentionality, and autonomous learning. I further demonstrate how all these elements may be integrated into a unified architecture to generate behavior and autonomous learning.

Insights into ordered microstructures and ordering mechanisms of ABC star terpolymers by integrating dynamic self-consistent field theory and variable cell shape methods

A theoretical approach coupling dynamic self-consistent field (SCF) theory for inhomogeneous polymeric fluids and variable cell shape (VCS) method for automatically adjusting cell shape and size is developed to investigate ordered microstructures and the ordering mechanisms of block copolymer melts. Using this simulation method, we first re-examined the microphase separation of the simplest AB diblock copolymers, and tested the validity and efficiency of the novel method by comparing the results with those obtained from the dynamic SCF theory. An appropriate relaxation parameter of the VCS method effectively accelerates the system towards a stable morphology without distortions or defects. The dynamic SCF/VCS method is then applied to identify the richness morphologies of ABC star terpolymers and explore the ordering mechanisms of star terpolymer melts quenched from homogenous states. A diverse range of ordered microstructures, including two-dimensional tiling patterns, hierarchical structures and ordinary microstructures, are predicted. Three types of ordering mechanisms, namely, one-step, quick-slow and step-wise procedures, are discovered in the disorder-to-order transition of ABC star terpolymers. The procedures of microphase separation in the ABC star terpolymer melts are remarkably affected by the composition of star terpolymers and the strength of interaction parameters.