Out-of-equilibrium dynamics of the XY spin chain from form factor expansion

We consider the XY spin chain with arbitrary time-dependent magnetic field and anisotropy. We argue that a certain subclass of Gaussian states, called Coherent Ensemble (CE) following [1], provides a natural and unified framework for out-of-equilibrium physics in this model. We show that all correlation functions in the CE can be computed using form factor expansion and expressed in terms of Fredholm determinants. In particular, we present exact out-of-equilibrium expressions in the thermodynamic limit for the previously unknown order parameter 1-point function, dynamical 2-point function and equal-time 3-point function.

Kinesin and Myosin Motors Compete to Drive Rich Multi-Phase Dynamics in Programmable Cytoskeletal Composites

The cytoskeleton of biological cells relies on a diverse population of motors, filaments, and binding proteins acting in concert to enable non-equilibrium processes ranging from mitosis to chemotaxis. The cytoskeleton’s versatile reconfigurability, programmed by interactions between its constituents, make it a foundational active matter platform. However, current active matter endeavors are limited largely to single force-generating components acting on a single substrate – far from the composite cytoskeleton in live cells. Here, we engineer actin-microtubule composites, driven by kinesin and myosin motors and tuned by crosslinkers, that restructure into diverse morphologies from interpenetrating filamentous networks to de-mixed amorphous clusters. Our Fourier analyses reveal that kinesin and myosin compete to delay kinesin-driven restructuring and suppress de-mixing and flow, while crosslinking accelerates reorganization and promotes actin-microtubule correlations. The phase space of non-equilibrium dynamics falls into three broad classes– slow reconfiguration, fast advective flow, and multi-mode ballistic dynamics – with structure-dynamics relations described by the relative contributions of elastic and dissipative responses to motor-generated forces.

Inhomogeneous Conformal Field Theory Out of Equilibrium

We study the non-equilibrium dynamics of conformal field theory (CFT) in 1+1 dimensions with a smooth position-dependent velocity v(x) explicitly breaking translation invariance. Such inhomogeneous CFT is argued to effectively describe 1+1-dimensional quantum many-body systems with certain inhomogeneities varying on mesoscopic scales. Both heat and charge transport are studied, where, for concreteness, we suppose that our CFT has a conserved U(1) current. Based on projective unitary representations of diffeomorphisms and smooth maps in Minkowskian CFT, we obtain a recipe for computing the exact non-equilibrium dynamics in inhomogeneous CFT when evolving from initial states defined by smooth inverse-temperature and chemical-potential profiles $$\beta (x)$$ β ( x ) and $$\mu (x)$$ μ ( x ) . Using this recipe, the following exact analytical results are obtained: (i) the full time evolution of densities and currents for heat and charge transport, (ii) correlation functions for components of the energy–momentum tensor and the U(1) current as well as for any primary field, and (iii) the thermal and electrical conductivities. The latter are computed by direct dynamical considerations and alternatively using a Green–Kubo formula. Both give the same explicit expressions for the conductivities, which reveal how inhomogeneous dynamics opens up the possibility for diffusion as well as implies a generalization of the Wiedemann–Franz law to finite times within CFT.

Russian ruble exchange rate: Modeling of comparative medium-term and long-term dynamics

The subject of the study is the dynamic mechanism of the formation of the exchange rate of the Russian ruble in a multilevel system of economic fundamental determinants-aggregates in the context of the independent floating rate of the national currency. The aim of the study is to develop the author’s theoretical and methodological conceptual approach to modeling the dynamics of the equilibrium exchange rate based on international flows (IFEER) and to develop a new model of the Russian ruble exchange rate dynamics on its basis. The methodological base of the research includes system analysis, fundamental methods of economic theory, classical methods of mathematical analysis, and economic and statistical analysis, and the provisions of national accounting. The paper presents data on the verifcation of the results of modeling mediumterm equilibrium dynamics. At the same time, the author pays considerable attention to the mathematical modeling of the long-term dynamics of the ruble exchange rate in comparison with the medium-term equilibrium dynamics and the mathematical analysis of internal functional relationships in modern conditions, which determines the scientifc novelty and relevance of the study. Based on the conducted mathematical modeling, the author concludes about the trends of a stronger ruble exchange rate in the long run, while maintaining the current long-term trends.

Towards a Theory of Quantum Gravity from Neural Networks

Neural network is a dynamical system described by two different types of degrees of freedom: fast-changing non-trainable variables (e.g., state of neurons) and slow-changing trainable variables (e.g., weights and biases). We show that the non-equilibrium dynamics of trainable variables can be described by the Madelung equations, if the number of neurons is fixed, and by the Schrodinger equation, if the learning system is capable of adjusting its own parameters such as the number of neurons, step size and mini-batch size. We argue that the Lorentz symmetries and curved space-time can emerge from the interplay between stochastic entropy production and entropy destruction due to learning. We show that the non-equilibrium dynamics of non-trainable variables can be described by the geodesic equation (in the emergent space-time) for localized states of neurons, and by the Einstein equations (with cosmological constant) for the entire network. We conclude that the quantum description of trainable variables and the gravitational description of non-trainable variables are dual in the sense that they provide alternative macroscopic descriptions of the same learning system, defined microscopically as a neural network.

Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54

We study the out-of-equilibrium dynamics of the quantum cellular automaton Rule 54 using a time-channel approach. We exhibit a family of (non-equilibrium) product states for which we are able to describe exactly the full relaxation dynamics. We use this to prove that finite subsystems relax to a one-parameter family of Gibbs states. We also consider inhomogeneous quenches. Specifically, we show that when the two halves of the system are prepared in two different solvable states, finite subsystems at finite distance from the centre eventually relax to the non-equilibrium steady state (NESS) predicted by generalised hydrodynamics. To the best of our knowledge, this is the first exact description of the relaxation to a NESS in an interacting system and, therefore, the first independent confirmation of generalised hydrodynamics for an inhomogeneous quench.

On computing non-equilibrium dynamics following a quench

Computing the non-equilibrium dynamics that follows a quantum quench is difficult, even in exactly solvable models. Results are often predicated on the ability to compute overlaps between the initial state and eigenstates of the Hamiltonian that governs time evolution. Except for a handful of known cases, it is generically not possible to find these overlaps analytically. Here we develop a numerical approach to preferentially generate the states with high overlaps for a quantum quench starting from the ground state or an excited state of an initial Hamiltonian. We use these preferentially generated states, in combination with a "high overlap states truncation scheme" and a modification of the numerical renormalization group, to compute non-equilibrium dynamics following a quench in the Lieb-Liniger model. The method is non-perturbative, works for reasonable numbers of particles, and applies to both continuum and lattice systems. It can also be easily extended to more complicated scenarios, including those with integrability breaking.

Dynamic maximum entropy provides accurate approximation of structured population dynamics

Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a dynamic maximum entropy method that combines a static maximum entropy with a quasi-stationary approximation. This allows us to reduce stochastic non-equilibrium dynamics expressed by the Fokker-Planck equation to a simpler low-dimensional deterministic dynamics, without the need to track microscopic details. Although the method has been previously applied to a few (rather complicated) applications in population genetics, our main goal here is to explain and to better understand how the method works. We demonstrate the usefulness of the method for two widely studied stochastic problems, highlighting its accuracy in capturing important macroscopic quantities even in rapidly changing non-stationary conditions. For the Ornstein-Uhlenbeck process, the method recovers the exact dynamics whilst for a stochastic island model with migration from other habitats, the approximation retains high macroscopic accuracy under a wide range of scenarios in a dynamic environment.

Molecular Communications in Complex Systems of Dynamic Supramolecular Polymers

Supramolecular polymers are composed of monomers that self-assemble non-covalently, generating distributions of monodimensional fibres in continuous communication with each other and with the surrounding solution. Fibres, exchanging molecular species, and external environment constitute a sole complex system, which intrinsic dynamics is hard to elucidate. Here we report coarse-grained molecular simulations that allow studying supramolecular polymers at the thermodynamic equilibrium, explicitly showing the complex nature of these systems, which are composed of exquisitely dynamic molecular entities. Detailed studies of molecular exchange provide insights into key factors controlling how assemblies communicate with each other, defining the equilibrium dynamics of the system. Using minimalistic and finer chemically relevant molecular models, we observe that a rich concerted complexity is intrinsic in such self-assembling systems. This offers a new dynamic and probabilistic (rather than structural) picture of supramolecular polymer systems, where the travelling molecular species continuously shape the assemblies that statistically emerge at the equilibrium.

Equilibrium dynamics in a model of growth and spatial agglomeration

We present a multiregional endogenous growth model in which forward-looking agents choose their regions to live in, in addition to consumption and capital accumulation paths. The spatial distribution of economic activity is determined by the interplay between production spillover effects and urban congestion effects. We characterize the global stability of the spatial equilibrium states in terms of economic primitives such as agents’ time preference and intra- and interregional spillovers. We also study how macroeconomic variables at the stable equilibrium state behave according to the structure of the spillover network.