相关论文: The Lorenz Renormalization Conjecture

We investigate theoretically soliton excitations and dynamics of their formation in strongly correlated systems of ultracold bosonic atoms in two and three dimensional optical lattices. We derive equations of nonlinear hydrodynamics in the…

In a neighborhood of a hyperbolic periodic orbit of a volume-preserving flow on a manifold of dimension 3, we define and show the existence of a normal form for the generator of the flow that encodes the dynamics. If the flow is a contact…

We investigate deformations of Lifshitz holography in $(n+1)$ dimensional spacetime. After discussing the situation for general Lifshitz scaling symmetry parameter $z$, we consider $z=n-1$ and the associated marginally relevant operators.…

We present a new version of the Grobman-Hartman's linearization theorem for random dynamics. Our result holds for infinite dimensional systems whose linear part is not necessarily invertible. In addition, by adding some restrictions on the…

We describe some recent results on the dynamics of singular-hyperbolic (or Lorenz-like) attractors: attractors in this class are expansive and so sensitive with respect to initial data; they admit a unique physical measure whose support is…

We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $\mathbb{R}^n$. A reformulation leads to a a stabilization problem for a multi-dimensional system of $n$ hyperbolic partial…

For a class of nonconservative hyperbolic systems of partial differential equations endowed with a strictly convex mathematical entropy, we formulate the initial value problem by supplementing the equations with a kinetic relation…

We propose an alternative paradigm to the conjectured Miransky scaling potentially underlying the physics describing the transition from the conformally broken to the conformally restored phase when tuning certain parameters such as the…

We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not…

Using the supersymmetry technique, we study the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems with a direction. In contrast to chains, our model captures the diffusive character of carriers' motion at…

The hyperbolic manifold is a smooth manifold of negative constant curvature. While the hyperbolic manifold is well-studied in the literature, it has gained interest in the machine learning and natural language processing communities lately…

Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…

In the context of Wilsonian Renormalization, renormalization group (RG) flows are a set of differential equations that defines how the coupling constants of a theory depend on an energy scale. These equations closely resemble…

We review our work on the application of the renormalization-group method to obtain first- and second-order relativistic hydrodynamics of the relativistic Boltzmann equation (RBE) as a dynamical system, with some corrections and new…

We consider a one-dimensional system of interacting bosons in a random potential. At zero temperature, it can be either in the superfluid or in the insulating phase. We study the transition at weak disorder and moderate interaction. Using a…

We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional…

In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially…

We introduce a notion of autonomous dynamical systems and apply it to prove rigidity of partially hyperbolic diffeomorphisms on closed compact three-manifolds under some smoothness hypothesis of their associated framing.

Reduced order models (ROMs) that capture flow dynamics are of interest for decreasing computational costs for simulation as well as for model-based control approaches. This work presents a data-driven framework for minimal-dimensional…

In a recent article [1] we have explored alternative decompositions of the Lorentz transformation by adopting the synchronization convention of the target frame at the end and alternately at the outset. In this note we develop the…