More Like this

1. Gauging anomalous unitary operators

   https://doi.org/10.1103/PhysRevB.104.155144  

   Liu, Yuhan; Shapourian, Hassan; Glorioso, Paolo; Ryu, Shinsei (October 2021, Physical Review B)

   null (Ed.)
2. Anomalous Anosov flows revisited

   https://doi.org/10.1112/plms.12321  

   Barthelmé, Thomas; Bonatti, Christian; Gogolev, Andrey; Rodriguez Hertz, Federico (May 2020, Proceedings of the London Mathematical Society)
3. Anomalous Dynamics in Macromolecular Liquids

   https://doi.org/10.3390/polym14050856  

   Guenza, Marina G. (March 2022, Polymers)

   Macromolecular liquids display short-time anomalous behaviors in disagreement with conventional single-molecule mean-field theories. In this study, we analyze the behavior of the simplest but most realistic macromolecular system that displays anomalous dynamics, i.e., a melt of short homopolymer chains, starting from molecular dynamics simulation trajectories. Our study sheds some light on the microscopic molecular mechanisms responsible for the observed anomalous behavior. The relevance of the correlation hole, a unique property of polymer liquids, in relation to the observed subdiffusive dynamics, naturally emerges from the analysis of the van Hove distribution functions and other properties. 

   more » « less
4. Davies’ method for anomalous diffusions

   https://doi.org/10.1090/proc/13324  

   Murugan, Mathav; Saloff-Coste, Laurent (April 2017, Proceedings of the American Mathematical Society)

   Davies’ method of perturbed semigroups is a classical technique to obtain off-diagonal upper bounds on the heat kernel. However Davies’ method does not apply to anomalous diffusions due to the singularity of energy measures. In this note, we overcome the difficulty by modifying the Davies’ perturbation method to obtain sub-Gaussian upper bounds on the heat kernel. 

   more » « less
5. An anomalous fractional diffusion operator

   https://doi.org/10.1007/s13540-025-00394-5  

   Zheng, Xiangcheng; Ervin, V_J; Wang, Hong (April 2025, Fractional Calculus and Applied Analysis)

   Abstract In this article, using that the fractional Laplacian can be factored into a product of the divergence operator, a Riesz potential operator and the gradient operator, we introduce an anomalous fractional diffusion operator, involving a matrixK(x), suitable when anomalous diffusion is being studied in a non homogeneous medium. For the case ofK(x) a constant, symmetric positive definite matrix we show that the fractional Poisson equation is well posed, and determine the regularity of the solution in terms of the regularity of the right hand side function. 

   more » « less