相关论文: The K-Theoretic Bulk-Boundary Principle for Dynami…

Oscillations in a stochastic dynamical system, whose deterministic counterpart has a stable steady state, are a widely reported phenomenon. Traditional methods of finding parameter regimes for stochastically-driven resonances are, however,…

Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space…

Time boundaries (TBs), temporal analogues of spatial interfaces, offer a powerful handle to engineer quantum systems. However, unlike the well-developed stationary scattering theory at spatial interfaces, a unified framework for quantum…

Cellular structures must organize themselves within strict physical constraints, operating with finite resources and well-defined boundaries. Classical systems demonstrate only passive responses to boundaries, from surface energy…

This paper studies quantitative deviation bounds for statistical ensembles evolving under the one-parameter flow of a nearly integrable Hamiltonian system. Combining Nekhoroshev-type stability estimates with phase-mixing arguments, we…

Quantum periodic cluster methods for strongly correlated electron systems are reformulated and developed. The reformulation and development are based on a canonical transformation which periodizes the fermions in the cluster space. The…

Topological phase of matter is now a mainstream of research in condensed matter physics, of which the classification, synthesis, and detection of topological states have brought excitements over the recent decade while remain incomplete…

Structural resonance involves the absorption of inertial loads by a tuned structural elasticity: a process playing a key role in a wide range of biological and technological systems, including many biological and bio-inspired locomotion…

Within the C*-algebraic framework of the resolvent algebra for canonical quantum systems, the structure of oscillating lattice systems with bounded nearest neighbor interactions is studied in any number of dimensions. The global dynamics of…

A topological group $G$ is topologically normally generated if there exists $g \in G$ such that the normal closure of $g$ is dense in $G$. Let $S$ be a tame, infinite type surface whose mapping class group $\mathrm{Map}(S)$ is generated by…

We present simple yet extremely accurate coupled-wave models describing the formation of bound states in the continuum (BICs) in 1D-periodic guided-mode resonant gratings (GMRGs) consisting of a slab waveguide layer with a binary grating…

We consider the relations between nonstationary quantum oscillators and their stationary counterpart in view of their applicability to study particles in electromagnetic traps. We develop a consistent model of quantum oscillators with…

We discuss how to formulate lattice gauge theories in the Tensor Network language. In this way we obtain both a consistent truncation scheme of the Kogut-Susskind lattice gauge theories and a Tensor Network variational ansatz for gauge…

An emerging paradigm proposes that neural computations can be understood at the level of dynamical systems that govern low-dimensional trajectories of collective neural activity. How the connectivity structure of a network determines the…

A system with equation and dynamic boundary condition of Cahn-Hilliard type is considered. This system comes from a derivation performed in Liu-Wu (Arch. Ration. Mech. Anal. 233 (2019), 167--247) via an energetic variational approach.…

This study proposes algorithms for building tilt grain boundary (GB) models with a boundary plane-oriented approach that does not rely on existence of a coincidence site lattice (CSL). As conventional GB model generation uses the CSL of…

An efficient algorithm to simulate dynamics of open quantum system is presented. The method describes the dynamics by unraveling stochastic wave functions converging to a density operator description. The stochastic techniques are based on…

Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a…

This is the first in a series of papers constructing geometric models of twisted differential K-theory. In this paper we construct a model of even twisted differential K-theory when the underlying topological twist represents a torsion…

Continuum lattice grid structures which consist of joined elastic beams subject to flexural deformations are ubiquitous. In this work, we establish a theoretical framework of the topological dynamics of continuum lattice grid structures,…