Research
Research
Research
Research
1,513+ open-access research outputs.
We investigate quantum transport in an off-diagonal Aubry--Andr\'e--Harper chain. The periodic hopping modulation generates effective internal boundaries that strongly influence the transmission chara…
Although random matrix theory provides a fundamental framework for characterizing quantum chaos, encompassing both ergodic and localized phases, a comprehensive understanding of the universal features…
We compute the dimension of the motivic Galois group of a 1-motive M defined over the field of complex numbers, expressing it explicitly in terms of the rank of the multiplicative group generated by t…
The concept of context-free grammar in Combinatorics was first introduced by Chen in 1993. In 1996, Dumont significantly extended the theory of context-free grammars to a variety of other combinatoria…
We consider the spectrum of the Almost Mathieu operator (AMO) and show that the moments of the restriction of the Lebesgue measure to the intersection spectrum $\text{Leb}|_{\Sigma_{\alpha,\lambda}}$ …
The authors previously formulated the hybrid conjecture, unifying Andr\'e-Pink-Zannier and Andr\'e-Oort conjectures, and proved it in Shimura varieties of abelian type. We study its analogue for mixed…
Diffusion models produce high-quality synthetic data but suffer from slow inference. We propose 3D Variable-Step Denoising Diffusion Probabilistic Model (VS-DDPM) a framework engineered to maintain ge…
We investigate the effect of a periodic electric field drive on the generalized Aubry-Andr\'e model, also known as the Ganeshan-Pixley-Das Sarma (GPD) model, which is well known as a host of mobility …
Let $\xi$ be a value, at an algebraic point, of a Siegel $E$-function. As a special case of a very general interpolation result, we prove that there exists an $E$-function $f$ such that $f(1)=\xi$, an…
Lattice quasi-periodicity is easily realized with ultracold atoms in optical lattices and has been used to study delocalization-localization transition at low dimensions. Models with true disorder, ho…
We investigate a two leg ladder system subjected to an external magnetic field. In the absence of a magnetic field, the system is described by a clean tight binding model, with no disorder in either t…
Ion temperature clamping -- the saturation of $T_i$ at a fixed fraction of $T_e$ regardless of heating power -- is observed across stellarator experiments. We propose a minimal model based on Anderson…
The all-to-all momentum coupling of the Hubbard interaction makes interacting lattice models generically unsolvable. In many settings, however, from Peierls instabilities to Moir\'e superlattice physi…
Group Relative Policy Optimization (GRPO) is widely used for reinforcement learning with verifiable rewards, but it often suffers from advantage collapse: when all rollouts in a group receive the same…
We investigate localization in a quasiperiodically engineered diamond lattice with strand-dependent Aubry-Andr\'e-Harper onsite modulations, highlighting the decisive roles of the modulation ratio $s$…
We investigate localization transitions and mobility edge phenomena in one-dimensional quasiperiodic lattice models using an information theoretic framework based on the Tsallis entropy of single part…
A recently introduced recurrence-relation ansatz applied to the Bose-Hubbard model is here used in the generalized Aubry-Andre model. The resulting modified Aubry-Andre model allows for a simple param…
Photonic systems provide a highly tunable platform for emulating quantum Hall physics. This tunability enables probing of the interplay between strong disorder and robust topological transport that re…
We extend the relative theory of admissible pairs and $p$-adic Hodge structures introduced in Part II to allow variation in the underlying local systems of $\mathbb{Q}_p$-vector spaces and isocrystals…
Given a Nori motivic local system over a smooth, connected complex algebraic variety, we define its exceptional locus as a way to measure the variation in the motivic complexity of its stalks. The def…
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