arXiv subjects

Yuanyuan Pan

Publications and source records attributed to Yuanyuan Pan.

7 recordsLinked to original sources

arXiv2026

The Parabolic Anderson Model's Total Mass at Small Times: Geometry, Fluctuations, and Renormalization

Let $D\subset\mathbb R^d$ be a bounded domain, let $\kappa>0$ be fixed, and let $W$ be a fractional Brownian sheet on $\mathbb R\times\mathbb R^d$. Consider the Stratonovich parabolic Anderson model (PAM) $\partial_tu_\kappa=(\frac12\Delta+\kappa W')u_\kappa$ with Dirichlet boundary condition on $D$ and the flat initial condition $u_\kappa(0,\cdot)=\mathbf 1_D$. We calculate exact asymptotics for the expectation and the standard deviation of the total mass $\int_Du_\kappa(t,x)~\mathrm d x$ as $t\to0$ under the assumption that $W$'s Hurst indices are all at least $1/2$ and that $u_\kappa$'s moments are finite for small enough $t>0$. In doing so, we uncover that these asymptotics are determined by a competition between three mechanisms: (1) $\mathbf{Geometry}$: The rate of heat diffusion through the boundary $\partial D$. (2) $\mathbf{Fluctuations}$: $W$'s time Hurst index. (3) $\mathbf{Renormalization}$: The singularity of deterministic Stratonovich corrections. As a result, we identify novel phase transition phenomena, which arise from the influence of $W$'s Hurst indices on the relative magnitudes of these contributions.

math.PR↗

arXiv2025

On the Spectral Geometry and Small Time Mass of Anderson Models on Planar Domains

We consider the Anderson Hamiltonian (AH) and the parabolic Anderson model (PAM) with white noise and Dirichlet boundary condition on a bounded planar domain $D\subset\mathbb R^2$. We compute the small time asymptotics of the AH's exponential trace up to order $O(\log t)$, and of the PAM's mass up to order $O(t\log t)$. Our proof is probabilistic, and relies on the asymptotics of intersection local times of Brownian motions and bridges in $\mathbb R^2$. Applications of our main result include the following: (i) If the boundary $\partial D$ is sufficiently regular, then $D$'s area and $\partial D$'s length can both be recovered almost surely from a single observation of the AH's eigenvalues. This extends Mouzard's Weyl law in the special case of bounded domains (Ann. Inst. H. Poincar\'e Probab. Statist. 58(3): 1385-1425). (ii) If $D$ is simply connected and $\partial D$ is fractal, then $\partial D$'s Minkowski dimension (if it exists) can be recovered almost surely from the PAM's small time asymptotics. (iii) The variance of the white noise can be recovered almost surely from a single observation of the AH's eigenvalues.

math.PR↗

arXiv2025

Spatial Offset of Excited States in Non-Hermitian Lattices

We investigate the behavior of light-wave packets injected into non-Hermitian microcavity lattices under highly dissipative conditions. While all eigenstates of the lattice exhibit exponential decay, a specifically excited state maintains coherent propagation. In a one-dimensional lattice, this state undergoes a spatial displacement shift away from the injection position, which is a fundamental property of non-Hermitian systems with a point gap when the spectrum encircles a finite region in the complex plane. Extending such a shift to two-dimensional lattices reveals a geometrically anomalous V-shaped wave packet formation with orientation-tunable arms. Notably, this geometric control mechanism enables all-optical steering of non-Hermitian photonic states without requiring structural modifications.

physics.optics↗

arXiv2023

The damped wave equation and associated polymer

Considering the damped wave equation with a Gaussian noise $F$ where $F$ is white in time and has a covariance function depending on spatial variables, we will see that this equation has a mild solution which is stationary in time $t$. We define a weakly self-avoiding polymer with intrinsic length $J$ associated to this SPDE. Our main result is that the polymer has an effective radius of approximately $J^{5/3}$.

math.PR↗

arXiv2015

Monolayer Phosphorene-Metal Interfaces

Recently, phosphorene electronic and optoelectronic prototype devices have been fabricated with various metal electrodes. We systematically explore for the first time the contact properties of monolayer (ML) phosphorene with a series of commonly used metals (Al, Ag. Cu, Au, Cr, Ni, Ti, and Pd) via both ab initio electronic structure calculations and more reliable quantum transport simulations. Strong interactions are found between all the checked metals, with the energy band structure of ML phosphorene destroyed. In terms of the quantum transport simulations, ML phosphorene forms a n-type Schottky contact with Au, Cu, Cr, Al, and Ag electrodes, with electron Schottky barrier heights (SBHs) of 0.30, 0.34, 0.37, 0.51, and 0.52 eV, respectively, and p-type Schottky contact with Ti, Ni, and Pd electrodes, with hole SBHs of 0.30, 0.26, and 0.16 eV, respectively. These results are in good agreement with available experimental data. Our findings not only provide an insight into the ML phosphorene-metal interfaces but also help in ML phosphorene based device design.

cond-mat.mes-hall↗

arXiv2015

Interfacial Properties of Monolayer and Bilayer MoS2 Contacts with Metals: Beyond the Energy Band Calculations

Although many prototype devices based on two-dimensional (2D) MoS2 have been fabricated and wafer scale growth of 2D MoS2 has been realized, the fundamental nature of 2D MoS2-metal contacts has not been well understood yet. We provide a comprehensive ab initio study of the interfacial properties of a series of monolayer (ML) and bilayer (BL) MoS2-metal contacts (metal = Sc, Ti, Ag, Pt, Ni, and Au). A comparison between the calculated and observed Schottky barrier heights (SBHs) suggests that many-electron effects are strongly suppressed in channel 2D MoS2 due to a charge transfer. The extensively adopted energy band calculation scheme fails to reproduce the observed SBHs in 2D MoS2-Sc interface. By contrast, an ab initio quantum transport device simulation better reproduces the observed SBH in the two types of contacts and highlights the importance of a higher level theoretical approach beyond the energy band calculation in the interface study. BL MoS2-metal contacts have a reduced SBH than ML MoS2-metal contacts due to the interlayer coupling and thus have a higher electron injection efficiency.

cond-mat.mes-hall↗

arXiv2014

Graphdiyne-metal contacts and graphdiyne transistors

Graphdiyne is prepared on metal surface, and making devices out of it also inevitably involves contact with metals. Using density functional theory with dispersion correction, we systematically studied for the first time the interfacial properties of graphdiyne contacting with a series of metals (Al, Ag, Cu, Au, Ir, Pt, Ni, and Pd). Graphdiyne is in an n-type Ohmic or quasi-Ohmic contact with Al, Ag, and Cu, while it is in a Schottky contact with Au (at source/drain interface), Pd, Pt, Ni, and Ir (at source/drain-channel interface), with high Schottky barrier heights of 0.39, 0.21 (n-type), 0.30, 0.41, and 0.45 (p-type) eV, respectively. A graphdiyne field effect transistor (FET) with Al electrodes is simulated by using quantum transport calculations. This device exhibits an on-off ratio up to 104 and a very large on-state current of 1.3 * 104 mA/mm in a 10 nm channel length. Thus, a new prospect is opened up for graphdiyne in high performance nanoscale devices.

cond-mat.mtrl-sci↗