arXiv subjects

Xuyang Lin

Publications and source records attributed to Xuyang Lin.

5 recordsLinked to original sources

arXiv2026

Path-Dependent Ergodic Optimal Control and Backward Stochastic Differential Equations

We investigate a new class of infinite-horizon backward stochastic differential equations for ergodic optimal control where the cost and state dynamics are time and path-dependent. The state process is defined on an unbounded underlying domain and satisfies an extended dissipativity condition. In contrast with the time-homogeneous Markovian setting, the optimal ergodic cost in our framework is characterized by the asymptotic behavior of a deterministic function, rather than by a single real constant. We obtain well-posedness, verification and stability properties, which extend the previous results in the literature on the Markov case.

math.PR↗

arXiv2025

Convergence rates for an Adaptive Biasing Potential scheme from a Wasserstein optimization perspective

Free-energy-based adaptive biasing methods, such as Metadynamics, the Adaptive Biasing Force (ABF) and their variants, are enhanced sampling algorithms widely used in molecular simulations. Although their efficiency has been empirically acknowledged for decades, providing theoretical insights via a quantitative convergence analysis is a difficult problem, in particular for the kinetic Langevin diffusion, which is non-reversible and hypocoercive. We obtain the first exponential convergence result for such a process, in an idealized setting where the dynamics can be associated with a mean-field non-linear flow on the space of probability measures. A key of the analysis is the interpretation of the (idealized) algorithm as the gradient descent of a suitable functional over the space of probability distributions.

math.PR↗

arXiv2024

Fourier-Laplace transforms in polynomial Ornstein-Uhlenbeck volatility models

We consider the Fourier-Laplace transforms of a broad class of polynomial Ornstein-Uhlenbeck (OU) volatility models, including the well-known Stein-Stein, Sch\"obel-Zhu, one-factor Bergomi, and the recently introduced Quintic OU models motivated by the SPX-VIX joint calibration problem. We show the connection between the joint Fourier-Laplace functional of the log-price and the integrated variance, and the solution of an infinite dimensional Riccati equation. Next, under some non-vanishing conditions of the Fourier-Laplace transforms, we establish an existence result for such Riccati equation and we provide a discretized approximation of the joint characteristic functional that is exponentially entire. On the practical side, we develop a numerical scheme to solve the stiff infinite dimensional Riccati equations and demonstrate the efficiency and accuracy of the scheme for pricing SPX options and volatility swaps using Fourier and Laplace inversions, with specific examples of the Quintic OU and the one-factor Bergomi models and their calibration to real market data.

q-fin.MF↗

arXiv2022

Room-temperature coherent optical manipulation of single-hole spins in solution-grown perovskite quantum dots

Manipulation of solid-state spin coherence is an important paradigm for quantum information processing. Current systems either operate at very low temperatures or are difficult to scale-up. Developing low-cost, scalable materials whose spins can be coherently manipulated at room temperature is thus highly-attractive for a sustainable future of quantum information science. Here we report ambient-condition all-optical initialization, manipulation and readout of single-hole spins in an ensemble of solution-grown CsPbBr3 perovskite QDs. Single-hole spins are obtained by sub-picosecond electron scavenging following a circularly-polarized femtosecond-pulse excitation. A transversal magnetic field induces spin precession, and a second off-resonance femtosecond-pulse coherently rotates hole spins via strong light-matter interaction. These operations accomplish nearly complete quantum-state control of single-hole spins at room temperature.

cond-mat.mes-hall↗

arXiv2022

Lattice distortion inducing exciton splitting and coherent quantum beating in CsPbI3 perovskite quantum dots

Anisotropic exchange-splitting in semiconductor quantum dots (QDs) results in bright-exciton fine-structure-splitting (FSS) important for quantum information processing. Direct measurement of FSS usually requires single/few QDs at liquid-helium temperatures, because of its sensitivity to QD size and shape, whereas measuring and controlling FSS at an ensemble-level seem to be impossible unless all the dots are made to be nearly the same. Here we report strong bright-exciton FSS up to 1.6 meV in solution-processed CsPbI3 perovskite QDs, manifested as quantum beats in ensemble-level transient absorption at liquid-nitrogen to room temperatures. The splitting is robust to QD size and shape heterogeneity, and increases with decreasing temperature, pointing towards a mechanism associated with orthorhombic distortion of perovskite lattice. Effective-mass-approximation calculations reveal an intrinsic "fine-structure gap" that agrees well with the observed FSS. This gap stems from an avoided crossing of bright-excitons confined in orthorhombically-distorted QDs that are bounded by the pseudocubic {100} family of planes.

cond-mat.mes-hall↗