Related papers: Dynamical Kernels for Optical Excitations
The theory of self-consistent effective interactions in nuclei is extended for a system with a velocity dependent mean potential. By means of the field coupling method, we present a general prescription to derive effective interactions…
Quantum beats in nonlinear spectroscopy of molecular aggregates are often attributed to electronic phenomena of excitonic systems, while nuclear degrees of freedom are commonly included into models as overdamped oscillations of bath…
Ultrafast photoinduced dynamics of electronic excitation in molecular dimers is drastically affected by the dynamic reorganization of inter- and intra- molecular nuclear configuration modeled by a quantized nuclear degree of freedom [Cina…
We present a comprehensive theoretical framework for calculating the linear and nonlinear optical responses of time-periodic quantum systems. Using density matrix evolution in the Floquet basis and adopting the length gauge, our approach…
Kernel density estimation (KDE) stands out as a challenging task in machine learning. The problem is defined in the following way: given a kernel function $f(x,y)$ and a set of points $\{x_1, x_2, \cdots, x_n \} \subset \mathbb{R}^d$, we…
We develop a systematic theory of multi-particle excitations in strongly interacting Fermi systems. Our work is the generalization of the time-honored work by Jackson, Feenberg, and Campbell for bosons, that provides, in its most advanced…
In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…
We analyze the spectra of general non-minimal second-order operators. To do this, we derive the local part of the trace of the second Seeley-DeWitt heat kernel coefficient for such operators in a completely model-independent way.…
We derive the divergence-kernel formula for the linear response of random dynamical systems. Specifically, the pathwise expression is for the parameter-derivative of the marginal or stationary density, not an averaged observable. Our…
In human cells, estrogenic signals induce cyclical association and dissociation of specific proteins with the DNA in order to activate transcription of estrogen-responsive genes. These oscillations can be modeled by assuming a large number…
We present a novel kernel-based method for learning multivariate stochastic differential equations (SDEs). The method follows a two-step procedure: we first estimate the drift term function, then the (matrix-valued) diffusion function given…
Motivated by applications, we consider here new operator theoretic approaches to Conditional mean embeddings (CME). Our present results combine a spectral analysis-based optimization scheme with the use of kernels, stochastic processes, and…
In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in $\mathbb{R}^d$. For two-dimensional surfaces embedded…
Time-dependent density functional theory has emerged as a method of choice for calculations of spectra and response properties in physics, chemistry, and biology, with its system-size scaling enabling computations on systems much larger…
In this paper, we employ probabilistic techniques to derive sharp, explicit two-sided estimates for the heat kernel of the nonlocal kinetic operator $$ \Delta^{\alpha/2}_v + v \cdot \nabla_x, \quad \alpha \in (0, 2),\ (x,v)\in {\mathbb…
We discuss the theoretical modelling of x-ray photoelectron diffraction (XPD) with hard x-ray excitation at up to 20 keV, using the dynamical theory of electron diffraction to illustrate the characteristic aspects of diffraction patterns…
Cavity dressing of molecular vibrational dynamics expands the role of characteristic vibrations as spectroscopic markers of underlying ultrafast dynamics. Interacting vibrational modes exhibit a pronounced excited state delocalization due…
Molecular absorption and photo-electron spectra can be efficiently predicted with real-time time-dependent density-functional theory (TDDFT). We show here how these techniques can be easily extended to study time-resolved pump-probe…
Measures of discrepancy between probability distributions (statistical distance) are widely used in the fields of artificial intelligence and machine learning. We describe how certain measures of statistical distance can be implemented as…
We consider the formal SDE dX t = b(t, X t)dt + dZ t , X 0 = x $\in$ R d , (E) where b $\in$ L r ([0, T ], B $\beta$ p,q (R d , R d)) is a time-inhomogeneous Besov drift and Z t is a symmetric d-dimensional $\alpha$-stable process, $\alpha$…