Related papers: Exponential decay of correlations for a real value…
We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. The method builds on the discrete truncated Wigner approximation for isolated systems, which…
We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to {iteratively} train a…
Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value…
We propose a machine learning based approach to develop the exchange-correlation potential of time dependent density functional theory (TDDFT). The neural network projection from the time-varying electron densities to the corresponding…
Considering an $N$-level system interacting factorizably with a continuous spectrum, we derive analytical expressions for the bound states and the dynamical evolution within this single-excitation Friedrichs model by using the projection…
The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary…
Moving beyond simple associations, researchers need tools to quantify how variables influence each other in space and time. Correlation functions provide a mathematical framework for characterizing these essential dependencies, revealing…
In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose…
We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the…
The correlation functions near higher-order glass-transition singularities are discussed for a schematic two-component model within the mode-coupling theory for ideal glass-transitions. The correlators decay in leading order like…
For over 30 years, mode-coupling theory (MCT) has been the de facto theoretic description of dense fluids and the liquid-glass transition. MCT, however, is limited by its ad hoc construction and lacks a mechanism to institute corrections.…
The correlation properties of the nonaffine elastic response in strongly disordered materials are investigated using the theory of correlated random matrices and supported by numerical models. While the nonaffine displacement field itself…
In this paper, models that approximate stochastic processes from the space $Sub_\varphi(\Omega)$ with given reliability and accuracy in $L_p(T)$ are considered for some specific functions $\varphi(t)$. For processes that are decomposited in…
Learning meaningful representations that disentangle the underlying structure of the data generating process is considered to be of key importance in machine learning. While disentangled representations were found to be useful for diverse…
Correlations between factors of variation are prevalent in real-world data. Exploiting such correlations may increase predictive performance on noisy data; however, often correlations are not robust (e.g., they may change between domains,…
We present a model of discrete quantum evolution based on quantum correlations between the evolving system and a reference quantum clock system. A quantum circuit for the model is provided, which in the case of a constant Hamiltonian is…
We identify peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory that are crucial for time-resolved electron scattering in a model one-dimensional system. These structures are…
Learning meaningful and compact representations with disentangled semantic aspects is considered to be of key importance in representation learning. Since real-world data is notoriously costly to collect, many recent state-of-the-art…
Our motivation in this paper is twofold. First, we study the geometry of a class of exploration sets, called exit sets, which are naturally associated with a 2D vector-valued GFF : $\phi : Z^2 \to R^N, N\geq 1$. We prove that, somewhat…
This is the second paper in a cycle investigating the exact solution of loop equations in decaying turbulence. We perform numerical simulations of the Euler ensemble, suggested in the previous work, as a solution to the loop equations. We…