Related papers: Universal limits of nonlinear measure redistributi…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
We describe an extension to the density matrix renormalization group method incorporating real time evolution into the algorithm. Its application to transport problems in systems out of equilibrium and frequency dependent correlation…
Time series classification is an important problem in real world. Due to its non-stationary property that the distribution changes over time, it remains challenging to build models for generalization to unseen distributions. In this paper,…
In this paper we calculate, in the large N limit, the eigenvalue density of an infinite product of random unitary matrices, each of them generated by a random hermitian matrix. This is equivalent to solving unitary diffusion generated by a…
Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the "negative sign problem'' when applied to fermions - causing an exponential increase of the computing time with the number of particles. A polynomial time…
Dynamical measurement schemes are an important tool for the investigation of quantum many-body systems, especially in the age of quantum simulation. Here, we address the question whether generic measurements can be implemented efficiently…
We study the long-time asymptotics of a certain class of nonlinear diffusion equations with time-dependent diffusion coefficients which arise, for instance, in the study of transport by randomly fluctuating velocity fields. Our primary goal…
First-passage time problems are ubiquitous across many fields of study including transport processes in semiconductors and biological synapses, evolutionary game theory and percolation. Despite their prominence, first-passage time…
We study the general moment problem for measures on the real line, with polynomials replaced by more general spaces of entire functions. As a particular case, we describe measures that are uniquely determined by a restriction of their…
The time evolution of a finite fermion system towards statistical equilibrium is investigated using analytical solutions of a nonlinear partial differential equation that had been derived earlier from the Boltzmann collision term. The…
Change-point problems have appeared in a great many applications for example cancer genetics, econometrics and climate change. Modern multiscale type segmentation methods are considered to be a statistically efficient approach for multiple…
We describe a method for removing the numerical errors in the modeling of linear evolution equations that are caused by approximating the time derivative by a finite difference operator. The method is based on integral transforms realized…
The dynamics of quantum systems can be approximated by the time propagation of Gaussian wave packets. Applying a time dependent variational principle, the time evolution of the parameters of the coupled Gaussian wave packets can be…
We analyze general enough models of repeated indirect measurements in which a quantum system interacts repeatedly with randomly chosen probes on which Von Neumann direct measurements are performed. We prove, under suitable hypotheses, that…
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the…
We study the influence of the preparation of an open quantum system on its reduced time evolution. In contrast to the frequently considered case of an initial preparation where the total density matrix factorizes into a product of a system…
An extension of standard quantum mechanics is proposed in which the Newtonian time appearing as a parameter in the unitary evolution operator is replaced with the time shown by a `quantum clock'. Such a clock is defined by the following…
The mystery of the infamous sign problem in quantum Monte Carlo simulations mightily restricts applications of the method in fermionic and frustrated systems. A recent work [Science 375, 418 (2022)] made a remarkable breakthrough in the…
This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation…
Problems with sign-changing coefficients occur, for instance, in the study of transmission problems with metamaterials. In this work, we present and analyze a generalized finite element method in the spirit of the Localized Orthogonal…