相关论文: Continuous Unitary Transformations

Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…

Density matrices evolved according the von Neumann equation are commonly used to simulate the dynamics of driven quantum systems. However, computational methods using density matrices are often too slow to explore the large parameter spaces…

In this paper we present a continuation method which transforms spatially distributed ODE systems into continuous PDE. We show that this continuation can be performed both for linear and nonlinear systems, including multidimensional, space-…

Adiabatic transformation can be approximated as alternating unitary operators of a Hamiltonian and its parameter derivative as proposed in a gate-based approach to counterdiabatic driving (van Vreumingen, arXiv:2406.08064). In this paper,…

There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a…

Continuous normalizing flows (CNFs) and diffusion models (DMs) generate high-quality data from a noise distribution. However, their sampling process demands multiple iterations to solve an ordinary differential equation (ODE) with high…

Carleman linearization is a mathematical technique that transforms nonlinear dynamical systems into infinite-dimensional linear systems, enabling simplified analysis. Initially developed for ordinary differential equations (ODEs) and later…

Functional equations (FE) arise quite naturally in the analysis of stochastic systems of different kinds : queueing and telecommunication networks, random walks, enumeration of planar lattice walks, etc. Frequently, the object is to…

Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and…

Unitary designs are unitary ensembles that emulate Haar-random unitary statistics. They provide a vital tool for studying quantum randomness and have found broad applications in quantum technologies. However, existing research has focused…

The method of continuous averaging can be regarded as a combination of the Lie method, where a change of coordinates is constructed as a shift along solutions of a differential equation and the Neishtadt method, well-known in perturbation…

We consider the unified transform method, also known as the Fokas method, for solving partial differential equations. We adapt and modify the methodology, incorporating new ideas where necessary, in order to apply it to solve a large class…

We discuss a new analytical approach to real-time evolution in quantum many-body systems. Our approach extends the framework of continuous unitary transformations such that it amounts to a novel solution method for the Heisenberg equations…

We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…

Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…

This article proposes a formalism which unifies Hamiltonian simulation techniques from different fields. This formalism leads to a competitive method to construct the Hamiltonian simulation with a comprehensible, simple-to-implement circuit…

The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…

The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…

Flow Oriented Perturbation Theory (FOPT) is a novel approach to Feynman diagrams based on the coordinate (position) space description of Quantum Field Theories (QFT). FOPT offers interesting features regarding the computation of higher-loop…

Considering a determinantal point process on the real line, we establish a connection between the sine-kernel asymptotics for the correlation kernel and the CLT for mesoscopic linear statistics. This implies universality of mesoscopic…