Related papers: Numerical sign problem and the tempered Lefschetz …
We propose a new method for solving the Gelfand-Levitan-Marchenko equation (GLME) based on the block version of the Toeplitz Inner-Bordering (TIB) with an arbitrary point to start the calculation. This makes it possible to find solutions of…
Quantum Monte Carlo (QMC) simulations constitute nowadays one of the most powerful methods to study strongly correlated quantum systems, provided that no "sign problem" arises. However, many systems of interest, including highly frustrated…
We consider multi-flavor massless $(1+1)$-dimensional QED with chemical potentials at finite spatial length and the zero-temperature limit. Its sign problem is solved using the mean-field calculation with complex saddle points.
Quantum simulators have made a remarkable progress towards exploring the dynamics of many-body systems, many of which offer a formidable challenge to both theoretical and numerical methods. While state-of-the-art quantum simulators are in…
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…
We show how sign problems in simulations of many-body systems can manifest themselves in the form of heavy-tailed correlator distributions, similar to what is seen in electron propagation through disordered media. We propose an alternative…
This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schr\"{o}dinger equations (NLS). The method is explicit, unconditionally stable and time transversal invariant.…
L\'{e}vy flight models whose jumps have infinite moments are mathematically used to describe the superdiffusion in complex systems. Exponentially tempering the Levy measure of L\'{e}vy flights leads to the tempered stable L\'{e}vy processes…
Here we develop a new scheme of projective quantum Monte-Carlo (QMC) simulation combining unbiased zero-temperature (projective) determinant QMC and variational Monte-Carlo based on Gutzwiller projection wave function, dubbed as…
We explore different ways of incorporating accurate trial wave functions into free projection auxiliary field quantum Monte Carlo (fp-AFQMC). Trial states employed include coupled cluster singles and doubles, multi-Slater, and symmetry…
We consider time-harmonic scalar transmission problems between dielectric and dispersive materials with generalized Lorentz frequency laws. For certain frequency ranges such equations involve a sign-change in their principle part. Due to…
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties, without the sign problem. The list spans condensed matter, nuclear physics, and…
We describe an approach for many-body calculations with a finite-temperature, grand canonical ensemble formalism using auxiliary-field quantum Monte Carlo (AFQMC) with a self-consistent constraint to control the sign problem. The usual…
High-fidelity numerical simulation serves as a cornerstone for exploring magnetization dynamics in micromagnetics. This work introduces a novel third-order temporally accurate and stable numerical scheme for the Landau-Lifshitz-Gilbert…
We derive a variational multiscale (VMS) finite element formulation for a viscoelastic, tensor-based blood damage model. The tensor equation is numerically stabilized by a logarithmic shape tensor description that prevents unphysical,…
The dynamics of magnetisation in a bounded ferromagnet in $\mathbb{R}^d$ ($d=1,2$) at high temperatures can be described by the stochastic Landau--Lifshitz--Bloch (sLLB) equation, which is a vector-valued quasilinear stochastic partial…
In this paper, Thermofield Dynamics (TFD) is applied to map a quantum optics nonlinear master equation into a Schrodinger-like equation for any arbitrary initial condition. This formalism provides a more efficient way for solving open…
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…
A fully implicit numerical scheme is established for solving the time fractional Swift-Hohenberg (TFSH) equation with a Caputo time derivative of order $\alpha\in(0,1)$. The variable-step L1 formula and the finite difference method are…
Temporal logics (TLs) have been widely used to formalize interpretable tasks for cyber-physical systems. Time Window Temporal Logic (TWTL) has been recently proposed as a specification language for dynamical systems. In particular, it can…