Related papers: Analysis of continuous and discrete Wigner approxi…
We develop a systematic framework for the spin adaptation of the cumulants of p-particle reduced density matrices (RDMs), with explicit constructions for p = 1 to 3. These spin-adapted cumulants enable rigorous treatment of both S_z and S^2…
The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences. In this paper we discuss the problem of discretizing vector-valued functions…
The dynamics of entanglement and uncertainty relation is explored by solving the time-dependent Schr\"{o}dinger equation for coupled harmonic oscillator system analytically when the angular frequencies and coupling constant are arbitrarily…
We reconsider the one-axis twisting Hamiltonian, which is commonly used for generating spin squeezing, and treat its dynamics within the Heisenberg operator approach. To this end we solve the underlying Heisenberg equations of motion…
We study analytically the performance of a recently proposed algorithm for learning the couplings of a random asymmetric kinetic Ising model from finite length trajectories of the spin dynamics. Our analysis shows the importance of the…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
Dynamic graph algorithms have seen significant theoretical advancements, but practical evaluations often lag behind. This work bridges the gap between theory and practice by engineering and empirically evaluating recently developed…
We consider the nearest-neighbor spacing distributions of mixed random matrix ensembles interpolating between different symmetry classes, or between integrable and non-integrable systems. We derive analytical formulas for the spacing…
We show that the Wigner equations describing the continuous spin representations can be obtained as a limit of massive higher-spin field equations. The limit involves a suitable scaling of the wave function, the mass going to zero and the…
Incorporating symmetries into the numerical solution of differential equations has been a mainstay of research over the last 40 years, however, one aspect is less known and under-utilised: discretisations of partial differential equations…
The dynamics of disordered two-dimensional systems is much less understood than the dynamics of disordered chains, mainly due to the lack of appropriate numerical methods. We demonstrate that a single-trajectory version of the fermionic…
We investigate many-body spin squeezing dynamics in an XXZ model with interactions that fall off with distance $r$ as $1/r^\alpha$ in $D=2$ and $3$ spatial dimensions. In stark contrast to the Ising model, we find a broad parameter regime…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
Ultracold Rydberg atom arrays are an emerging platform for quantum simulation and computing. However, decoherence in these systems remains incompletely understood. Recent experiments [Guardado-Sanchez et al. Phys. Rev. X 8, 021069 (2018)]…
We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…
We study variational problems for curves approximated by B-spline curves. We show that, one can obtain discrete Euler-Lagrange equations, for the data describing the approximated curves. Our main application is to the curve completion…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are…
A dynamics of the precession of coupled atomic moments in the tight-binding (TB) approximation is presented. By implementing an angular penalty functional in the energy that captures the magnetic effective fields self-consistently, the…
Dynamics simulation with frictional contacts is important for a wide range of applications, from cloth simulation to object manipulation. Recent methods using smoothed lagged friction forces have enabled robust and differentiable simulation…