Related papers: Analysis of continuous and discrete Wigner approxi…
We present a comprehensive numerical investigation of the cluster Truncated Wigner Approximation (cTWA) applied to quench dynamics in bond-disordered Heisenberg spin chains with power-law interactions. We find that cTWA yields highly…
Nonequilibrium dynamics of highly-controlled quantum systems is a challenging issue in statistical physics and quantum many-body physics, relevant to recent experimental developments of analog and digital quantum simulations. In this work,…
The standard spinor connection in curved space-time is represented in a compact form. In this form the calculation is complicated, and its physical effects are concealed. In this paper, we split spinor connection into two vectors…
The semi-classical discrete truncated Wigner approximation (dTWA) has recently been proposed as a simulation method for spin-$1/2$ systems. While it appears to provide a powerful approach which shows promising results in higher dimensions…
The central spin model has a wide applicability, it is ideally suited to describe a small quantum system, for instance a quantum bit, in contact to a bath of spins, e.g., nuclear spins, or other small quantum systems in general. According…
A regularization method is presented to deduce dynamic correlation functions from exact diagonalization calculations. It is applied to dimer-dimer correlation functions in quantum spin chains relevant for the description of spin-Peierls…
We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…
We describe how to approximate the Riemann curvature tensor as well as sectional curvatures on possibly infinite-dimensional shape spaces that can be thought of as Riemannian manifolds. To this end, we extend the variational time…
We show how mapping techniques inherent to $N^{2}$-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the…
We report analytical equations for the derivatives of spin dynamics simulations with respect to pulse sequence and spin system parameters. The methods described are significantly faster, more accurate and more reliable than the finite…
In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. The truncated Wigner…
In random matrix theory, the spacing distribution functions $p^{(n)}(s)$ are well fitted by the Wigner surmise and its generalizations. In this approximation the spacing functions are completely described by the behavior of the exact…
This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications.…
Integrable discretizations are introduced for the rational and hyperbolic spin Ruijsenaars--Schneider models. These discrete dynamical systems are demonstrated to belong to the same integrable hierarchies as their continuous--time…
We prove two inequalities for the direct and truncated correlation for the nearest-neighboor one-dimensional Edwards-Anderson model with symmetric quenched disorder. The second inequality has the opposite sign of the GKS inequality of type…
We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This…
Any model order reduced dynamical system that evolves a modal decomposition to approximate the discretized solution of a stochastic PDE can be related to a vector field tangent to the manifold of fixed rank matrices. The Dynamically…
The exact solution of the Dirac equation for fermions coupled to an external periodic chiral condensate (chiral spiral) is used to obtain the exact formula for the Wigner function (up to the quantum loop corrections). We find that the…
We present a semiclassical phase-space method to calculate thermal and ground states of large interacting spin systems. To this end, we extend the recently developed truncated Wigner approximation for spins (TWA) to the imaginary time,…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…