Related papers: Quantum Lattice Representation of Nonlinear Classi…
Several classic one-dimensional problems of variational calculus originating in non-relativistic particle mechanics have solutions that are analogues of spatially homogeneous and isotropic universes. They are ruled by an equation which is…
Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schr\"odinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately…
To approximate solutions of complex nonlinear partial differential equations remains a computational challenge, especially for sets of equations relevant in industry, such as Euler or Navier-Stokes equations. Even the most sophisticated…
In the present study a particular case of Gross-Pitaevskii or non-linear Schr\"odinger equation is rewritten to a form similar to a hydrodynamic Euler equation using the Madelung transformation. The obtained system of differential equations…
The quantum dynamics of a single particle in a discrete two-dimensional tilted lattice is analyzed from the perspective of the classical-quantum correspondence. Utilizing the fact that tilting the lattice results in oscillatory dynamics, we…
Four-dimensional quantum electrodynamics has been formulated on a hypercubic Minkowski finite-element lattice. The equations of motion have been derived so as to preserve lattice gauge invariance and have been shown to be unitary. In…
There is a growing interest in the relation between classical turbulence and quantum turbulence. Classical turbulence arises from complicated dynamics of eddies in a classical fluid. In contrast, quantum turbulence consists of a tangle of…
We generalize the non-linear one-dimensional equation of a fluid layer for any depth and length as an infinite order differential equation for the steady waves. This equation can be written as a q-differential one, with its general solution…
Nonlinear Hamiltonian systems describing the abstract Vlasov and Hartree equations are considered in the framework of algebraic Poissonian theory. The concept of uniformization is introduced; it generalizes the method of second quantization…
We develop a classical theoretical description for nonlinear many-body dynamics that incorporates the back-action of a continuous measurement process. The classical approach is compared with the exact quantum solution in an example with an…
Presented is a quantum lattice gas algorithm to efficiently model a system of Dirac particles interacting through an intermediary gauge field. The algorithm uses a fixed qubit array to represent both the spacetime and the particles…
Being able to perform explicit computations in a nonperturbative, Planckian regime is key to understanding quantum gravity as a fundamental theory of gravity and spacetime. Rather than a variety of different approaches to quantum gravity,…
The evolution of a turbulent tangle of quantum vortices in presence of finite-size active particles is studied by means of numerical simulations of the Gross-Pitaevskii equation. Particles are modeled as potentials depleting the superfluid…
Quantum algorithms for computing classical nonlinear maps are widely known for toy problems but might not suit potential applications to realistic physics simulations. Here, we propose how to compute a general differentiable invertible…
The Vlasov-Poisson equations, fundamental in plasma physics and astrophysical applications, are rendered linear, finite-dimensional, and discrete by second quantization. Conditions for correspondence between the pre-quantized and quantized…
Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…
We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of…
We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory…
The formulation of quantum mechanics on spaces of constant curvature is studied. It is shown how a transition from a classical system to the quantum case can be accomplished by the quantization of the Noether momenta. These can be…
The gauge invariant electromagnetic Wigner equation is taken as the basis for a fluid-like system describing quantum plasmas, derived from the moments of the gauge invariant Wigner function. The use of the standard, gauge dependent Wigner…