Related papers: Quantum Lattice Representation of Nonlinear Classi…
We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of…
We investigate a relativistic adaptation of the Lattice Boltzmann Method that reproduces the equations of motion for a turbulent, two-dimensional, massless hydrodynamic system. The classical Lattice Boltzmann Method and its extension to…
We generalize the nonlinear one-dimensional equation for a fluid layer surface to any geometry and we introduce a new infinite order differential equation for its traveling solitary waves solutions. This equation can be written as a…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
Studies of strongly nonlinear dynamical systems such as turbulent flows call for superior computational prowess. With the advent of quantum computing, a plethora of quantum algorithms have demonstrated, both theoretically and…
The effect of nonlinear friction forces in quantum mechanics is studied via dissipative Madelung hydrodynamics. A new thermo-quantum diffusion equation is derived, which is solved for the particular case of quantum Brownian motion with a…
Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and…
Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and…
We study mathematically a system of partial differential equations arising in the modelling of an aging fluid, a particular class of non Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and…
We develop a quantum representation for Newtonian viscous fluid flows by establishing a mapping between the Navier-Stokes equation (NSE) and the Schr\"odinger-Pauli equation (SPE). The proposed nonlinear SPE incorporates the two-component…
There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing the limiting individual behavior of particles inside a large ensemble of identical…
We propose a regular way to construct lattice versions of $W$-algebras, both for quantum and classical cases. In the classical case we write the algebra explicitly and derive the lattice analogue of Boussinesq equation from the Hamiltonian…
The irreducible representations of the extended Galilean group are used to derive infinite sets of symmetric and asymmetric second-order differential equations with constant coeffcients. All derived equations are local and their Lagrangians…
We formulate the lattice QCD simulation with background classical gravitational fields. This formulation enables us to study nonperturbative aspects of quantum phenomena in curved spacetimes from the first principles. As the first…
Recently the general form of a translation-covariant quantum Boltzmann equation has been derived which describes the dynamics of a tracer particle in a quantum gas. We develop a stochastic wave function algorithm that enables full…
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation,…
Turbulence is one of the most prototypical phenomena of systems driven out of equilibrium. While turbulence has been studied mainly with classical fluids like water, considerable attention is now drawn to quantum turbulence (QT), observed…
This article proposes a Variational Quantum Algorithm to solve linear and nonlinear thermofluid dynamic transport equations. The hybrid classical-quantum framework is applied to problems governed by the heat, wave, and Burgers' equation in…
The mathematical representation of the physical objects determines which mathematical branch will be applied during the physical analysis in the systems studied. The difference among non-quantum physics, like classic or relativistic…
Simulating large scale lattice dynamics directly is computationally demanding due to the high complexity involved, yet such simulations are crucial for understanding the mechanical and thermal properties of many physical systems. In this…