相关论文: Morphing quantum mechanics and fluid dynamics

We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form valued 2-forms, and their divergence as a covariant exterior derivative. We review…

We investigate an undamped random phase-space dynamics in deterministic external force fields (conservative and magnetic ones). By employing the hydrodynamical formalism for those stochastic processes we analyze microscopic kinetic-type…

In this paper we briefly introduce the quantum methods for computations of the drag coefficients for flows around a body, using the flows around a rigid sphere as an example, and we aim for comparing the wake under quantized environment and…

For a dense and strongly interacting system, such as a nucleus or a strongly-coupled quark-gluon plasma, the foundation of hydrodynamics can be better found in the quantum description of constituents moving in the strong mean fields…

We study the dynamics of compressible fluids in rotating heterogeneous porous media. The fluid flow is of {F}orchheimer-type and is subject to a mixed mass and volumetric flux boundary condition. The governing equations are reduced to a…

In this paper we review recent results by the author on the problem of quantization of measures. More precisely, we propose a dynamical approach, and we investigate it in dimensions 1 and 2. Moreover, we discuss a recent general result on…

We formulate hydrodynamic equations and spectrally accurate numerical methods for investigating the role of geometry in flows within two-dimensional fluid interfaces. To achieve numerical approximations having high precision and level of…

We consider quasi-free quantum systems and we derive the Euler equation using the so-called hydrodynamic limit. We use Wigner's well-known distribution function and discuss an extension to band distribution functions for particles in a…

Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…

In this paper we apply quantum hydrodynamics (QHD) to study the quantum evolution of a system of spinning particles and particles that have the electric dipole moments EDM in the rotating reference frame. The method presented is based on…

The Madelung equations offer a hydrodynamic description of quantum systems, from single particles to quantum fluids. In this formulation, the probability density is mapped onto the fluid density and the phase is treated as a scalar…

This paper surveys various aspects of the hydrodynamic formulation of the nonlinear Schrodinger equation obtained via the Madelung transform in connexion to models of quantum hydrodynamics and to compressible fluids of the Korteweg type.

We present a numerical method to deal efficiently with large numbers of particles in incompressible fluids. The interactions between particles and fluid are taken into account by a physically motivated ansatz based on locally defined drag…

The gradient-flow dynamics of an arbitrary geometric quantity is derived using a generalization of Darcy's Law. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification…

Considered is the Schr\"odinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting…

Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…

A correspondence between scalar field fluctuations and generalized fluctuations in a hydrodynamic approximation of fields is obtained. The results presented here are of interest to field-fluid correspondences and form part of theoretical…

We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed…

We present the development of the realistic geometro-hydrodynamical formalism of quantum mechanics for the spinning particle, that involves the vortical flows and is based on the idea, that the spinor wave represents a new type of physical…

We present numerical simulations of diffusio-osmotic flow, i.e. the fluid flow generated by a concentration gradient along a solid-fluid interface. In our study, we compare a number of distinct approaches that have been proposed for…