相关论文: Weakly nonlocal fluid mechanics - the Schrodinger …

We provide a complete derivation of hydrodynamic equations for nonrelativistic systems based on quantum field theories of spinless Schr\"odeinger fields, assuming that an initial density operator takes a special form of the local Gibbs…

Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the…

The Boltzmann factor comes from the linear change in entropy of an infinite heat bath during a local fluctuation; small systems have significant nonlinear terms. We present theoretical arguments, experimental data, and Monte-Carlo…

The key questions of uniqueness and existence in time-dependent density functional theory are usually formulated only for potentials and densities that are analytic in time. Simple examples, standard in quantum mechanics, lead however to…

The most usual formulation of the Laws of Thermodynamics turns out to be suitable for local or simple materials, while for non-local systems there are two different ways: either modify this usual formulation by introducing suitable extra…

We study the effective approximation for a nonlocal stochastic Schrodinger equation with a rapidly oscillating, periodically time-dependent potential. We use the natural diffusive scaling of heterogeneous system and study the limit…

In this paper we consider the nonlinear one-dimensional time-dependent Schroedinger equation with a periodic potential and a local perturbation. In the limit of large periodic potential the time behavior of the wavefunction can be…

Stochastic extensions of the Schrodinger equation have attracted attention recently as plausible models for state reduction in quantum mechanics. Here we formulate a general approach to stochastic Schrodinger dynamics in the case of a…

Quantum nonlocality is revisited from a novel point of view by studying the problem of an originally classical particle immersed in the stochastic zero-point radiation field (zpf). The entire system is left to evolve until it reaches a…

Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of…

We consider several modifications of the Euler system of fluid dynamics including its pressureless variant driven by non-local interaction repulsive-attractive and alignment forces in the space dimension $N=2,3$. These models arise in the…

For general second order evolution equations, we prove an optimal condition on the degree of unboundedness of the damping, that rules out finite-time extinction. We show that control estimates give energy decay rates that explicitly depend…

The static second hyperpolarizability is derived from the space-fractional Schr\"{o}dinger equation in the particle-centric view. The Thomas-Reiche-Kuhn sum rule matrix elements and the three-level ansatz determines the maximum second…

We derive equations for fluid dynamics from a non-extensive Boltzmann transport equation consistent with Tsallis' non-extensive entropy formula. We evaluate transport coefficients employing the relaxation time approximation and investigate…

In relativistic quantum field theory with local interactions, charge is locally conserved. This implies local conservation of probability for the Dirac and Klein-Gordon wavefunctions, as special cases; and then in turn for non-relativistic…

The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the structure of the equation, in particular…

We are concerned with the energy equality for weak solutions to Newtonian and non-Newtonian incompressible fluids. In particular, the results obtained for non-Newtonian fluids, after restriction to the Newtonian case, equal or improve the…

Newton's second law may be used to obtain a wave equation, which reduces to Schrodinger's equation in the nonrelativistic limit and for a conservative force.

We investigate multidimensional model for incompressible non-Newtonian fluids. Using method of energy estimates we prove the property of finite speed of propagations of the solution support for this problem. We find sharp bounds of the…

In this paper we prove that the initial-boundary value problem for the forced non-linear Schroedinger equation with a potential on the half-line is locally and (under stronger conditions) globally well posed, i.e. that there is a unique…