Related papers: Lighthill equation for quantum liquids
We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…
We introduce a generalized Lagrangian density - involving a non-Hermitian kinetic term - for a quantum particle with the generalized momentum operator. Upon variation of the Lagrangian, we obtain the corresponding Schrodinger equation. The…
A unified framework for coupled Navier-Stokes/Cahn-Hilliard equations is developed using, as a basis, a balance law for microforces in conjunction with constitutive equations consistent with a mechanical version of the second law. As a…
The Schroedinger equation with an energy-dependent complex absorbing potential, associated with a scattering system, can be reduced for a special choice of the energy-dependence to a harmonic inversion problem of a discrete pseudo-time…
We show that Kompaneetz equation describing photon diffusion in an environment of an electron gas, when linearized around its equilibrium distribution, coincides with the relativistic diffusion discussed in recent publications. The model of…
We consider a particle undergoing Brownian motion in Euclidean space of any dimension, forced by a Gaussian random velocity field that is white in time and smooth in space. We show that conditional on the velocity field, the quenched…
The fact that the probability density expression provided by the Klein-Gordon equation can take on negative values is usually seen as an obstacle to formulating a particle interpretation of quantum mechanics. Nevertheless, reconciling this…
In this paper, we are interested in a generalised Vlasov equation, which describes the evolution of the probability density of a particle evolving according to a generalised Vlasov dynamic. The achievement of the paper is twofold. Firstly,…
The hydrodynamic equation for the spatial and temporal evolution of the electron temperature T_e in the breakdown of the quantum Hall effect at even-integer filling factors in a uniform current density j is derived from the Boltzmann-type…
We derive linear fluctuating hydrodynamics as the low density limit of a deterministic system of particles at equilibrium. The proof builds upon previous results of the authors where the asymptotics of the covariance of the fluctuation…
Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type. The advantage of…
Under spectral conditions, we prove a LLN type result for superdiffusions, where the convergence is meant in probability. The main tool is a space-time H-transformation.
As a continuation of a previous work, here we examine the admittance of Birkhoff's theorem in a class of higher derivative theories of gravity. This class is contained in a larger class of theories which are characterized by the property…
We discuss the density fluctuations of a fluid due to zero point motion. These can be regarded as density fluctuations in the phonon vacuum state. We assume a linear dispersion relation with a fixed speed of sound and calculate the density…
We consider the kinetic transport equation that arise in the Boltzmann-Grad limit of the two-dimensional periodic Lorentz Gas. This equation has been obtained by extending the phase space of positions and velocities through the introduction…
The Einstein field equation as an equation of state of a thermodynamical system of spacetime is reconsidered in the present Letter. We argue that a consistent interpretation leads us to identify scalar curvature and cosmological constant…
We consider the Cauchy problem for strictly hyperbolic $m$-th order partial differential equations with coefficients low-regular in time and smooth in space. It is well-known that the problem is $L^2$ well-posed in the case of Lipschitz…
The method of flow equations is applied to QED on the light front. Requiring that the partical number conserving terms in the Hamiltonian are considered to be diagonal and the other terms off-diagonal an effective Hamiltonian is obtained…
This work shows that in the frame of the stochastic generalization of the quantum hydrodynamic analogy (QHA) the uncertainty principle can be derived by the postulate of finite transmission speed of light and information . The theory shows…
Within Bohm`s interpretation of quantum mechanics particles follow classical trajectories that are determined by the full solution of the time dependent Schroedinger equation. If this interpretation is consistent it must be possible to…