相关论文: The Approximating Hamiltonian Method for the Imper…
The mean-field approximations of many-boson dynamics are known to be effective in many physical relevant situations. The mathematical justifications of such approximations rely generally on specific considerations which depend too much on…
We show under general assumptions that the mean-field approximation for quan- tum many-boson systems is correct. Our contribution unifies and improves on most of the known results. The proof uses general properties of quantization in…
We present a fully-explicit, iteration-free, weakly-compressible method to simulate immiscible incompressible two-phase flows. To update pressure, we circumvent the computationally expensive Poisson equation and use the general pressure…
We give a two parameter variational formula for the grand-canonical pressure of the Pair Boson Hamiltonian model. By using the Approximating Hamiltonian Method we provide a rigorous proof of this variational principle.
The active mass density in Einstein's theory of gravitation in the analog of Poisson's equation in a local inertial system is proportional to $\rho+3p/c^2$. Here $\rho$ is the density of energy and $p$ its pressure for a perfect fluid. By…
A method of deriving the Hamiltonian of the interacting boson model, that is based on the microscopic framework of the nuclear energy density functional, is presented. The constrained self-consistent mean-field calculation with a given…
The envelope theory, also known as the auxiliary field method, is a simple technique to compute approximate solutions of Hamiltonians for $N$ identical particles in $D$-dimension. The accuracy of this method is tested by computing the…
We investigate ground-state and thermal properties of a system of non-relativistic bosons interacting through repulsive, two-body interactions in a self-consistent gaussian mean-field approximation wich consists in writing the variational…
Classical fields approximation to cold weakly interacting bosons allows for a unified treatment of condensed and uncondensed parts of the system. Until now, however, the quantitative predictions were limited by a dependence of the results…
The weakly interacting trapped Bose gases have been customarily described using the mean-field approximation in the form of the Gross-Pitaevskii equation. The mean-field approximation, however, has certain limitations, in particular it can…
A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds.…
A crucial issue in fluid dynamics is related to the knowledge of the fluid pressure. A new general pressure equation is derived from compressible Navier-Stokes equation. It is argued that this new pressure equation allows unifying…
The random point field which describes the position distribution of the system of ideal boson gas in a state of Bose-Einstein condensation is obtained through the thermodynamic limit. The resulting point field is given by convolution of two…
We study the existence theory of solutions of the kinetic Bohmian equation, a nonlinear Vlasov-type equation proposed for the phase-space formulation of Bohmian mechanics. Our main idea is to interpret the kinetic Bohmian equation as a…
The concept of local pressure is pivotal to describe many important physical phenomena, such as buoyancy or atmospheric phenomena, which always require the consideration of space-varying pressure fields. These fields have precise…
Damping in a dilute Bose gas is investigated using a mean-field approximation which describes the coupled oscillations of condensate and non-condensate atoms in the collisionless regime. Explicit results for both Landau and Beliaev damping…
An asymptotic formula for the number of states of Boson gas whose Hamiltonian is given by a positive elliptic pseudo-differential operator of order one on a compact manifold is given under a integrality assumption on the spectrum of the…
The auxiliary field method is a technique to obtain approximate closed formulae for the solutions of both nonrelativistic and semirelativistic eigenequations in quantum mechanics. For a many-body Hamiltonian describing identical particles,…
The Hamiltonian formulation for perfect fluid equations with the l-conformal Galilei symmetry is proposed. For an arbitrary half-integer value of the parameter l, the Hamilton and non-canonical Poisson brackets are found, in terms of which…
Atomic high-precision measurements have become a competitive and essential technique for tests of fundamental physics, the Standard Model, and our theory of gravity. It is therefore self-evident that such measurements call for a consistent…