A dynamic correspondence between Bose-Einstein condensates and Friedmann-Lema\^itre-Robertson-Walker and Bianchi I cosmology with a cosmological constant

In some interesting work of James Lidsey, the dynamics of Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmology with positive curvature and a perfect fluid matter source is shown to be modeled in terms of a time-dependent, harmonically trapped Bose-Einstein condensate. In the present work, we extend this dynamic correspondence to both FLRW and Bianchi I cosmologies in arbitrary dimension, especially when a cosmological constant is present

High impact pressure regulator Patent

High impact pressure regulator having minimum number of lightweight movable element

Elliptic function solutions in Jackiw-Teitelboim dilaton gravity

We present a new family of solutions for the Jackiw-Teitelboim model of two-dimensional gravity with a negative cosmological constant. Here, a metric of constant Ricci scalar curvature is constructed, and explicit linearly independent solutions of the corresponding dilaton field equations are determined. The metric is transformed to a black hole metric, and the dilaton solutions are expressed in terms of Jacobi elliptic functions. Using these solutions we compute, for example, Killing vectors for the metric

High impact pressure regulator withstands impacts of over 15,000 g

High impact pressure regulator used with a high impact gas scannograph withstands impacts of over 15,000 g. By the passage of fluid through the first and second chambers of the regulator, the pressure of the scannograph is regulated from a specific input valve to the desired output pressure valve

On Generalized Monopole Spherical Harmonics and the Wave Equation of a Charged Massive Kerr Black Hole

We find linearly independent solutions of the Goncharov-Firsova equation in the case of a massive complex scalar field on a Kerr black hole. The solutions generalize, in some sense, the classical monopole spherical harmonic solutions previously studied in the massless cases.Comment: Accepted for publication, Mod. Phys. Lett. A. 13 pages, including reference

The Equivalence Postulate of Quantum Mechanics

The Equivalence Principle (EP), stating that all physical systems are connected by a coordinate transformation to the free one with vanishing energy, univocally leads to the Quantum Stationary HJ Equation (QSHJE). Trajectories depend on the Planck length through hidden variables which arise as initial conditions. The formulation has manifest p-q duality, a consequence of the involutive nature of the Legendre transform and of its recently observed relation with second-order linear differential equations. This reflects in an intrinsic psi^D-psi duality between linearly independent solutions of the Schroedinger equation. Unlike Bohm's theory, there is a non-trivial action even for bound states. No use of any axiomatic interpretation of the wave-function is made. Tunnelling is a direct consequence of the quantum potential which differs from the usual one and plays the role of particle's self-energy. The QSHJE is defined only if the ratio psi^D/psi is a local self-homeomorphism of the extended real line. This is an important feature as the L^2 condition, which in the usual formulation is a consequence of the axiomatic interpretation of the wave-function, directly follows as a basic theorem which only uses the geometrical gluing conditions of psi^D/psi at q=\pm\infty as implied by the EP. As a result, the EP itself implies a dynamical equation that does not require any further assumption and reproduces both tunnelling and energy quantization. Several features of the formulation show how the Copenhagen interpretation hides the underlying nature of QM. Finally, the non-stationary higher dimensional quantum HJ equation and the relativistic extension are derived.Comment: 1+3+140 pages, LaTeX. Invariance of the wave-function under the action of SL(2,R) subgroups acting on the reduced action explicitly reveals that the wave-function describes only equivalence classes of Planck length deterministic physics. New derivation of the Schwarzian derivative from the cocycle condition. "Legendre brackets" introduced to further make "Legendre duality" manifest. Introduction now contains examples and provides a short pedagogical review. Clarifications, conclusions, ackn. and references adde