THE CLASSICAL LIMIT OF A SELF-CONSISTENT QUANTUM-VLASOV EQUATION IN 3D

1993 ◽  
Vol 03 (01) ◽  
pp. 109-124 ◽  
Author(s):  
PETER A. MARKOWICH ◽  
NORBERT J. MAUSER
Keyword(s):  
Kinetic Energy ◽  
Initial Density ◽  
Poisson System ◽  
Planck Constant ◽  
Density Matrices ◽  
Accumulation Points ◽  
Schmidt Norm ◽  
Bounded Trace ◽  
The Given ◽  
Uniformly Bounded

Under natural assumptions on the initial density matrix of a mixed quantum state (Hermitian, non-negative definite, uniformly bounded trace, Hilbert-Schmidt norm and kinetic energy) we prove that accumulation points (as the scaled Planck constant tends to zero) of solutions of a corresponding slightly regularized Wigner-Poisson system are distributional solutions of the classical Vlasov-Poisson system. The result holds for the gravitational and repulsive cases. Also, for every phase-space density in [Formula: see text] (with bounded kinetic energy) we prepare a sequence of density matrices satisfying the above assumptions, such that the given density is the limit of the Wigner transforms of these density matrices.

scholarly journals Average of Uncertainty Product for Bounded Observables

2018 ◽  
Vol 25 (02) ◽  
pp. 1850008 ◽  
Author(s):  
Lin Zhang ◽  
Jiamei Wang
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Quantum States ◽  
Density Matrices ◽  
Finite Dimensional ◽  
Uncertainty Product ◽  
Schmidt Norm ◽  
Rank One ◽  
Pure States ◽  
Average Uncertainty

The goal of this paper is to calculate exactly the average of uncertainty product of two bounded observables and to establish its typicality over the whole set of finite dimensional quantum pure states. Here we use the uniform ensembles of pure and isospectral states as well as the states distributed uniformly according to the measure induced by the Hilbert-Schmidt norm. Firstly, we investigate the average uncertainty of an observable over isospectral density matrices. By letting the isospectral density matrices be of rank-one, we get the average uncertainty of an observable restricted to pure quantum states. These results can help us check how large is the gap between the uncertainty product and any lower bounds obtained for the uncertainty product. Although our method in the present paper cannot give a tighter lower bound of uncertainty product for bounded observables, it can help us drop any one that is not substantially tighter than the known one.

scholarly journals The ELENA facility

2018 ◽  
Vol 376 (2116) ◽  
pp. 20170266 ◽  
Author(s):  
Wolfgang Bartmann ◽  
Pavel Belochitskii ◽  
Horst Breuker ◽  
Francois Butin ◽  
Christian Carli ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Beam Energy ◽  
Low Energy ◽  
Electron Cooler ◽  
Transfer Lines ◽  
Experimental Area ◽  
Active User ◽  
Lower Beam ◽  
The Status ◽  
The Given

The CERN Antiproton Decelerator (AD) provides antiproton beams with a kinetic energy of 5.3 MeV to an active user community. The experiments would profit from a lower beam energy, but this extraction energy is the lowest one possible under good conditions with the given circumference of the AD. The Extra Low Energy Antiproton ring (ELENA) is a small synchrotron with a circumference a factor of 6 smaller than the AD to further decelerate antiprotons from the AD from 5.3 MeV to 100 keV. Controlled deceleration in a synchrotron equipped with an electron cooler to reduce emittances in all three planes will allow the existing AD experiments to increase substantially their antiproton capture efficiencies and render new experiments possible. ELENA ring commissioning is taking place at present and first beams to a new experiment installed in a new experimental area are foreseen in 2017. The transfer lines from ELENA to existing experiments in the old experimental area will be installed during CERN Long Shutdown 2 (LS2) in 2019 and 2020. The status of the project and ring commissioning will be reported. This article is part of the Theo Murphy meeting issue ‘Antiproton physics in the ELENA era’.

scholarly journals Note on the Application of Compound Poisson Processes to Sickness and Accident Statistics

1960 ◽  
Vol 1 (4) ◽  
pp. 224-237 ◽  
Author(s):  
Carl Philipson
Keyword(s):  
Random Process ◽  
Conditional Probability ◽  
Compound Poisson Process ◽  
Compound Poisson ◽  
Continuous Parameter ◽  
Absolute Probability ◽  
Image Position ◽  
The Given ◽  
Accident Statistics ◽  
Uniformly Bounded

In order to fix our ideas an illustration of the theory for (a) a general elementary random process, (b) a compound Poisson process and (c) a Polya process shall be given here below following Ove Lundberg (On Random Processes and Their Application to Accident and Sickness Statistics, Inaug. Diss., Uppsala 1940).Let the continuous parameter t* be measured on an absolute scale from a given point of zero and consider the random function N* (t*) which takes only non-negative and integer values with N* (o) = o. This function constitutes a general elementary random process for which the conditional probability that N* (t*) = n relative to the hypothesis that shall be denoted , while the absolute probability that N* (t) = n i.e. shall be written If quantities of lower order than dt* are neglected, we may write for the conditional probability that N* (t* + dt*) = n + 1 relative to thehyp othesis that N* (t*) = n, i.e. is the intensity function of the process which is assumed to be a continuous function of t* (the condition of existence for the integral over the given interval of t* for every n > m may be substituted for the condition of continuity). The expectations for an arbitrary but fix value of t* of N* (t*) and p* (t*) will be denoted by the corresponding symbol with a bar so thatIf is uniformly bounded for all n in the interval o ≤ t* < T*, where T* is an arbitrary but fix value of t*, we have i.a. that

scholarly journals A Stone-Weierstrass theorem for random functions

1970 ◽  
Vol 2 (2) ◽  
pp. 233-236 ◽  
Author(s):  
A. Mukherjea
Keyword(s):  
Random Function ◽  
Random Variables ◽  
Compact Set ◽  
Mean Square ◽  
Weierstrass Theorem ◽  
Random Functions ◽  
The Given ◽  
Uniformly Bounded

It is shown in this note that if Q is an algebra of uniformly bounded mean-square continuous real-valued random functions indexed in a compact set T, containing all bounded random variables and separating points of T (i.e., given t1 and t2 in T, there is a random function Xt in Q such that , then given any mean square continuous random function, there is a sequence in Q converging in mean square to the given random function uniformly on T.

Influence of the Axisymmetric Contraction Ratio on Free-Stream Turbulence

1976 ◽  
Vol 98 (3) ◽  
pp. 506-515 ◽  
Author(s):  
V. Ramjee ◽  
A. K. M. F. Hussain
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulence Intensity ◽  
Free Stream ◽  
Mesh Size ◽  
Turbulence Level ◽  
Free Stream Turbulence ◽  
Contraction Ratio ◽  
The Given ◽  
Screen Mesh

The effect of axisymmetric contractions of a given shape and of contraction ratios c = 11, 22, 44.5, 64, and 100 on the free-stream turbulence of an incompressible flow has been studied experimentally with hot-wires. It is found that the longitudinal and lateral kinetic energies of turbulence increase along the contraction. The monotonic increase of the longitudinal turbulent kinetic energy with increasing c is in contrast with the linear (Batchelor-Proudman-Ribner-Tucker) theory. The variation of the lateral turbulent kinetic energy with c is in qualitative agreement with the theory; however, the increase is much lower than that predicted by the theory. The linear theory overpredicts the decrease in the longitudinal turbulence intensity with increasing c and under-predicts the decrease in the lateral turbulence intensity with increasing c. For the given flow tunnel, it is found that a contraction ratio c greater than about 45 is not greatly effective in reducing longitudinal turbulence levels further; the lateral turbulent intensity continues to decrease with increasing c. In the design of a low turbulence-level tunnel, the panacea for the reduction of the turbulence level does not lie in an indefinite increase of the contraction ratio alone. Studies with various upstream screens and a given contraction of c = 11 suggest that the exit turbulence intensities are essentially independent of the Reynolds number based on the screen-mesh size or screen-wire diameter of the upstream screen.

scholarly journals Collisions through liquid layers

1949 ◽  
Vol 45 (3) ◽  
pp. 488-488
Author(s):  
F. R. Eirich ◽  
D. Tabor
Keyword(s):  
Kinetic Energy ◽  
Liquid Film ◽  
Plug Flow ◽  
Vertical Direction ◽  
Velocity Change ◽  
Image Position ◽  
The Right ◽  
The Given ◽  
Original Derivation ◽  
Derivation Equation

The initial collision (see pp. 571–2). The instantaneous velocity change of the hammer (from V0 to V) when it first strikes the liquid film should be calculated from energy and not momentum considerations, since the hammer has momentum in the vertical direction whilst the liquid is expressed in a horizontal direction and its total momentum is, by symmetry, zero at every instant. The kinetic energy dE of an annulus of liquid of radius r will be ½mc2, where m = 2πrhρdr, and c, the radial velocity of flow, is ½rV/h, since the liquid starts moving in plug flow. Integrating from r = 0 to r = R, we find that the total kinetic energy E imparted to the liquid film is . Assuming that extraneous energy losses, including any energy imparted to the anvil, are negligible, we may equate this to the energy loss of the hammer . HenceTo a first approximation this yieldsThe term at the right-hand side of the denominator is one-half that given in the original derivation (equation (20)), so that the instantaneous decrease in the velocity of the hammer is even less marked. For the given case where M = 400g., R = 1 cm., ρ = 1.6 and h = 5 × 10−2 cm., the velocity decrease is less than 2%.Vol. 44 (1948), pp. 566–80.

scholarly journals Influence of drop size distribution and kinetic energy in precipitation modelling for laboratory rainfall simulators

2021 ◽  
Author(s):  
Harris Ramli ◽  
Siti Aimi Nadia Mohd Yusoff ◽  
Mastura Azmi ◽  
Nuridah Sabtu ◽  
Muhd Azril Hezmi
Keyword(s):  
Kinetic Energy ◽  
Size Distribution ◽  
Drop Size ◽  
Drop Size Distribution ◽  
Scale Model ◽  
Simulated Rainfall ◽  
Rainfall Simulator ◽  
Natural Rainfall ◽  
Set Up ◽  
The Given

Abstract. It is difficult to define the hydrologic and hydraulic characteristics of rain for research purposes, especially when trying to replicate natural rainfall using artificial rain on a small laboratory scale model. The aim of this paper was to use a drip-type rainfall simulator to design, build, calibrate, and run a simulated rainfall. Rainfall intensities of 40, 60 and 80 mm/h were used to represent heavy rainfall events of 1-hour duration. Flour pellet methods were used to obtain the drop size distribution of the simulated rainfall. The results show that the average drop size for all investigated rainfall intensities ranges from 3.0–3.4 mm. The median value of the drop size distribution or known as D50 of simulated rainfall for 40, 60 and 80 mm/h are 3.4, 3.6, and 3.7 mm, respectively. Due to the comparatively low drop height (1.5 m), the terminal velocities monitored were between 63–75 % (8.45–8.65 m/s), which is lower than the value for natural rainfall with more than 90 % for terminal velocities. This condition also reduces rainfall kinetic energy of 25.88–28.51 J/m2mm compared to natural rainfall. This phenomenon is relatively common in portable rainfall simulators, representing the best exchange between all relevant rainfall parameters obtained with the given simulator set-up. Since the rainfall can be controlled, the erratic and unpredictable changeability of natural rainfall is eliminated. Emanating from the findings, drip-types rainfall simulator produces rainfall characteristics almost similar to natural rainfall-like characteristic is the main target.

scholarly journals APPLICATION THE BASIC CONCEPTS AND LAWS OF METHAMATICS IN THE FIELD OF MODERN TECHNOLOGY

2020 ◽  
Vol 2020 (1) ◽  
pp. 43-48
Author(s):  
N Khudoyberdiyev ◽  
◽  
N Tolipova
Keyword(s):  
Power Plant ◽  
Kinetic Energy ◽  
Modern Technology ◽  
Circuit Diagram ◽  
Fluid Distribution ◽  
Mathematical Formula ◽  
Basic Concepts ◽  
The Given

This article we will discuss the mathematical formula and basic terms specific to engineering practitioners. Mathematics can solve a given problem quickly and easily in the form of a definition, even if it is used as an integral or matrix. In this article, it can be tried to apply the advanced portion of the mathematics matrix to the generation of electricity, i.e.by adding various additions and notes to the given circuit diagram, we can identify the current matrix.Several physical bodies, such as conical cushioning objects, were used to calculate the kinetic energy produced by rotating axes and to provide precise integrative methods for determining fluid distribution in power plant construction.When addressing various parts of mathematics, such as mechanics, physics and engineering, integrative calculus is called continuously of mathematics. The reasons for integrating the integrated kangi into practice are, first, the opposite of integral differentiation, and second, integral cohesion coefficient and threshold.This article mainly illustrates the ways in which problems can be solved in a very comprehensive way.

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