135 research outputs found
Classical kinetic energy, quantum fluctuation terms and kinetic-energy functionals
We employ a recently formulated dequantization procedure to obtain an exact
expression for the kinetic energy which is applicable to all kinetic-energy
functionals. We express the kinetic energy of an N-electron system as the sum
of an N-electron classical kinetic energy and an N-electron purely quantum
kinetic energy arising from the quantum fluctuations that turn the classical
momentum into the quantum momentum. This leads to an interesting analogy with
Nelson's stochastic approach to quantum mechanics, which we use to conceptually
clarify the physical nature of part of the kinetic-energy functional in terms
of statistical fluctuations and in direct correspondence with Fisher
Information Theory. We show that the N-electron purely quantum kinetic energy
can be written as the sum of the (one-electron) Weizsacker term and an
(N-1)-electron kinetic correlation term. We further show that the Weizsacker
term results from local fluctuations while the kinetic correlation term results
from the nonlocal fluctuations. For one-electron orbitals (where kinetic
correlation is neglected) we obtain an exact (albeit impractical) expression
for the noninteracting kinetic energy as the sum of the classical kinetic
energy and the Weizsacker term. The classical kinetic energy is seen to be
explicitly dependent on the electron phase and this has implications for the
development of accurate orbital-free kinetic-energy functionals. Also, there is
a direct connection between the classical kinetic energy and the angular
momentum and, across a row of the periodic table, the classical kinetic energy
component of the noninteracting kinetic energy generally increases as Z
increases.Comment: 10 pages, 1 figure. To appear in Theor Chem Ac
Optical Arbitrary Waveform Measurement (OAWM) on the Silicon Photonic Platform
We demonstrate optical arbitrary waveform measurement (OAWM) using a silicon pho-tonic spectral slicer. Exploiting maximal-ratio combining (MRC), we demonstrate the viability of the scheme by reconstructing 100-GBd 64QAM signals with high quality
Perturbations of Noise: The origins of Isothermal Flows
We make a detailed analysis of both phenomenological and analytic background
for the "Brownian recoil principle" hypothesis (Phys. Rev. A 46, (1992), 4634).
A corresponding theory of the isothermal Brownian motion of particle ensembles
(Smoluchowski diffusion process approximation), gives account of the
environmental recoil effects due to locally induced tiny heat flows. By means
of local expectation values we elevate the individually negligible phenomena to
a non-negligible (accumulated) recoil effect on the ensemble average. The main
technical input is a consequent exploitation of the Hamilton-Jacobi equation as
a natural substitute for the local momentum conservation law. Together with the
continuity equation (alternatively, Fokker-Planck), it forms a closed system of
partial differential equations which uniquely determines an associated
Markovian diffusion process. The third Newton law in the mean is utilised to
generate diffusion-type processes which are either anomalous (enhanced), or
generically non-dispersive.Comment: Latex fil
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