A pictorial representation of zero-point energy and tunnelling contributions to primary hydrogen isotope effects

2010 ◽  
Vol 23 (7) ◽  
pp. 572-579 ◽  
Author(s):  
R. A. More O'Ferrall
Keyword(s):  
Hydrogen Isotope ◽  
Isotope Effects ◽  
Zero Point ◽  
Pictorial Representation ◽  
Zero Point Energy ◽  
Point Energy

scholarly journals An investigation into the existence of zero-point energy in the Rock-Salt Lattice by an X-Ray Diffraction Method

1928 ◽  
Vol 118 (779) ◽  
pp. 334-350 ◽  
Keyword(s):  
Rock Salt ◽  
Diffraction Method ◽  
Zero Point ◽  
Temperature Factor ◽  
X Rays ◽  
Zero Point Energy ◽  
Chlorine Atoms ◽  
Point Energy ◽  
X Ray ◽  
State Of Rest

In the present paper we shall attempt to collate the results of four separate lines of research which, taken together, appear to provide some interesting checks between theory and experiment. The investigations to be considered are (1) the discussion by Waller* and by Wentzel,† on the basis of the quantum (wave) mechanics, of the scattering of radiation by an atom ; (2) the calculation by Hartree of the Schrödinger distribution of charge in the atoms of chlorine and sodium ; (3) the measurements of James and Miss Firth‡ of the scattering power of the sodium and chlorine atoms in the rock-salt crystal for X-rays at a series of temperatures extending as low as the temperature of liquid air ; and (4) the theoretical discussion of the temperature factor of X-ray reflexion by Debye§ and by Waller.∥ Application of the laws of scattering to the distribution of charge calculated for the sodium and chlorine atoms, enables us to calculate the coherent atomic scattering for X-radiation, as a function of the angle of scattering and of the wave-length, for these atoms in a state of rest, assuming that the frequency of the X-radiation is higher than, and not too near the frequency of the K - absorption edge for the atom.¶ From the observed scattering power at the temperature of liquid air, and from the measured value of the temperature factor, we can, by applying the theory of the temperature effect, calculate the scattering power at the absolute zero, or rather for the atom reduced to a state of rest. The extrapolation to a state of rest will differ according to whether we assume the existence or absence of zero point energy in the crystal lattice. Hence we may hope, in the first place to test the agreement between the observed scattering power and that calculated from the atomic model, and in the second place to see whether the experimental results indicate the presence of zero-point energy or no.

scholarly journals Zero-Point Energy Leakage in Quantum Thermal Bath Molecular Dynamics Simulations

2016 ◽  
Vol 12 (12) ◽  
pp. 5688-5697 ◽  
Author(s):  
Fabien Brieuc ◽  
Yael Bronstein ◽  
Hichem Dammak ◽  
Philippe Depondt ◽  
Fabio Finocchi ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Zero Point ◽  
Thermal Bath ◽  
Zero Point Energy ◽  
Point Energy ◽  
Energy Leakage ◽  
Dynamics Simulations

Electric field induced phase transition in first order ferroelectrics with large zero point energy

2008 ◽  
Vol 387 (1) ◽  
pp. 115-122 ◽  
Author(s):  
C.L. Wang ◽  
J.C. Li ◽  
M.L. Zhao ◽  
J.L. Zhang ◽  
W.L. Zhong ◽  
...  
Keyword(s):  
Phase Transition ◽  
Electric Field ◽  
Zero Point ◽  
Zero Point Energy ◽  
Point Energy ◽  
First Order
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