Quantum Electromagnetic Zero‐Point Energy of a Conducting Spherical Shell

1972 ◽  
Vol 13 (9) ◽  
pp. 1324-1329 ◽  
Author(s):  
B. Davies
Keyword(s):  
Spherical Shell ◽  
Zero Point ◽  
Zero Point Energy ◽  
Point Energy

scholarly journals ZERO-POINT ENERGY OF A CONDUCTING SPHERICAL SHELL

1999 ◽  
Vol 14 (02) ◽  
pp. 281-300 ◽  
Author(s):  
GIAMPIERO ESPOSITO ◽  
ALEXANDER YU. KAMENSHCHIK ◽  
KLAUS KIRSTEN
Keyword(s):  
Boundary Conditions ◽  
Spherical Shell ◽  
Zero Point ◽  
Casimir Energy ◽  
Complete Agreement ◽  
Gauge Parameter ◽  
Zero Point Energy ◽  
Point Energy ◽  
Longitudinal Modes ◽  
Temporal Modes

The zero-point energy of a conducting spherical shell is evaluated by imposing boundary conditions on the potential Aμ, and on the ghost fields. The scheme requires that temporal and tangential components of Aμ perturbations should vanish at the boundary, jointly with the gauge-averaging functional, first chosen to be of the Lorentz type. Gauge invariance of such boundary conditions is then obtained provided that the ghost fields vanish at the boundary. Normal and longitudinal modes of the potential obey an entangled system of eigenvalue equations, whose solution is a linear combination of Bessel functions under the above assumptions, and with the help of the Feynman choice for a dimensionless gauge parameter. Interestingly, ghost modes cancel exactly the contribution to the Casimir energy resulting from transverse and temporal modes of Aμ, jointly with the decoupled normal mode of Aμ. Moreover, normal and longitudinal components of Aμ for the interior and the exterior problem give a result in complete agreement with the one first found by Boyer, who studied instead boundary conditions involving TE and TM modes of the electromagnetic field. The coupled eigenvalue equations for perturbative modes of the potential are also analyzed in the axial gauge, and for arbitrary values of the gauge parameter. The set of modes which contribute to the Casimir energy is then drastically changed, and comparison with the case of a flat boundary sheds some light on the key features of the Casimir energy in noncovariant gauges.

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

The zero-point energy for rotation

1978 ◽  
Vol 285 (1) ◽  
pp. 93-99 ◽  
Author(s):  
P. -G. Reinhard
Keyword(s):  
Zero Point ◽  
Zero Point Energy ◽  
Point Energy
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