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A novel Approach to
Quantum Plasma
N. L. Tsintsadze
Co-author: Levan N. Tsintsadze
Salam Chair in Physics , GC University Lahore 54000Department of Plasma Physics, E. Andronikashvili
Institute of Physics, Tbilisi, Georgia
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White dwarfA white dwarf-a degenerate dwarf is a small star and its volume is
comparable to that of the Earth, the mass is comparable to that of sun.
They are composed of carbon and oxygen. Over a very long time, a
white dwarf will cool to temperatures at which it will no longer be
visible, and become a cold black dwarf.
The number density
The temperatures extend from 150.000K to 4.000 K
Magnetic fields have been discovered in well over 100 white dwarfs,
ranging from to gauss.
The relationship between mass and radius
330 /10 cmn ≅
3102 ×
3/1
1~
MR
910
S. Chandrasekhar limit (1931)
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PulsarWhen the volume per atom becomes less than the usual size of the atom, the atoms lose their
individuality, and so the substance is transformed into a
highly compressed plasma of electrons and nuclei. In this case a medium becomes a degenerate Fermi gas,
and nuclear reactions consisting in the capture of electrons by nuclei decreases the charge on the
nucleus, so
Pulsar is the neutron star in which 99% electrons have been captured by protons. 1% are electrons and
protons.
ν+→+ −nep
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The density of neutrons
For electrons we have ,
which means they are in strongly degenerate state.
The radius of a neutron star ~
The magnetic field
The pulsar is a radio, optical, X-ray and gamma-emitting neutron star associated with Supernova Remnant.
Another application of the quantum theory is in a nanotechnology, where size of natural and artificial
structures is the nanometer scale, i.e., in the range of from .
338 cm/10≅n
336 cm/10~ ≅pe nn
cm10 6
gauss1010 1311 −≅
010A down toµm1
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Quantum Particles: , light ions as proton,
and at a high density and low temperatures. In
semiconductors with a large number of light carriers
(electrons), , a mass
and . The degeneracy of heavy charge
carriers (holes) occurs at lower temperatures.
+−ee , 3, HeD
+
4He
31816 1010 −→≥ cmne ee mm2* 10−≈
KTF
210<
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KTe
F
3105~ ×
For ions: Km
mT
p
ei
F
3105~ ×
For proton gas : KTp
F 6.2~
For dusty compounds: KKm
mT
D
eD
F
83 105105~ −×=×
For electrons:
If and gmD
1610 −= 32210~ −cmn D
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In a pure state the Wigner distribution function
hrrrrrrr
h
rr /*
3)2/()2/(
)2(
1),,( xpiw
exrxrxdtprf⋅−Ψ+Ψ= ∫π
0)2
sin(2
=
∂
∂⋅
∂
∂−
∂
∂⋅+
∂
∂fU
rprm
p
trr
h
hr
r
yy ≈)sin(
and
( ) 0=∂
∂⋅
∂
∂−∇⋅+
∂
∂
p
f
r
Ufv
t
frr
rr
1
density.y probabilit a is this~),(
2
2
=
Ψ
∫ Ψrd
tr
r
r
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� Condition for quasi-classical motion is that the particle de Broglie
wavelength be small compared with the characteristic
length L over which the density varies considerably,
� The same we obtain from
� In the fluid equation, we have two terms
� From this expression follows that the first term is much greater than
the second one, as
FP/h
3
1
3
1
or ~ , 1
~−
>><<<< nnpkk
Lp
F
F
λhhh
ωε h>>F
nnm
pn
F ∆∇+∇−1
2
1 2h
3/1
1
n>>λ
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The Non-relativistic Pauli equation
At
(2)
(1)
(3)
(4)
(5)
(6)
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We introduce a density of probability distribution in phase space for the
single particleSf
(7)
(8)
(9)
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(10)
(11)
(12)
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(13)
(14)
(15)
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(14)
(16)
(17)
(18)
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(19)
(20)
(21)
(22)
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(23)
(24)
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(26)
(27)
(28)
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(29)
(30)
(31)
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