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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)

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(19)

(20)

(21)

(22)

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(26)

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(29)

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(31)

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