S?s?et?se?? Bose-Einstein st? f?s??? ?????? e?e??e???

1

• S?s?et?se?? Bose-Einstein st? f?s??? ??????
  e?e??e???
• ?st?????
• St?? a???? t?? de?aet?a? t?? 1920 ? S.N. Bose,
  ?a????t?? t?? ?a?ep?st?µ??? ?t??a st? ß?eta????
  ??d?a ep??easµ???? ap? t? ?e???a t?? Einstein ??a
  ta f?t???a as???????e µe t? µa??µat??? ?eµe???s?
  t?? t?p?? t?? a?t???ß???a? µ??a??? s?µat?? t??
  Planck, st?? ?p??a ? Planck e??e ?ata???e? se
  µe???? ßa?µ? d?a?s??t???. 
• ???s?µ?p????ta? t? s?µat?d?a?? e????a t??
  ???st???, ? Bose ?at????e st?? t?p? t??
  a?t???ß???a? µ?s? t?? s?st?µat???? a??pt???? µ?a?
  stat?st???? ?e???a? ??a ?µa?a s?µat?d?a.
• ???te??e d?af??et???? d?a???t?? ?atast?se?? ??a
  t? f?t????, ?ftase se µ?a stat?st??? s????t?s?
  ?ata??µ?? t?? f?t????? µe d?? ep?t?ept??
  ?atast?se?? ?a? ß???e ?t? pa???s?????? p?????
  s?µµet????? ??µat?s??a?t?se??.
• S????t?s? ep?µe??sµ?? t?? f?t?????
• ?ph(T, V)?8r1 1/(1-exp(-ßer)) gt ni
  gi/(exp(ßei)-1).
•  

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• Stat?st??? Bose-Einstein
• ? stat?st??? Bose-Einstein ?a?????e? t?? ?ata??µ?
  t?? µp??????? st?? d??f??e? e?e??e?a???
  ?atast?se?? se ?e?µ??? ?s????p?a.
• ?? stat?st???? ?-? ?a? F-D efa?µ????ta? ?ta? ta
  ?ßa?t??? fa???µe?a ?????ta? s?µa?t???. ?ta? ?
  s?????t??s? t?? s?µat?d???
• (N / V) nq
• Fermi-Dirac gt fe?µ????a Bose-Einstein gt
  µp?????a
• Spin
• ?pa???e?t??? ???? t?? Pauli
• ?a µp?????a, se a?t??es? µe ta fe?µ????a, de?
  ?pa???? st?? a??? Pauli pe??ss?te?a ap? ??a
  s?µat?d?a ep?t??peta? ?a ?ata?aµß????? t?? ?d?a
  ?ßa?t??? ?at?stas?. ??t? e???e? ??at?, se ?aµ????
  ?e?µ???as?e?, ta µp?????a ?a ????? t?? t?s? ?a
  s???e?t?????ta? st?? ?d?a ?at?stas? ?aµ???te???
  e????e?a?, fa???µe?? t? ?p??? e??a? ???st? ??
  s?µp????s? B-E. 

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• S?s?et?se?? Bose-Einstein
• ? s?µß??? µeta?? d?? (? pe??ss?te???) ??µ?t??
  s???st? ??p??a s?s??t?s? µeta?? a?t?? t??
  ??µ?t??. St? s?µat?d?a?? f?s???, ?p?? ??a ???e
  s?µat?d?? a?t?st???e? ??a ??µa, s??a?t??µe
  fa???µe?a s?µß???? ?a? s?s?et?se?? µeta?? d?? (?
  pe??ss?te???) s?µat?d???, p?? pe?????f??ta?
  µa??µat??? ap? s??a?t?se?? s?s??t?s?? de?te??? ?
  ?????te??? t????. ??t?? ?? s?s?et?se?? ????? p???
  s???e???µ??e? ?d??t?te? ??a pa??µ???t?pa
  s?µat?d?a. 
• ??a??????µe t?te s?s?et?se?? B-E ??a µp?????a ?a?
  s?s?et?se?? F-D ??a fe?µ????a. 
• ??a d?????s? µeta?? t?? BEC ?a? FDC e??a? ?t?
  µ??? ?? BEC µp????? ?a pa???s??s??? ?ßa?t???
  s?µf???a (Quantum Coherence).
• ?ßa?t??? s?µf???a ????? s?µat?d?a ?????? ?????
  ???s? µ?a? ?ßa?t???? ?at?stas?? ? ?p??a d??peta?
  ap? µ?a µa???s??p??? ??µat?s????t?s? - a?t? ??e?
  s?????? t? ???µa ?ßa?t??? s?µf???a ?a?
  s??d?eta? ste?? µe t? s?µp????s? B-E. "?? e??a?
  ? ?ßa?t??? s?µf???a ??t? a?af??eta? st??
  s?????e? ?p? t?? ?p??e? µe????? a???µ?? t??
  s?µat?d??? p?? µp????? s???????? ?a s??e??ast???
  se µ?a e??a?a ?ßa?t??? ?at?stas? ..."Roger
  Penrose

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• ? ?????a t?? ?ßa?t???? s?µf???a? pa???s??st??e
  p??t? f??? ap? t?? Glauber. ??? a?????
  ???s?µ?p?????ta? ?????? ??a ?a e????se? t?
  ?e?t?????a t?? ????e?, s??t?µa d?ap?st????e ?t?
  e??a? a?t? p?? ?d??e? st? s?µp????s? B-E. 
• ? s?µp????s? B-E e??a? a?t?a s?µa?t????
  fa???µ???? st?? f?s??? s?µp????µ???? ????, ?p?? ?
  ?pe?a????µ?t?ta ?a? ? ?pe?e?st?t?ta, a???
  e?d????eta? ep?s?? ?a? st? s?µß???µet??a
  a?d??????. 
• ????? ?e??µ???? ap? t?? de?aet?a t?? 1980 ?? BEC
  ap?te???? ?a? s?µe?a p??? e?d?af????ta ??t?µata
  ??a t? f?s??? ?????? e?e??e???. ??a? ????? ??
  'a?t? t? e?d?af???? e??a? t? ?e????? ?t? ?? BEC
  e??a? µ???? t??a ? µ??? µ???d?? ??a t??
  p??sd????sµ? t?? µe?e??? ?a? t?? d????e?a? ????
  t?? p???? t?? st???e??d?? s?µat?d???.

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• S?µß???µet??a ??tas?? ?a? Fa???µe?? HBT
• ?? Robert Hanbury-Brown ?a? Richard Q. Twiss ?ta?
  ?? p??t? p?? ef??µ?sa? t??? BEC ??a t?? µ?t??s?
  t?? a?t??a? µa?????? ast????. (1956)
• ? µ???d?? efa?µ?st??e p??t? f??? ap? t??? G.
  Goldhaber, S. Goldhaber, W. Lee, ?a? A.Pais
  (GGLP) st? s?µat?d?a?? f?s???.(1959)
• ? ßas??? ?d?a t?? fa???µ???? HBT e??a? ?
  s????t?s? s?s??t?s?? t?? ??tas?? d??
  pa??µ???t?p?? ??µ?t?? st?? ???? t?? ??µ??
  s??d?eta? µe t? ??????????? ?ata??µ? t?? p????
  t??? µe ??a µetas??µat?sµ? Fourier.

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• ???s?µ?p????ta? t?? s????t?s? s?s??t?s?? t?? d??
  s?µat?d??? st?? ???? t?? ??µ??, µp????µe ?a
  p??sd????s??µe t?? a?t??a ?a? t?? ????? ???? µ?a?
  p????.
• ??a t??a?? ??µa µp??e? ?a pe????afe? ap? µ?a
  ??µat?s????t?s?
• µe u(r, t) ReU(r, t).
• G?a pa??de??µa, ??a µ??????µat??? f?? ????µe
  u(r,t) U(r)exp(j2p?t) ? ?p??a µp??e? ?a e??a?
  ?????sµa p????? pa??µ???? s??a?t?se??
  d?af??et???? s????t?t?? ?.
• 
  s????t?s? s?s??t?s??
• ?? ?? U(t), U(tt) de? s?et????ta?, t?te ? ????a
  µeta?? t?? fas???? t??? ?a p?????e? ap? 0 ??? 2p,
  ?ts? ? s????t?s? s?s??t?s?? ???eta?. ?? ?µ??
  s?et????ta? ??a ??a ???st? t, t?te ?? f?s????
  t??? ?a d?at???s??? ??p??a s??s?.
• ?a?µ?? ???????? s?µf???a?
• ??a µ?t?? t?? s?µf???a? a?e???t?t? t?? ??tas??
  t?? f?t?? d??eta? ap? t?? ?a??????p???µ???
  s????t?s? s?s??t?s??
• p?? ???µ??eta? ßa?µ?? ???????? s?s??t?s??.

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S??????se?? ?????? e?e??e???
B
A
8
S??????se?? ?????? e?e??e???
Quantum statistics
9

• S????t?s? s?s??t?s?? Bose - Einstein
• G?a n µp?????a

Se pe???µata a?t?d??se?? a?d??????, ßa????
???t??, e?a???s?? ee-, s??????se?? d?? f?t?????
pa?at??????e e??s??s? t?? pa?a????? ?e????
p?????? µe ?d?? f??t?? ?a? pa??µ??a ??µ?. ??
fa???µe?? a?t?, ???st? ?? s?s??t?s? Bose-Einstein
? ep?d?as? GGLP pa?at??????e p??t? f??? st??
e?a???s? p??t?????. ? s????t?s? s?s??t?s?? ??a
d?? µp?????a
P(p1,p2)
p1,p2 e??a? ta d?a??sµata t?? tet?a??µ??
t?? ???e s?µat?d?o?
C2(p1,p2) ?
?p??

P(p1)P(p2)
P(p1,p2) ? s????t?s? p????t?ta? p??a??t?ta? t??
d?? s?µat?d???
P(p1)P(p2) t? ????µe?? t?? s??a?t?se??
p????t?ta? p??a??t?ta? t?? ???e
s?µat?d???
10
p1
A
x1
x2
p2
B
11
BEC
A
B
12
FDC
p1
A
x1
FDC
x2
p2
B
13
??t??s? t?? µe?????? t?? p????
?etas??µat?sµ?? Fourier
P(p1,p2)
C2(p1,p2) ?

1 ?(p1-p2)2
P(p1)P(p2)
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G?at? µet??µe t??? BEC ?..

• G?a ?a p??sd????s??µe t?? t??p? p?? a?apt?sseta?
  ?
• pe????? pa?a????? t?? µp???????.
• ??? ep?d?as? t?? BEC st?? µ?t??s? t?? µ??a? t??
• s?µat?d??? W.
• G?a ?a µe?et?s??µe t?? ep?d??se?? s?s?et?sµ??
  ?????te???
• t???? ?a? t?? s???pe??? t???.
• ? µ?t??s? t?? µe?????? t?? p???? pa?a????? t??
  s?µat?d??? se
• s??????se?? ?????? e?e??e??? ??e? ?d?a?te??
  s?µas?a
• ????????ta? t? µ??e??? t?? p???? ?a? t??
  e????e?a p?? e??a?
• ap????e?µ??? se a?t?, µp????µe ?a
  p??sd????s??µe t?? e?e??e?a??
• p????t?ta e??? ?e????t??, ??t? p?? ap?te?e?
  t?? p?s?t?ta ??e?d? ??a t?
• d?e?e???s? t?? p??sµat?? quark-?????????
  (QGP).

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• ??ß?????af?a
• Multi-pion Bose-Einstein correlation effects on
  two-pion interferometry, W.Q. Chaoft, C S Gaots
  and Q.H. Zhang (IOP Science)
• Bose-Einstein correlations in ee- collisions, T.
  Schaad and R.F. Schwitters
• Saleh B.E.A., Teich M.C. Fundamentals of
  photonics (Wiley, 1991)(ISBN 0471839655)
• Institute of Science in Society
  http//www.i-sis.org.uk/QPAQC.php
• ?t?µ??? ?a? ????a?? F?s??? http//users.ntua.gr/f
  okitis/Lecture20120atomic20and20molecular20ph
  ysics202007.pdf
• ??sa???? st?? ?ßa?t??? ?pt??? ?a? ????e??, se?.
  167-169
• http//en.wikipedia.org/wiki/Hanbury_Brown_and_Twi
  ss_effect
• http//en.wikipedia.org/wiki/BoseEinstein_condens
  ate

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?????t???? d?af??e?e?
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