Kvant statistikaları haqqında anlayış

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Kvant statistikası klassik statistikada olduğu kimi çoxlu sayda zərrəciklərdən təşkil olunmuş makroskopik sistemlərin (cisimlərin) tarazlıq hallarında fiziki xassələrini öyrənir. Buna görə də, statistik fizikanın hər iki statistikada istifadə etdiyi tədqiqat metodları demək olar ki, eynidir. Fərq ondan ibarətdir ki, klassik statistik fizikada sistemi təşkil edən zərrəciklərin hərəkəti klassik mexanika qanunları ilə kvant statistikasında isə kvant mexanikasının qanunları ilə təsvir olunur.

Kvant mexanikasında sistemin halı diskret olaraq dəyişir. Başqa sözlə, sistemin enerjisi (0 ÷ ∞) intervalında olan bütün qiymətləri almayıb, yalnız mümkün kvant qiymətlərini alır. Bu zaman zərrəcik hər bir kvant halında sonlu zaman fasiləsində qaldığından onun bu halda olmasının ehtimalından danışılır.

Kvant mexanikasında zərrəciklər iki qrupa ayrılırlar:

  • Bozonlar
  • Fermionlar

Bozonlar spinləri sıfır və tam ədədlər olan zərrəciklərdir. Məsələn, fotonlar, fononlar, π-mezonlar və s. bozon zərrəciklərdir.

Bozonların halı simmetrik hal funksiyaları ilə müəyyən olunur. Enerjisi Ek olan bozonların verilmiş T temperaturunda orta sayı aşağıdakı ifadə ilə təyin olunur:

 

      

Bu eyni zamanda bozonların kvant hallarının sayıdır. (1) ifadəsinə Boze-Eynşteyn paylanması da deyilir. Bu paylanma ilk dəfə Boze tərəfindən foton sistemi üçün verilmişdir. Foton üçün kimyəvi potensial sıfra bərabərdir: Kimyəvi potensial isə bir zərrəciyə düşən sərbəst enerjidir.

Sistemin halları arasıkəsilməz dəyişirsə, enerjisi E, E+dE intervalındakı boze-zərrəciklərinin orta sayı üçün

     

İfadəsi alınır. Bu düsturda V – həcm, g – enerjinin vahid intervalına düşən özəklərin sayı və ya kvant hallarının sıxlığı adlanır.

Boze-Eynşteyn statistikasının əsas xüsusiyyəti hər bir kvant halında istənilən sayda bozonun olmasıdır. Bozonlar seçilməzlik prinsipinə tabedirlər və eyni növdən olan bozonlar bir-birindən heç bir xassə ilə fərqlənmirlər. Məsələn, fotonları nömrələmək və onların hərəkətini izləmək mümkün deyil. Bozonların fərqləndirici cəhəti budur ki, onların enerjisi diskret və kəsilməz də ola bilər.

Yüksək temperaturlarda (olduğu üçün), yəni nk-nın kiçik qiymətlərində Boze-Eynşteyn statistikası Maksvell-Bolsman statistikasına keçir. Boze-Eynşteyn statistikasına tabe olan hissəciklər çoxluğu Boze-qaz, hissəciklərin özü isə bozonlar adlanır.

Müəyyən temperaturdan başlayaraq bu qazın hissəcikləri, impulsu sıfır olan hala keçməyə çalışırlar. Bu hadisəyə Boze-Eynşteyn kondensasiyası və ya cırlaşması deyilir. Real qazların Boze-Eynşteyn ifrat axıcılıq hadisəsini izah etməyə imkan verir. Boze-Eynşteyn statistikası klassik statistikasının izah edə bilmədiyi bir çox fiziki hadisələri izah etməyə imkan verir. Məsələn, bərk istilik tutumunun temperaturdan asılılığını, mütləq qara cismin şüalanma qanunlarının və s.

 


Ədəbiyyat:

E.M.Qocayev, Ə.Ə.Əbdürrəhimov,A.Ə.Abasov,S.İ.Tağıyev – Ümumi fizika kursu.

Савельев И.В. «Курс общей физики», I, II, III т. «Наука».

 

Redaktə etdi: Şəfiqə Babayeva

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