حساب أنماط القصّ الطولية لسائل فيرمي بتابعية بارامترات لانداو حتى المرتبةl≤3
Abstract
اعتماداً على نظرية سائل فيرمي (FERMI LIQUID THEORY)، تم ّحساب أنماط القصّ الطولية لسائل فيرميوني متفاعل، السويات الطاقية الدنيا لجسيماته في حالة مقاربة مع السويات الطاقية لجسيمات الغازالفيرميوني الحرّ، أو ما يعرف بسوائل فيرمي النظامية، وذلك بتابعية معاملات (بارامترات)لانداو حتى المرتبة في منشور تابع التأثير المتبادل ما بين أشباه الجسيمات.
لقد عددنا في أثناء الدراسة أنّ درجة الحرارة من رتبة ، بحيث تتحقق من أجلها العلاقة الآتية ،حيث إنّ تمثل درجة الحرارة على سطح فيرمي (FERMI SURFACE)، وتكون هذه الدرجة من رتبة كلفن في معظم المعادن. بفرض أنّ الاضطراب الذي يؤدي إلى انحراف السائل عن حالة التوازن عبارة عن كمون شعاعي يتحقق فيه الشرط الآتي:
علماً أنّ عبارة عن طاقة ومتجهة الموجة على سطح فيرمي على التوالي، بينما متجهة الموجة والتواتر للكمون الخارجي المطبق. تبين لنا أنّ هذه الأنماط الطولية تكون تابعة للمقدار ، حيث عبارة عن سرعة أشباه الجسيمات على سطح فيرمي.
Depending on Fermi liquid theory we calculated the longitudinal shears modulus of interacting fermions liquid. Its low energy levels in corresponding with that one in free fermion gas which we call normal Fermi liquids. The expression of the longitudinal shears was calculated in terms of Landau parameters with in the expansion of the interacting function between quasi particles.
In our search we have been considered the temperature from order since the relation is true, where is the temperature on Fermi surface and it is from order kelvinin most metals. The external potential which causes the liquid to deviate from its equilibrium state was considered a vector potential such that:
Where are the energy and vector wave on Fermi surface consequently, while are the frequency and wave vector of the vector potential. We have found that this longitudinal shears modulus is a function to the quantity where is the velocity of quasi particles on Fermi surface.
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