کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1899984 | 1045212 | 2006 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Energy landscape properties studied using symbolic sequences
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
We investigate a classical lattice system with N particles. The potential energy V of the scalar displacements is chosen as a Ï4 on-site potential plus interactions. Its stationary points are solutions of a coupled set of nonlinear equations. Starting with Aubry's anti-continuum limit it is easy to establish a one-to-one correspondence between the stationary points of V and symbolic sequences Ï=(Ï1,â¦,ÏN) with Ïn=+,0,â. We prove that this correspondence remains valid for interactions with a coupling constant ϵ below a critical value ϵc and that it allows the use of a “thermodynamic” formalism to calculate statistical properties of the so-called “energy landscape” of V. This offers an explanation for why topological quantities of V may become singular, like in phase transitions. In particular, we find that the saddle index distribution is maximum at a saddle index nsmax=1/3 for all ϵ<ϵc. Furthermore there exists an interval (vâ,vmax) in which the saddle index ns as a function of the average energy vÌ is analytical in vÌ and it vanishes at vâ, above the ground state energy vgs, whereas the average saddle index nÌs as a function of the energy v is highly nontrivial. It can exhibit a singularity at a critical energy vc and it vanishes at vgs, only. Close to vgs,nÌs(v) exhibits power law behavior which even holds for noninteracting particles.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 216, Issue 1, 1 April 2006, Pages 157-166
Journal: Physica D: Nonlinear Phenomena - Volume 216, Issue 1, 1 April 2006, Pages 157-166
نویسندگان
Rolf Schilling,