ترغب بنشر مسار تعليمي؟ اضغط هنا

On the geometry of ground states and quasicrystals for lattice systems

138   0   0.0 ( 0 )
 نشر من قبل Chazottes
 تاريخ النشر 2010
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

This paper has been withdrawn. It will be split into two separate papers. New results will be added in both papers.



قيم البحث

اقرأ أيضاً

111 - Sven Bachmann 2012
In this short note, I review some recent results about gapped ground state phases of quantum spin systems and discuss the notion of topological order.
The Embedded-Atom Model (EAM) provides a phenomenological description of atomic arrangements in metallic systems. It consists of a configurational energy depending on atomic positions and featuring the interplay of two-body atomic interactions and no nlocal effects due to the corresponding electronic clouds. The purpose of this paper is to mathematically investigate the minimization of the EAM energy among lattices in two and three dimensions. We present a suite of analytical and numerical results under different reference choices for the underlying interaction potentials. In particular, Gaussian, inverse-power, and Lennard-Jones-type interactions are addressed.
77 - L. Betermin 2021
We consider pairwise interaction energies and we investigate their minimizers among lattices with prescribed minimal vectors (length and coordination number), i.e. the one corresponding to the crystals bonds. In particular, we show the universal mini mality -- i.e. the optimality for all completely monotone interaction potentials -- of strongly eutactic lattices among these structures. This gives new optimality results for the square, triangular, simple cubic (SC), face-centred-cubic (FCC) and body-centred-cubic (BCC) lattices in dimensions 2 and 3 when points are interacting through completely monotone potentials. We also show the universal maximality of the triangular and FCC lattices among all lattices with prescribed bonds. Furthermore, we apply our results to Lennard-Jones type potentials, showing the minimality of any universal minimizer (resp. maximizer) for small (resp. large) bond lengths, where the ranges of optimality are easily computable. Finally, a numerical investigation is presented where a phase transition of type square-rhombic-triangular (resp. SC-rhombic-BCC-rhombic-FCC) in dimension $d=2$ (resp. $d=3$) among lattices with more than 4 (resp. 6) bonds is observed.
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for systems wit h time-dependent nonlinear nonholonomic constraints and time-dependent Lagrangian. For discrete open systems, the~time-dependent nonlinear constraint is associated with the rate of internal entropy production of the system. We show that this constraint on the solution curve systematically yields a constraint on the variations to be used in the action functional. The proposed variational formulation is intrinsic and provides the same structure for a wide class of discrete open systems. We illustrate our theory by presenting examples of open systems experiencing mechanical interactions, as well as internal diffusion, internal heat transfer, and their cross-effects. Our approach yields a systematic way to derive the complete evolution equations for the open systems, including the expression of the internal entropy production of the system, independently on its complexity. It might be especially useful for the study of the nonequilibrium thermodynamics of biophysical systems.
119 - Piergiulio Tempesta 2014
A categorical theory for the discretization of a large class of dynamical systems with variable coefficients is proposed. It is based on the existence of covariant functors between the Rota category of Galois differential algebras and suitable catego ries of abstract dynamical systems. The integrable maps obtained share with their continuous counterparts a large class of solutions and, in the linear case, the Picard-Vessiot group.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا