Breakdown of a conservation law in incommensurate systems

Breakdown of a conservation law in incommensurate systems.

We show that invariance properties of the Lagrangian of an incommensurate system, as described by the Frenkel-Kontorova model, imply the existence of a generalized angular momentum that is an integral of motion if the system remains floating. The behavior of this quantity can therefore monitor the character of the system as floating (when it is conserved) or locked (when it is not). We find tha...

Conservation law of operator current in open quantum systems

Incommensurate diffusion in confined systems.

Molecular simulations corroborate the existence of the disputed window effect, i.e., an increase in diffusion rate by orders of magnitude when the alkane chain length increases so that the shape of the alkane is no longer commensurate with that of a zeolite cage. This window effect is shown to be characteristic for molecular sieves with pore openings that approach the diameter of the adsorbate....

Dynamical transitions in incommensurate systems

PACS. 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems. PACS. 64.60.Ht – Dynamical critical phenomena. PACS. 68.35.-p – Solid surfaces and solid-solid interfaces: structure and energetics. Abstract. – In the dynamics of the undamped Frenkel-Kontorova model with kinetic terms, we find a transition between two regimes, a floating incommensurate and a pinned incommen-surate phase. Thi...

A Conservation Law Method in Optimization

Abstract We propose some algorithms to find local minima in nonconvex optimization and to obtain global minima in some degree from the Newton Second Law without friction. With the key observation of the velocity observable and controllable in the motion, the algorithms simulate the Newton Second Law without friction based on symplectic Euler scheme. From the intuitive analysis of analytical sol...