Dimensional-scaling estimate of the energy of a large system from that of its building blocks: Hubbard model and Fermi liquid

A simple, physically motivated, scaling hypothesis, which becomes exact in important limits, yields estimates for the ground-state energy of large, composed, systems in terms of the ground-state energy of its building blocks. The concept is illustrated for the electron liquid, and the Hubbard model. By means of this scaling argument the energy of the one-dimensional half-filled Hubbard model is estimated from that of a 2-site Hubbard dimer, obtaining quantitative agreement with the exact one-dimensional Bethe-Ansatz solution, and the energies of the two- and three-dimensional half-filled Hubbard models are estimated from the one-dimensional energy, recovering exact results for $U\to 0$ and $U\to \infty$ and coming close to Quantum Monte Carlo data for intermediate $U$.Comment: 3 figure

Synchronization in the presence of memory

We study the effect of memory on synchronization of identical chaotic systems driven by common external noises. Our examples show that while in general synchronization transition becomes more difficult to meet when memory range increases, for intermediate ranges the synchronization tendency of systems can be enhanced. Generally the synchronization transition is found to depend on the memory range and the ratio of noise strength to memory amplitude, which indicates on a possibility of optimizing synchronization by memory. We also point out on a close link between dynamics with memory and noise, and recently discovered synchronizing properties of networks with delayed interactions