Borland Lisa; Menchero J. G.
Description:
Consequences of long-range hopping in one-dimensional tight-binding models are studied. a hopping term proportional to <img src="http:/img/fbpe/bjp/v29n1/liab1.gif" alt="liab1.gif (146 bytes)" align="absmiddle"> is used, where rij denotes the distance between atoms i and j and <FONT FACE="Symbol">a</font> determines the range of the interactions within the system. Calculations of the diffusion of an electron along the lattice yield interesting effects of nonextensivity. In particular, we find that the mean square displacement scales anomalously as Dt<FONT FACE="Symbol">g</font> in the following way: For 0 < <FONT FACE="Symbol">a</font> < 1, we find D <FONT FACE="Symbol">µ</font> NN*, where N is the number of atoms on the lattice and <img src="http:/img/fbpe/bjp/v29n1/liab2.gif" alt="liab2.gif (238 bytes)" align="absmiddle"> is related to the number of elements interacting at a given <FONT FACE="Symbol">a</font>. In this regime the behaviour is subdiffusive (.5 <FONT FACE="Symbol">£ g</font> < 1) but approaches normal diffusion (<FONT FACE="Symbol">g</font> = 1) for <FONT FACE="Symbol">a</font> = 1. There exists a transition region between 1 < <FONT FACE="Symbol">a</font> < 2, where the diffusion coefficient loses its system size dependency and becomes size independent for all <FONT FACE="Symbol">a</font> <FONT FACE="Symbol">³ </font>2. In addition, we find 1< <FONT FACE="Symbol">g</font> <FONT FACE="Symbol">£ </font>2 (superdiffusion) for <FONT FACE="Symbol">a</font> >1. Ballistic motion (<FONT FACE="Symbol">g</font> = 2) is recovered for all <FONT FACE="Symbol">a</font> <FONT FACE="Symbol">³ </font>1.5 and is maintained in the nearest neighbour limit. Specific heat and internal energy as a function of temperature and system size are also analyzed. They appear extensive on the macroscopic level for all values of <FONT FACE="Symbol">a</font>.