the charge density (SI unit: coulombs per cubic metre), in which is the number of particles per unit volume ("number density") (SI unit: m−3); is the charge of the individual particles with density (SI unit: coulombs). A common approximation to the current density assumes the current simply is proportional to the electric field, as expressed by: where is the electric field and is the electrical conductivity. Conductivity is the reciprocal (inverse) of electrical resistivity and has the SI units of siemens per metre (S⋅m−1), and has the SI units of newtons per coulomb (N⋅C−1) or, equivalently, volts per metre (V⋅m−1). A more fundamental approach to calculation of current density is based upon: indicating the lag in response by the time dependence of , and the non-local nature of response to the field by the spatial dependence of , both calculated in principle from an underlying microscopic analysis, for example, in the case of small enough fields, the linear response function for the conductive behaviour in the material. See, for example, Giuliani & Vignale (2005) or Rammer (2007). The integral extends over the entire past history up to the present time. The above conductivity and its associated current density reflect the fundamental mechanisms underlying charge transport in the medium, both in time and over distance. A Fourier transform in space and time then results in: where is now a complex function. In many materials, for example, in crystalline materials, the conductivity is a tensor, and the current is not necessarily in the same direction as the applied field. Aside from the material properties themselves, the application of magnetic fields can alter conductive behaviour. Polarization and magnetization currents Currents arise in materials when there is a non-uniform distribution of charge. In dielectric materials, there is a current density corresponding to the net movement of electric dipole moments per unit volume, i.e. the polarization : Similarly with magnetic materials, circulations of the magnetic dipole moments per unit volume, i.e. the magnetization , lead to magnetization currents: Together, these terms add up to form the bound current density in the material (resultant current due to movements of electric and magnetic dipole moments per unit volume): Total current in materials The total current is simply the sum of the free and bound currents: Displacement current There is also a displacement current corresponding to the time-varying electric displacement field : which is an important term in