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NEOCLASSICAL THEORY OF INTERACTION 73

is to avoid the deep diving into quantum mechanics and not going faraway beyond Newtonian
classical mechanics.
Fortunately, in 1900 Paul Drude proposed the transport properties of electrons in materials
(especially metals) which later in 1905 was extended by Hendrik Antoon Lorentz. This model
is based on assumptions that any highly conductive material consists of relatively motionless,
much heavier positive ion cores and the ocean of non-interacting with each other electrons
developing an electron “cloud” or “gas” around the peripheries of these ions. Because of the
erratic, random movements of electrons, the total macroscopic conduction current defined by
these chaotic activities is zero or close to zero. In the presence of external E-field, the “cloud”
seizes some drift velocity, i.e. the statistically average electron starts its movement with the
“cloud.”
2.5.2 Drude-Lorentz’s Model of Metal Dielectric Constant

At first glance, the title of this section sounds slightly confusing. We are sure that metal is a
good conductor. If so, how it is possible to describe it the same way as a dielectric. Nevertheless,
a closer look reveals the substantial similarity between them. We already have mentioned that
the electrical field vector of harmonic fields varies in time as shown in Figure 2.4.1 and turns
upside down each half of its time period. Unquestionably, the negatively charged electrons must
follow such switches in the field polarity changing their path direction with some delay
periodically and taking part in additional “collisions” (in quantum meaning) with ions.
According to the Drude-Lorentz’s model, three leading forces define each electron movement

1. The first one is the Coulomb force exerted by the applied E-field and equals to ΔqE(t) (see
the equation (1.11)). Here Δq = -e is the negative charge of a single electron.
2. The second one is the frictional or damping force (–()( /)) that is proportional to

electron mass and its speed (). This force drags the electron back from ion after their

“collisions” reducing electron kinetic energy. The damping or relaxation coefficient [s]
is usually predicted by quantum mechanical analysis, or measured experimentally. For such
−14
good conductor as a copper = 2.4 ⋅ 10 [s] meaning that the ratio / ≅ 3.8 ⋅

10 −17 [kg/s] is fairly tiny at the macroscopic
level. By contrast, in a good dielectric the
relaxation time is of the order of days.
3. The third one takes into consideration
such effect as the electron oscillation around

Figure 2.5.1 Coil spring model of ions. Recall that through Coulomb binding force
ion-electron interaction a negatively charged electron with mass is

attracted by positively charged ion with
mass . Evidently, the external monochromatic E-field favors this attraction for half

period and disrupts it for another half period (see Figure 2.4.1). Thus, the electron starts
the forced back and forth oscillation following E-field variation. Such ion-electron
interaction is a quantum by nature but can be modeled as though a positively charged ion
and negatively charge electron is connected by a one-dimensional coil spring shown in
Figure 2.5.1 Since ≫ the ion practically does not participates in this oscillation.

Without losing meaning, we may assume that the spring deprived of shape-memory and
loss is perfectly flexible while the external mechanical force dislocating the electron from