  Electronic transport properties through some model quantum systems are
re-visited. A simple tight-binding framework is given to describe the systems
where all numerical calculations are made using the Green's function formalism.
First, we demonstrate electronic transport in four different polycyclic
hydrocarbon molecules, namely, benzene, napthalene, anthracene and tetracene.
It is observed that electron conduction through these molecular wires is highly
sensitive to molecule-to-electrode coupling strength and quantum interference
of electronic waves passing through different branches of the molecular ring.
Our investigations predict that to design a molecular electronic device, in
addition to the molecule itself, both the molecular coupling and
molecule-to-electrode interface geometry are highly important. Next, we make an
in-depth study to design classical logic gates with the help of simple
mesoscopic rings, based on the concept of Aharonov-Bohm effect. A single
mesoscopic ring or two such rings are used to establish the logical operations
where the key controlling parameter is the magnetic flux threaded by the ring.
The analysis might be helpful in fabricating meso-scale or nano-scale logic
gates. Finally, we address multi-terminal quantum transport through a single
benzene molecule using Landauer-B\"{u}ttiker formalism. Quite interestingly we
see that a three-terminal benzene molecule can be operated as an electronic
transistor and this phenomenon is justified through current-voltage
characteristics. All these essential features of electron transport may provide
a basic theoretical framework to examine electron conduction through any
multi-terminal quantum system.
