  The concept of dynamical hidden symmetries in the physics of electron
tunneling through composite quantum dots (CQD) and quantum ladders (QL) is
developed and elucidated. Quite generally, dynamical symmetries are realizable
in the space of low energy excited states in a given charge sector of
nanoobjects, which involve spin variables and/or electron-hole pairs. While
spin multiplets in an individual rung of a QL or in an isolated CQD form a
representation space of the usual rotation group, this SU(2) symmetry is broken
due to spin transfer (in QL) electron cotunneling through CQD. Dynamical
symmetries in the space of spin multiplets are then unravelled in these
processes. The corresponding symmetry groups are described by SO(n) or SU(n)
depending on the origin of rotation group symmetry breaking. The effective spin
Hamiltonians of QL and CQD are derived and expressed in terms of the pertinent
group generators. We employ fermionization procedure for analyzing the physical
content of these dynamical symmetries, including Kondo tunneling through CQD
and Haldane gap formation in QL.
