many dimensional tunneling is equated to the tunneling of complex (i.e., many particle) systems.

Key aspects of the quantum mechanical tunneling of complex systems were analyzed by Zakhariev [*et al.*]{} [@Zakhariev1964; @Amirkhanov1966] in the mid-1960s; nevertheless, this problem has become an area of active research only in the past few decades (see, e.g., Refs. [@Tomsovic1998; @Takagi2002; @Zakhariev2002; @Razavy2003a; @Ankerhold2007] and references therein). Tunneling of a diatomic molecule has been studied in Refs. [@Goodvin2005; @Goodvin2005a; @Lee2006; @Hnybida2008; @Shegelski2008; @Kavka2010]. Mechanisms of single and double proton transfer have been modelled by multidimensional tunneling [@Smedarchina1995; @Smedarchina2007; @Smedarchina2008]. Time-dependent numerical study of tunneling dynamics of a two-particle quantum system with an internal degree of freedom has been analyzed in Ref. [@Volkova2006], and an enhancement of the tunneling probability due to the formation of a long-lived resonant state of the system in the barrier region has been discovered (similar analytical studies have been done in Ref. [@Yamamoto1996]). It has also been suggested that collective tunneling of electrons may have an important contribution to multiple ionization of atoms in a superstrong laser field [@Kornev2009]. Quantum tunneling of complex systems is not only of theoretical interest. Recent experiments where this phenomenon is observed directly include tunneling of 