a singe hydrogen atom [@Lauhon2000], resonant tunneling of Cooper pairs [@Toppari2007], and a bosonic Josephson junction consisting of two weakly coupled Bose-Einstein condensates in a macroscopic double-well potential [@Albiez2005].

We present a class of 2D systems which has a counterintuitive property that contradicts the semi classical intuition: A 2D quantum particle “prefers” tunneling through to flying above a barrier. According to our analysis, such “paradoxical” dynamics is caused by a peculiar symmetry of the barrier that leads to excitations of an interparticle degree of freedom. There is no 1D counterpart of such systems.

The rest of the article is organized as follows: In Sec. \[Sec2\], we present the systems and describe the counterintuitive effect. The observed “paradox” is explained in Sec. \[Sec3\]. Connections between the phenomenon and classical physics are discussed in Sec. \[Sec4\]. Concluding remarks and a possible application of the effect to quantum control are presented in the last section.

Formulation of the “paradox” {#Sec2}
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Let us consider a particle moving in 2D (coordinates $x_1$ and $x_2$) toward a barrier located at the origin $x_1=x_2=0$. The initial velocity of the particle is chosen to be directed along the diagonal $x_1=x_2$, incident on the barrier from the third 