the same mass. The essence of the effect lies in possibility of tuning the potential barriers such that the intraparticle degree of freedom is excited. (iii) Dynamics of tunneling crucially depends on whether the intraparticle potential supports one or more bound states (an exact number is irrelevant for the qualitative description).

Classical Physics and The “paradox” {#Sec4}
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A classical counterpart of the quantum system at hand \[Eq. (\[HamiltonianCartesianDef\])\] is a mechanical system with the Hamiltonian $$\begin{aligned}
\label{ClassicalHamiltonianCartesian}
\mathrsfs{H}(p_1, p_2; x_1, x_2) = \left( p_1^2 + p_2^2 \right)/2 + \Omega_N (\alpha; x_1, x_2),\end{aligned}$$ where $p_{1,2}$ and $x_{1,2}$ are canonically conjugate variables. One may perform the canonical transformation to rewrite the Hamiltonian (\[ClassicalHamiltonianCartesian\]) in terms of the new canonical variables $P_R$, $P_{\rho}$ and $R$, $\rho$, where the latter pair being the center of mass and relative coordinates \[Eq. (\[SimpleCMandRelativeCoord\])\], $$\begin{aligned}
\label{ClassicalHamiltonianCM_Relative}
\mathrsfs{H}\left( P_R, P_{\rho}; R, \rho\right) = P_R^2 /4 + P_{\rho}^2 + \tilde{\Omega}_N (\alpha; R, \rho).\end{aligned}$$ The connection between new and old canonical momenta reads: $
p_1 = P_R/2 - P_{\rho}, \quad p_2 = P_R/2 + P_{\rho}.
$

The initial condition for the classical counterpart that corresponds to the initial condition (\[InitialCondition\]) is $x_1(0) = x_2(0) = \bar{R}$ and $p_1(0) = 