General computational method for two-electron systems

Instability of dynamic localization in the intense terahertz-driven semiconductor Wannier-Stark ladder due to the dynamic Fano resonance

“…According to a simple perturbation picture, the parent band with j = 0 is believed to be predominantly coupled with an adjacent PSB with |j| = 1, and higher-order interactions with |j| ≥ 2 generally assume greater importance with an increase in F ac . Here, this new mechanism is termed dynamic Fano resonance (DFR) because it is similar to the conventional Fano effect [27] that arises from static couplings, for instance, an electron-electron interaction in a helium atom [28] and an electron-phonon coupling in a heavily doped p-type silicon crystal [29]. Unlike in the case of such static couplings, the strength of the ac-ZT coupling for the DFR can be tuned by changing F ac and the THz frequency; in the present DWSL problem, the Bloch frequency is set to be equal to an integer multiple of the THz frequency.…”

Independent eigenstates of angular momentum in a quantumN-body system

“…Since the partial angular momenta are generally not conserved, one has to deal with, in principle, an infinite number of partial angular momentum states. This problem also occurs in the hyperspherical harmonic function method and its improved versions [17][18][19][20][21][22]. It causes unnecessary degeneracy of the hyperspherical harmonic states because, as Wigner proved, only (2ℓ + 1) base functions with angular momentum ℓ are involved in the calculation.…”

“…One is that the generalized harmonic polynomial Q ℓτ q (R 1 , R 2 ) is a homogeneous polynomial in the components of two Jacobi coordinate vectors R 1 and R 2 , where the Euler angles do not appear explicitly. The other is the well chosen internal variables (22), where the internal variables ζ j have odd parity. It is due to the existence of ζ j that Q ℓ0 q (R 1 , R 2 ) and Q ℓ1 q (R 1 , R 2 ) appear together in the expansion of the wave function.…”

“…From Eq. (22) we are able to express all the components R ′ jb of the Jacobi coordinate vectors R j in the body-fixed frame by the internal variables:…”

“…In the present paper we will separate the global rotational variables in the Schrödinger equation for an N-body system from the internal ones by a generalized method following the approach described above. In our approach, the number of base functions with the given angular momentum is finite, but that number in the hyperspherical harmonic function method and its improved versions [13,[17][18][19][20][21][22] is infinite due to the unconserved partial angular momenta. We also avoid the heavy differential calculus with respect to the Euler angles which is sometimes necessary for expressing kinetic energy operators.…”