Quantum Tunneling on Newton’s Terms

Geoff Brumfiel

Tunneling, a quantum mechanical effect, can be described in mostly classical terms in a new computational scheme.

Juan Pedro Palomares-Báez, Boris I. Ivlev, José Luis Rodríguez‐López

Quantum tunneling through a nonstationary barrier is studied analytically and by a direct numerical solution of Schr\"odinger equation. Both methods are in agreement and say that the main features of the phenomenon can be described in terms of classical trajectories which are solutions of Newton's equation in complex time. The probability of tunneling is governed by analytical properties of a time-dependent perturbation and the classical trajectory in the plane of complex time. Some preliminary numerical calculations of Euclidean resonance (an easy penetration through a classical nonstationary barrier due to an underbarrier interference) are presented.

S. Withington, P. Kennedy

The paper describes a numerical procedure for simulating, in the frequency domain, the large-signal quantum behaviour of superconducting tunnel-junction circuits. It is shown that the steady-state dynamics of a circuit can be decomposed by using the method of harmonic balance, and that the resulting system of coupled nonlinear algebraic equations can be solved through harmonic Newton. The presentation is generalised in a number of ways: first, the scheme is described in terms of a generic circuit comprising a tunnel junction and a Thevenin voltage source; secondly, the circuit equations are normalised to the gap voltage and the gap current of the tunnel barrier; and thirdly, an imperfect junction is modelled by convolving an ideal BCS current/voltage characteristic with a Gaussian function.

Benjamin Bähr, Boris Lemmer, Rina Piccolo