Quantum triangles can work as interferometers. Depending on their geometric size and interactions between paths, "beats" and/or "steps" patterns are observed. We show that when inter-level distances between level positions in quantum triangles periodically change with time, formation of beats and/or steps no longer depends only on the geometric size of the triangles but also on the characteristic frequency of the transverse signal. For large-size triangles, we observe the coexistence of beats and steps when the frequency of the signal matches that of non-adiabatic oscillations and for large frequencies, a maximum of four steps instead of two as in the case with constant interactions is observed. Small-size triangles also revealed counter-intuitive interesting dynamics for large frequencies of the field: unexpected two-step patterns are observed. When the frequency is large and tuned such that it matches the uniaxial anisotropy, three-step patterns are observed. We have equally observed that when the transverse signal possesses a static part, steps maximize to six. These effects are semi-classically explained in terms of Fresnel integrals and quantum mechanically in terms of quantized fields with a photon-induced tunneling process. Our expressions for populations are in excellent agreement with the gross temporal profiles of exact numerical solutions. We compare the semi-classical and quantum dynamics in the triangle and establish the conditions for their equivalence.

We investigate the Landau-Zener transition in two-and three-level systems subject to a classical Gaussian noise. Two complementary limits of the noise being fast and slow compared to characteristic Landau-Zener tunnel times are discussed. The analytical solution of a density matrix (Bloch) equation is given for a long time asymptotic of transition probability. It is demonstrated that the transition probability induced/assisted by the fast noise can be obtained through a procedure of Bloch's equation averaging with further reducing it to a master equation. In contrast to the case of fast noise, the transition probability for LZ transition induced/assisted by the slow classical noise can be obtained by averaging the solution of Bloch's equation over the noise realization. As a result, the transition probability is described by the activation Arrhenius law. The approximate solution of the Bloch's equation at finite times is written in terms of Fresnel's integrals and interpreted in terms of interference pattern. We discuss consequences of a local isomorphism between SU (2) and SO(3) groups and connections between Schrödinger and Bloch descriptions of spin dynamics. Based on this isomorphism we establish the relations between S = 1/2 and S = 1 transition probabilities influenced by the noise. A possibility to use the slow noise as a probe for tunnel time is discussed.

Abstract. The tunneling between the 2S+1 Zeeman multiplets of an arbitrary spin S using the SU (2) Lie group exponential ordering Wei-Norman technique is investigated. A spin subjected to a regular time-dependent magnetic field and a transverse colored noise is considered and the regimes of fast and slow noise examined.