A large class of solvable multistate Landau–Zener models and quantum integrability. (24th May 2018)

• Record Type: Journal Article
• Authors: Chernyak, Vladimir Y; Sinitsyn, Nikolai A; Sun, Chen
• Is Part Of: Journal of physics. Volume 51:Number 24(2018)
• Publication Date: 2018-05-24
• Subjects: Landau–Zener -- quantum integrability -- exact solution -- ordinary differential equations -- quantum scattering; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aac3b2
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians (Sinitsyn et al 2018 Phys. Rev. Lett .120 190402). Within the multistate Landau–Zener (MLZ) theory, however, there has been a successful alternative approach to identify and solve complex time-dependent models (Sinitsyn and Chernyak 2017 J. Phys. A: Math. Theor .50 255203). Here we compare both methods by applying them to a new class of exactly solvable MLZ models. This class contains systems with an arbitrary number of interacting states and shows quick growth with N number of exact adiabatic energy crossing points, which appear at different moments of time. At each N, transition probabilities in these systems can be found analytically and exactly but complexity and variety of solutions in this class also grow with N quickly. We illustrate how common features of solvable MLZ systems appear from quantum integrability and develop an approach to further classification of solvable MLZ problems.