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Quantum Physics

Title: A large class of solvable multistate Landau-Zener models and quantum integrability

Abstract: The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians. Within the multistate Landau-Zener (MLZ) theory, however, there has been a successful alternative approach to identify and solve complex time-dependent models. 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 $N\ge 4$ of interacting states and shows a quickly growing 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.
Comments: The 2nd version contains considerable changes, including new sections, that are based on recent advances in arXiv/1711.09945 (new Ref.[1])
Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Mathematical Physics (math-ph)
Cite as: arXiv:1707.04963 [quant-ph]
  (or arXiv:1707.04963v3 [quant-ph] for this version)

Submission history

From: Chen Sun [view email]
[v1] Mon, 17 Jul 2017 00:03:07 GMT (1168kb,D)
[v2] Sat, 19 Aug 2017 03:57:10 GMT (1168kb,D)
[v3] Sat, 17 Mar 2018 20:21:20 GMT (755kb,D)