2026年度

Math-Fi seminar on 9 Apr.

2026.04.09 Thu up
  • Date: 9 Apr. (Thu.)
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50-17:50
  • Speaker : Yohei Tanaka (Ritsumeikan University)
  • Title: On understanding chiral unitaries via real parts
  • Abstract: 
We study unitary operators with chiral symmetry, that is, unitary operators associated with a fixed involution. Such operators naturally arise in the study of quantum walks and related areas. A standard approach is to decompose the underlying Hilbert space according to this symmetry, which leads to a convenient block representation. In this framework, we focus on the real part of the unitary and use it as a useful tool to understand its spectral structure. Based on this viewpoint, we present several related topics and results, illustrating how the real-part perspective provides a simple and unified way to analyze chiral unitaries.

Math-Fi seminar on 2 Apr.

2026.04.07 Tue up
  • Date: 2 Apr. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 12:00-13:30
  • Speaker :  VU HUY HOANG (University of California, Santa Barbara)
  • Commentator :  Ju-Yi Yen (University of Cincinnati)
  • Title: Molchanov’s Formula and Quantum Walks: A Probabilistic Approach 
  • Abstract: 
This paper establishes a robust link between quantum dynamics and classical ones by deriving a probabilistic representation for both continuous-time and discrete-time quantum walks. We first adapt the Molchanov formula, originally employed in the study of Schrodinger operators on multidimensional integer lattices, to characterize the evolution of continuous time quantum walks. Extending this framework, we develop a probabilistic method to represent discrete time quantum walks on an infinite integer line, bypassing the locality constraints that typically inhibit direct application of the Molchanov formula. The validity of our representation is empirically confirmed through a benchmark analysis of the Hadamard walk, demonstrating high fidelity with traditional unitary evolution. Our results suggest that this probabilistic lens offers a powerful alternative for learning multidimensional quantum walks and provides new analytical pathways for investigating quantum systems via classical stochastic processes.