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7 papers · 2 filters
Recurrence Relations of the Multi-Indexed Orthogonal Polynomials VI : Meixner-Pollaczek and continuous Hahn types
Satoru Odake
In previous papers, we discussed the recurrence relations of the multi-indexed orthogonal polynomials of the Laguerre, Jacobi, Wilson, Askey-Wilson, Racah and -Racah types. In t…
Explicit Diagonalization of Pair Interaction Models
Yasumichi Matsuzawa, Itaru Sasaki, Kyosuke Usami
We provide a general method for constructing bosonic Bogoliubov transformations that diagonalize a general class of quadratic Hamiltonians. These Hamiltonians describe the pair int…
Exactly Solvable Discrete Quantum Mechanical Systems and Multi-indexed Orthogonal Polynomials of the Continuous Hahn and Meixner-Pollaczek Types
Satoru Odake
We present new exactly solvable systems of the discrete quantum mechanics with pure imaginary shifts, whose physical range of the coordinate is the whole real line. These systems a…
The Witten Index for 1D Supersymmetric Quantum Walks with Anisotropic Coins
Akito Suzuki, Yohei Tanaka
Chirally symmetric discrete-time quantum walks possess supersymmetry, and their Witten indices can be naturally defined. The Witten index gives a lower bound for the number of topo…
Continuous limits of linear and nonlinear quantum walks
Masaya Maeda, Akito Suzuki
In this paper, we consider the continuous limit of a nonlinear quantum walk (NLQW) that incorporates a linear quantum walk as a special case. In particular, we rigorously prove tha…
Time operators for continuous-time and discrete-time quantum walks
Daiju Funakawa, Yasumichi Matsuzawa, Akito Suzuki +2
We construct concrete examples of time operators for both continuous and discrete-time homogeneous quantum walks, and we determine their deficiency indices and spectra. For a discr…
On the Feynman path integral for the magnetic Schroedinger equation with a polynomially growing electromagnetic potential
Wataru Ichinose
The Feynman path integrals for the magnetic Schroedinger equations are defined mathematically, in particular, with polynomially growing potentials in the spatial direction. For exa…