1 citations · 3 across the 6 of their papers we have counts for
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Self-adjointness of unbounded time operators
Fumio Hiroshima, Noriaki Teranishi
Time operators for an abstract semi-bounded self-adjoint operator with purely discrete spectrum is considered. The existence of a bounded self-adjoint time operator for …
Conjugate Operators of 1D-harmonic Oscillator
Fumio Hiroshima, Noriaki Teranishi
A conjugate operator of one-dimensional harmonic oscillator is defined by an operator satisfying canonical commutation relation $[N,T]=-i\one$ on some domain but not necess…
Spectral mapping theorem of an abstract non-unitary quantum walk
Keisuke Asahara, Daiju Funakawa, Etsuo Segawa +2
This paper continues the previous work (Quantum Inf. Process (2019)) by two authors of the present paper about a spectral mapping property of chiral symmetric unitary operators. In…
Time Operators of Harmonic Oscillators and Their Representations
Fumio Hiroshima, Noriaki Teranishi
A time operator $\hat T_\eps$ of the one-dimensional harmonic oscillator $ \hat h_\eps=\half(p^2+\eps q^2)$ is rigorously constructed. It is formally expressed as $ \hat T_\eps=\ha…
The Witten index for one-dimensional split-step quantum walks under the non-Fredholm condition
Yasumichi Matsuzawa, Akito Suzuki, Yohei Tanaka +2
It is recently shown that a split-step quantum walk possesses a chiral symmetry, and that a certain well-defined index can be naturally assigned to it. The index is a well-defined…
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…