26 citations · 45 across the 11 of their papers we have counts for
10 papers · 1 filter
Two-dimensional quantum central limit theorem by quantum walks
Keisuke Asahara, Daiju Funakawa, Motoki Seki +1
The weak limit theorem (WLT), the quantum analogue of the central limit theorem, is foundational to quantum walk (QW) theory. Unlike the universal Gaussian limit of classical walks…
Spectral analysis of Dirac operators for fermion scattering on topological solitons in the nonlinear -model
Daiju Funakawa, Satoshi Okumura, Yuki Ueda
We investigate the existence of discrete positive or negative energy ground states of the Dirac operator which describe the fermion scattering on topological solitons in the no…
Eigenvalues and threshold rezonances of a two-dimensional split-step quantum walk with strong shift
Toru Fuda, Daiju Funakawa, Satoshi Sasayama +1
In this paper, we derive sufficient conditions for the localization of two-dimensional split-step quantum walks with a strong shift. For this purpose, we analyze the zero points of…
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…
The Witten Index for One-dimensional Non-unitary Quantum Walks with Gapless Time-evolution
Keisuke Asahara, Daiju Funakawa, Motoki Seki +1
Recent developments in the index theory of discrete-time quantum walks allow us to assign a certain well-defined supersymmetric index to a pair of a unitary time-evolution and…
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…
Spectral analysis of an abstract pair interaction model
Keisuke Asahara, Daiju Funakawa
We consider an abstract pair-interaction model in quantum field theory with a coupling constant and analyze the Hamiltonian of the model. In the massive c…
Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations
Toru Fuda, Daiju Funakawa, Akito Suzuki
For given two unitary and self-adjoint operators on a Hilbert space, a spectral mapping theorem was proved in \cite{HiSeSu}. In this paper, as an application of the spectral mappin…
Weak limit theorem for a one-dimensional split-step quantum walk
Toru Fuda, Daiju Funakawa, Akito Suzuki
This paper proves a weak limit theorem for a one-dimensional split-step quantum walk and investigates the limit density function. In the density function, the difference between tw…
Localization of a multi-dimensional quantum walk with one defect
Toru Fuda, Daiju Funakawa, Akito Suzuki
In this paper, we introduce a multidimensional generalization of Kitagawa's split-step discrete-time quantum walk, study the spectrum of its evolution operator for the case of one…