Daiju Funakawa
YOU?
Author Swipe
View article: Two-dimensional quantum central limit theorem by quantum walks
Two-dimensional quantum central limit theorem by quantum walks Open
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, deriving analytical forms of the limiting probability den…
View article: Spectral analysis of Dirac operators for fermion scattering on topological solitons in the nonlinear $O(3)$ $σ$-model
Spectral analysis of Dirac operators for fermion scattering on topological solitons in the nonlinear $O(3)$ $σ$-model Open
We investigate the existence of discrete positive or negative energy ground states of the Dirac operator $H$ which describe the fermion scattering on topological solitons in the nonlinear $O(3)$ $σ$-model. Additionally, we provide a suffic…
View article: Eigenvalues and threshold rezonances of a two-dimensional split-step quantum walk with strong shift
Eigenvalues and threshold rezonances of a two-dimensional split-step quantum walk with strong shift Open
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 the function $f$ introduced by Fuda et. al. (Quantum Inf P…
View article: Spectral mapping theorem of an abstract non-unitary quantum walk
Spectral mapping theorem of an abstract non-unitary quantum walk Open
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 physics, they treat non-unitary time-evolution operators t…
View article: The Witten Index for One-dimensional Non-unitary Quantum Walks with\n Gapless Time-evolution
The Witten Index for One-dimensional Non-unitary Quantum Walks with\n Gapless Time-evolution Open
Recent developments in the index theory of discrete-time quantum walks allow\nus to assign a certain well-defined supersymmetric index to a pair of a unitary\ntime-evolution $U$ and a $\\mathbb{Z}_2$-grading operator $\\varGamma$ satisfyin…
View article: Time operators for continuous-time and discrete-time quantum walks
Time operators for continuous-time and discrete-time quantum walks Open
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 discrete-time quantum walk, the time operator can be self-adjoin…
View article: Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations
Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations Open
For given two unitary and self-adjoint operators on a Hilbert space, a spectral mapping theorem was proved in the work of Higuchi et al. (e-print arXiv:1506.06457) [see also E. Segawa and A. Suzuki, Quantum Stud.: Math. Found. 3, 11 (2016)…
View article: Spectral analysis of an abstract pair interaction model
Spectral analysis of an abstract pair interaction model Open
We consider an abstract pair-interaction model in quantum field theory with a coupling constant $λ\in {\mathbb R}$ and analyze the Hamiltonian $H(λ)$ of the model. In the massive case, there exist constants $λ_{\rm c}<0$ and $λ_{{\rm c},0}…
View article: Weak limit theorem for a one-dimensional split-step quantum walk
Weak limit theorem for a one-dimensional split-step quantum walk Open
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 two Konno's functions appears.
View article: Localization of a multi-dimensional quantum walk with one defect
Localization of a multi-dimensional quantum walk with one defect Open
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 defect coins, and prove localization of the walk. Using a s…
View article: Upper Bounds on the Degeneracy of the Ground State in Quantum Field Models
Upper Bounds on the Degeneracy of the Ground State in Quantum Field Models Open
Axiomatic abstract formulations are presented to derive upper bounds on the degeneracy of the ground state in quantum field models including massless ones. In particular, given is a sufficient condition under which the degeneracy of the gr…