• Corpus ID: 231639156

Feynman Integral in Quantum Walk, Barrier-top Scattering and Hadamard Walk

@inproceedings{Higuchi2021FeynmanII,
  title={Feynman Integral in Quantum Walk, Barrier-top Scattering and Hadamard Walk},
  author={Ken Higuchi},
  year={2021}
}
  • Ken Higuchi
  • Published 19 January 2021
  • Mathematics, Physics
The aim of this article is to relate the discrete quantum walk on Z with the continuous Schrödinger operator on R in the scattering problem. Each point of Z is associated with a barrier of the potential, and the coin operator of the quantum walk is determined by the transfer matrix between bases of WKB solutions on the classically allowed regions of both sides of the barrier. This correspondence enables us to represent each entry of the scattering matrix of the Schrödinger operator as a… 
1 Citations

Figures from this paper

Comfortable place for quantum walkers on finite path
We consider the stationary state of a quantum walk on the finite path, where the sink and source are set at the left and right boundaries. The quantum coin is uniformly placed at every vertex of the

References

SHOWING 1-10 OF 14 REFERENCES
Semiclassical Representation of the Scattering Matrix by a Feynman Integral
Abstract:We study the scattering problem for one-dimensional Schrödinger equations in the semiclassical limit when the energy level is close to the quadratic maxima of the potential. Starting from
Semiclassical study of quantum scattering on the line
We study the well-known problem of 1-d quantum scattering by a potential barrier in the semiclassical limit. Using the so-called exact WKB method and semiclassical microlocal analysis techniques, we
Generalized eigenfunctions and scattering matrices for position-dependent quantum walks
We study the spectral analysis and the scattering theory for time evolution operators of position-dependent quantum walks. Our main purpose of this paper is the construction of generalized
Resonant-tunneling in discrete-time quantum walk
We show that discrete-time quantum walks on the line, $$\mathbb {Z}$$Z, behave as “the quantum tunneling”. In particular, quantum walkers can tunnel through a double-well with the transmission
Explicit expression of scattering operator of some quantum walks on impurities
In this paper, we consider the scattering theory for a one-dimensional quantum walk with impurities which make reflections and transmissions. We focus on an explicit expression of the scattering
A dynamical system induced by quantum walk
We consider the Grover walk model on a connected finite graph with two infinite length tails and we set an $\ell^\infty$-infinite external source from one of the tails as the initial state. We show
Quantum graph walks I: mapping to quantum walks
We clarify that coined quantum walk is determined by only the choice of local quantum coins. To do so, we characterize coined quantum walks on graph by disjoint Euler circles with respect to
The Weber equation as a normal form with applications to top of the barrier scattering
In the paper we revisit the basic problem of tunneling near a nondegenerate global maximum of a potential on the line. We reduce the semiclassical Schr\"odinger equation to a Weber normal form by
Semi-classical analysis for Harper's equation. III : Cantor structure of the spectrum
In this paper we continue our study of Harper's operator coshD+cosx in L^R), by means of microlocal analysis and renormalization. A rather complete description of the spectrum is obtained in the case
...
...