arXiv subjects

Manami Yamagishi

Publications and source records attributed to Manami Yamagishi.

3 recordsLinked to original sources

arXiv2026

Introducing a Kondo-type interaction to the model of quantum walkers

We introduce a model of discrete-time quantum walkers interacting with a lozalized magnetic impurity. Each quantum walker interacts with an impurity, through which multiple quantum walkers indirectly interact with each other, as in the Kondo model. We first identify a quantum walker as a massless Dirac particle propagating in continuous space via a series of Dirac's delta potentials. Based on the identification, we add a spin-$1/2$ degree of freedom to Dirac's potential at the origin. We derive all scattering matrices for massless Dirac particles arising from the impurity. First, for a simple set of parameter values, we analytically obtain the eigenvalues and eigenvectors of the bound states, in which a quantum walker is bound to the magnetic impurity. Second, we study two quantum walkers indirectly interacting with each other via the magnetic impurity. We numerically simulate the collision dynamics in one dimension when the spin-spin interaction at the origin is of the XX type and the SU(2) Heisenberg type. In the case of the XX interaction, we calculate the entanglement negativity to quantify how much the two quantum walkers are entangled with each other, and find that the negativity increases drastically upon the collision of the two walkers. In the case of the SU(2) Heisenberg interaction, we simulate the dynamics starting from the initial state in which one fermionic walker is in a bound eigenstate around the origin and the other fermionic walker is a delta function colliding with the first walker. We find that a bound eigenstate closest to the singlet state of the first walker and the magnetic impurity is least perturbed by the collision of the second walker. We speculate that this finding may be related to Kondo screening-like behavior at the lowest level of the real-space renormalization-group procedure.

quant-ph↗

arXiv2024

Proposal of a quantum version of active particles via a nonunitary quantum walk

The main aim of the present paper is to define an active particle in a quantum framework as a minimal model of quantum active matter and investigate the differences and similarities of quantum and classical active matter. Although the field of active matter has been expanding, most research has been conducted on classical systems. Here, we propose a truly deterministic quantum active-particle model with a nonunitary quantum walk as the minimal model of quantum active matter. We aim to reproduce results obtained previously with classical active Brownian particles; that is, a Brownian particle, with finite energy take-up, becomes active and climbs up a potential wall. We realize such a system with nonunitary quantum walks. We introduce new internal states, the ground state and the excited state, and a new nonunitary operator $N(g)$ for an asymmetric transition between the two states. The non-Hermiticity parameter $g$ promotes the transition to the excited state; hence, the particle takes up energy from the environment. For our quantum active particle, we successfully observe that the movement of the quantum walker becomes more active in a nontrivial manner as we increase the non-Hermiticity parameter $g$, which is similar to the classical active Brownian particle. We also observe three unique features of quantum walks, namely, ballistic propagation of peaks in one dimension, the walker staying on the constant energy plane in two dimensions, and oscillations originating from the resonant transition between the ground state and the excited state both in one and two dimensions.

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arXiv2023

Multi-Dimensional Quantum Walks: a Playground of Dirac and Schrödinger Particles

We propose a new multi-dimensional discrete-time quantum walk (DTQW), whose continuum limit is an extended multi-dimensional Dirac equation, which can be further mapped to the Schrödinger equation. We show in two ways that our DTQW is an excellent measure to investigate the two-dimensional (2D) extended Dirac Hamiltonian and higher-order topological materials. First, we show that the dynamics of our DTQW resembles that of a 2D Schrödinger harmonic oscillator. Second, we find in our DTQW topological features of the extended Dirac system. By manipulating the coin operators, we can generate not only standard edge states but also corner states.

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