arXiv subjects

Naomichi Hatano

Publications and source records attributed to Naomichi Hatano.

At least 19 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.

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arXiv2026

Roles of the Internal Coupling: From Equilibrium to Non-Equilibrium Dynamics

We identify the precise thermodynamic roles of internal coupling in quantum thermal machines by analyzing the quantum Otto cycle across thermalized Gibbs-state limit cycles (GSLC) and finite-time non-equilibrating limit cycles (NELC). By systematically comparing the internally coupled system with standard and dressed-spectrum models, we resolve previous misconceptions regarding the physical origins of performance variations. First, we establish that the internally coupled system outperforms the standard system solely due to the Hamiltonian spectrum update, which intrinsically broadens the operating regimes. Second, we reveal that time-dependent efficiency and coefficient of performance (COP) are not caused by general quantum coherence, but specifically by eigenbasis mismatch arising from the non-commutativity of Hamiltonians across different strokes. The mismatch acts as quantum internal friction, reducing efficiency and COP and generating dissipative thermal modes. This results in the power-efficiency trade-off law, which we should find in realistic engines. However, we would not find the trade-off law when coherence exists but the eigenbasis mismatch does not exist, because there would be no friction, and hence the efficiency and COP would remain completely time-independent. Third, we isolate the distinct impact of coherence on power output. Validated by the global approach of the GKSL master equation, we demonstrate that coherence inherently reduces power by suppressing kinetic thermalization rates, regardless of eigenbasis mismatch.

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arXiv2026

Fractional power-law decay in the spontaneous emission of a two-level system

It has been shown for various systems that the decay rate of an unstable quantum system deviates from exponential behavior in short- and long-time regimes associated with memory effects. In particular, it is widely believed that in the short-time regime, the decay is quadratic, inducing the quantum Zeno effect, in which the decay is suppressed by rapidly repeated measurements. In our study, we find that when the environment of the unstable system has an energy spectrum with a lower bound but without an upper one, the decay rate in both regimes is scaled in terms of the spatial dimension and the exponent of the energy dispersion of the environment. Surprisingly, we find that in the short-time regime the decay exhibits fractional scaling, which leads to a quantum Zeno effect with a different scaling of the Zeno time.

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arXiv2026

Dynamics of two interacting dipolar two-level systems in a multi-mode electromagnetic cavity: sudden death and revival of the entanglement within the Born-Markov approximation

Interacting dipolar two-level systems form a special class of qubits that interact with a cavity in a particular way. We first prove that the Markovian dynamics of one 1/2-spin in interaction with a quantised magnetic field from a multi-mode cavity at thermal equilibrium is equivalent to a two-level atom interacting in the dipole approximation with the electric field of the cavity. We then use the Born-Markov approximation to study the dynamics of two spins interacting through the antiferromagnetic Heisenberg coupling in the same environment. By solving the GKSL equation, we find the exact expression of the density matrix of the system, with the off-diagonal coherence decay time and spin relaxation time. The concurrence for the stationary state is explicitly derived for any kind of initial state and the role of the singlet state is brought to light. The temporal evolution of the concurrence is numerically computed for different initial states, the phenomenon of sudden death and revival of the entanglement is observed for this dynamics. A detailed analysis of the sudden death and revival of the concurrence is conducted for Werner states, with new analytical results obtained thanks to the solution of the GKSL equation. We finally derive the equations and the stationary concurrence for the XXZ coupling.

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arXiv2026

Markovianity and non-Markovianity of Particle Bath with Dirac Dispersion Relation

The dynamics of a two-level system coupled to a particle bath with the Dirac dispersion relation is studied. We analytically show that closing the Dirac gap results in a transition of the survival probability of the two-level system from non-exponential to exponential decay in the long-time regime, while the short-time regime remains exponential. The exact time-evolving state is also calculated. With the Dirac gap closing smoothly, the time-evolving state converges to a time-evolving resonant state, which is normalizable due to causality. We numerically show that introducing a finite cutoff to the Dirac dispersion relation leads to a transition from exponential to non-exponential decay both in short- and long-time regimes, with the time-evolving resonant state resolved to a time-evolving state. Furthermore, we propose several experimental setups that act as a particle bath with the Dirac dispersion relation. We give a detailed calculation for one of them, namely an optical array in the Su-Schrieffer-Heeger configuration. In this case, we show that our theoretical results can be observed experimentally with realistic parameters in an existing experimental setup of an optical waveguide array.

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arXiv2026

Quantum transport on Bethe lattices with non-Hermitian sources and a drain

We consider quantum transport in a tight-binding model on the Bethe lattice of finite generation, which we expect to be the first step toward analyzing electronic transport in a light-harvesting molecule. We seek conditions under which the electronic current from the peripheral light-harvesting sites to the central site reaches its maximum. As a new feature for analyzing quantum transport, we add complex potentials for sources at peripheral sites and a drain at the central site, and solve a non-Hermitian eigenvalue problem, instead of simulating an initial-value problem. Solving the eigenvalue problem clearly reveals which electronic channels contribute most to the quantum transport. The number of eigenstates that can penetrate from the peripheral sites to the central site is quite limited among the total number of eigenstates. All the other eigenstates are localized around the peripheral sites and cannot reach the central site. The former eigenstates can carry current, reducing the problem to quantum transport on a parity-time ($\PT$)-symmetric tight-binding chain. The current has a maximum with respect to the strengths of the sources and the drain. The current decreases as we increase the strengths beyond the maximum and vanishes in the limit of infinite strength. Moreover, the current maximum is given by a zero mode. When the number of links is common to all generations, the current takes the maximum value at the exceptional point where two eigenstates coalesce to a zero mode, which emerges because of the non-Hermiticity due to the $\PT$-symmetric complex potentials. By introducing randomness either into the hopping amplitude or the number of links in each generation of the tree, we obtain a random-hopping tight-binding model, in which the current reaches its maximum not exactly, but approximately, for a zero mode, although it is no longer located at an exceptional point in general.

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arXiv2026

Exact time-evolving resonant states for open double quantum-dot systems with spin degrees of freedom

We study time-evolving resonant states in an open double quantum-dot system, taking into account spin degrees of freedom as well as both on-dot and interdot Coulomb interactions. We exactly derived a non-Hermite effective Hamiltonian acting on the subspace of two quantum dots, where the non-Hermiticity arises from an effect of infinite external leads connected to the quantum dots. By diagonalizing the effective Hamiltonian, we identify four types of two-body resonant states. For the initial states of localized two electrons with opposite spins on the quantum dots, we exactly solve the time-dependent Schroedinger equation and obtain time-evolving two-body resonant states. The time-evolving resonant states are normalizable since their wave function grows exponentially only inside a finite space interval that expands in time with electron velocity. By using the exact solution, we analyze the survival and transition probabilities of localized two electrons on the quantum dots.

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arXiv2026

Non-Hermitian Quantum Mechanics of Open Quantum Systems: Revisiting The One-Body Problem

We review analyses of open quantum systems. We show how non-Hermiticity arises in an open quantum system with an infinite environment, focusing on the one-body problem. One of the reasons for taking the present approach is that we can solve the problem completely, making it easier to see the structures of problems involving open quantum systems. We show that this results in the discovery of a new complete set, which is one of the main topics of the present article. Another reason for focusing on the one-body problem is that the theory permits the strong coupling between the system and the environment. In the current research landscape, it is valuable to revisit the one-body problem for open quantum systems, which can be solved accurately for arbitrary strengths of the system-environment couplings. A rigorous understanding of the problem structures in the present approach will be helpful when we tackle problems with many-body interactions. First, we consider potential scattering and directly define the resonant state as an eigenstate of the Schrödinger equation under the Siegert outgoing boundary condition. We show that the resonant eigenstate can have a complex energy eigenvalue, even though the Hamiltonian is seemingly Hermitian. Second, we introduce the Feshbach formalism, which eliminates the infinite degrees of freedom of the environment and represents its effect as a complex potential. The resulting effective Hamiltonian is explicitly non-Hermitian. By unifying these two ways of defining resonant states, we obtain a new complete set of bases for the scattering problem that contains all discrete eigenstates, including resonant states. We finally mention the non-Markovian dynamics of open quantum systems. We emphasize the time-reversal symmetry of the dynamics that continuously connects the past and the future. We can capture it using the new complete set that we develop here.

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arXiv2025

Non-equilibrium Dynamics of Three-Level Absorption Refrigerator at Third-Order Liouvillian Exceptional Points

We analyze the influence of Liouvillian exceptional points (LEPs) in the three-level quantum absorption refrigerator, putting emphasis on the non-equilibrium process before the convergence to the steady state. We search for the second-order and third-order LEPs in the system with two types of couplings. Focusing on the third-order LEPs, we analyze the damping of the system state in the long term analytically and numerically. In addition, we analyze the damping of heat currents and the influence of the non-equilibrium process in the heat extraction from the cold bath. Critical damping at LEPs of both the system state and the heat currents is achieved, implying the fastest convergence to the equilibrium system. During the non-equilibrium process, we find that much heat transfer from the cold bath to the hot bath with less energy cost of the work bath is achieved at the third-order LEP, leading to better performance of the refrigerator.

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arXiv2025

Exact time-evolving scattering states in open quantum-dot systems with an interaction: Discovery of time-evolving resonant states

We study exact time-evolving many-electron states of an open double quantum-dot system with an interdot Coulomb interaction. A systematic construction of the time-evolving states for arbitrary initial conditions is proposed. For any initial states of one- and two-electron plane waves on the electrical leads, we obtain exact solutions of the time-evolving scattering states, which converge to known stationary scattering eigenstates in the long-time limit. For any initial states of localized electrons on the quantum dots, we find exact time-evolving states of a new type, which we refer to as time-evolving resonant states. In contrast to stationary resonant states, whose wave functions spatially diverge and not normalizable, the time-evolving resonant states are normalizable since their wave functions are restricted to a finite space interval due to causality. The exact time-evolving resonant states enable us to calculate the time-dependence of the survival probability of electrons on the quantum dots for the system with the linearized dispersions. It decays exponentially in time on one side of an exponential point of resonance energies while, on the other side, it oscillates during the decay as a result of the interference of the two resonance energies.

cond-mat.mes-hall↗

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

Advantages of the Kirkwood-Dirac distribution among general quasi-probabilities for finite-state quantum systems

We investigate features of the quasi-joint-probability distribution for finite-state quantum systems, especially the two-state and three-state quantum systems, comparing different types of quasi-joint-probability distributions based on the general framework of quasi-classicalization. We show from two perspectives that the Kirkwood-Dirac distribution is the quasi-joint-probability distribution that behaves nicely for the finite-state quantum systems. One is the similarity to the genuine probability and the other is the information that we can obtain from the quasi-probability. By introducing the concept of the possible values of observables, we show for the finite-state quantum systems that the Kirkwood-Dirac distribution behaves more similarly to the genuine probability distribution in contrast to most of the other quasi-probabilities including the Wigner function. We also prove that the states of the two-state and three-state quantum systems can be completely distinguished by the Kirkwood-Dirac distribution of only two directions of the spin and point out for the two-state system that the imaginary part of the quasi-probability is essential for the distinguishability of the state.

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arXiv2023

Maximum Power of Coupled-Qubit Otto Engines

We put forward four schemes of coupled-qubit quantum Otto machine, a generalization of the single-qubit quantum Otto machine, based on work and heat transfer between an internal system consisting of a coupled pair of qubits and an external environment consisting of two heat baths and two work storages. The four schemes of our model are defined by the positions of attaching the heat baths, which play a key role in the power of the coupled-qubit engine. Firstly, for the single-qubit heat engine, we find a maximum-power relation, and the fact that its efficiency at the maximum power is equal to the Otto efficiency, which is greater than the Curzon-Ahlborn efficiency. Second, we compare the coupled-qubit engines to the single-qubit one from the point of view of achieving the maximum power based on the same energy-level change for work production, and find that the coupling between the two qubits can lead to greater powers but the system efficiency at the maximum power is lower than the single-qubit system's efficiency and the Curzon-Ahlborn efficiency.

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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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arXiv2022

Switching the function of the quantum Otto cycle in non-Markovian dynamics: heat engine, heater and heat pump

Quantum thermodynamics explores novel thermodynamic phenomena that emerge when interactions between macroscopic systems and microscopic quantum ones go into action. Among various issues, quantum heat engines, in particular, have attracted much attention as a critical step in theoretical formulation of quantum thermodynamics and investigation of efficient use of heat by means of quantum resources. In the present paper, we focus on heat absorption and emission processes as well as work extraction processes of a quantum Otto cycle. We describe the former as non-Markovian dynamics, and thereby find that the interaction energy between a macroscopic heat bath and a microscopic qubit is not negligible. Specifically, we reveal that the interaction energy is divided into the system and the bath in a region of the short interaction time and remains negative in the region of the long interaction time. In addition, a counterintuitive energy flow from the system and the interaction energy to the hot bath occurs in another region of the short interaction time. We quantify these effects by defining an index of non-Markovianity in terms of the interaction energy. With this behavior of the interaction energy, we show that a non-Markovian quantum Otto cycle can switch functions such as an engine as well as a heater or a heat pump by controlling the interaction time with the heat bath. In particular, the qubit itself loses its energy if we shorten the interaction time, and in this sense, the qubit is cooled through the cycle. This property has a possibility of being utilized for cooling the qubits in quantum computing. We also describe the work extraction from the microscopic system to a macroscopic system like us humans as an indirect measurement process by introducing a work storage as a new reservoir.

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arXiv2021

Delocalization of non-Hermitian Quantum Walk on Random Media in One Dimension

Delocalization transition is numerically found in a non-Hermitian extension of a discrete-time quantum walk on a one-dimensional random medium. At the transition, an eigenvector gets delocalized and at the same time the corresponding energy eigenvalue (the imaginary unit times the phase of the eigenvalue of the time-evolution operator) becomes complex. This is in accordance with a non-Hermitian extension of the random Anderson model in one dimension, called, the Hatano-Nelson model. We thereby numerically find that all eigenstates of the Hermitian quantum walk share a common localization length.

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arXiv2021

Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems

For a system consisting of a quantum emitter coupled near threshold (band edge) to a one-dimensional continuum with a van Hove singularity in the density of states, we demonstrate general conditions such that a characteristic triple level convergence occurs directly on the threshold as the coupling $g$ is shut off. For small $g$ values the eigenvalue and norm of each of these states can be expanded in a Puiseux expansion in terms of powers of $g^{2/3}$, which suggests the influence of a third-order exceptional point. However, in the actual $g \rightarrow 0$ limit, only two discrete states in fact coalesce as the system can be reduced to a $2 \times 2$ Jordan block; the third state instead merges with the continuum. Moreover, the decay width of the resonance state involved in this convergence is significantly enhanced compared to the usual Fermi golden rule, which is consistent with the Purcell effect. However, non-Markovian dynamics due to the branch-point effect are also enhanced near the threshold. Applying a perturbative analysis in terms of the Puiseux expansion that takes into account the threshold influence, we show that the combination of these effects results in quantum emitter decay of the unusual form $1 - C t^{3/2}$ on the key timescale during which most of the decay occurs. We then present two conditions that must be satisfied at the threshold for the anomalous exceptional point to occur: the density of states must contain an inverse square-root divergence and the potential must be non-singular. We further show that when the energy of the quantum emitter is detuned from threshold, the anomalous exceptional point splits into three ordinary exceptional points, two of which appear in the complex-extended parameter space. These results provide deeper insight into a well-known problem in spontaneous decay at a photonic band edge.

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arXiv2021

What is the resonant state in open quantum systems?

The article reviews the theory of open quantum system from a perspective of the non-Hermiticity that emerges from the environment with an infinite number of degrees of freedom. The non-Hermiticity produces resonant states with complex eigenvalues, resulting in peak structures in scattering amplitudes and transport coefficients. After introducing the definition of resonant states with complex eigenvalues, we answer typical questions regarding the non-Hermiticity of open quantum systems. What is the physical meaning of the complex eigenmomenta and eigenenergies? How and why do the resonant states break the time-reversal symmetry that the system observes? Can we make the probabilistic interpretation of the resonant states with diverging wave functions? What is the physical meaning of the divergence of the wave functions? We also present an alternative way of finding resonant states, namely the Feshbach formalism, in which we eliminate the infinite number of the environmental degrees of freedom. In this formalism, we attribute the non-Hermiticity to the introduction of the retarded and advanced Green's functions.

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