Naomichi Hatano | The University of Tokyo (original) (raw)

Papers by Naomichi Hatano

Springer eBooks, Nov 16, 2005

This article is based on a talk presented at a conference "Quantum Annealing and Other Optimizati... more This article is based on a talk presented at a conference "Quantum Annealing and Other Optimization Methods" held at Kolkata, India on March 2-5, 2005. It will be published in the proceedings "Quantum Annealing and Other Optimization Methods" (Springer, Heidelberg) pp. 39-70.

Springer eBooks, 2010

The concept of communicability is introduced for complex socioeconomic networks. The communicabil... more The concept of communicability is introduced for complex socioeconomic networks. The communicability function expresses how an impact propagates from one place to another in the network. This function is used to define unambiguously the concept of socioeconomic community. The concept of temperature in complex socioeconomic networks is also introduced as a way of accounting for the external stresses to which such systems are submitted. This external stress can change dramatically the structure of the communities in a network. We analyze here a trade network of countries exporting 'miscellaneous manufactures of metal.' We determine the community structure of this network showing that there are 27 communities with diverse degree of overlapping. When only communities with less than 80% of overlap are considered we found 5 communities which are well characterized in terms of geopolitical relationships. The analysis of external stress on these communities reveals that several countries are very much influenced by these critical situations, i.e., economical crisis. These weakest links are clearly identified and represent countries that are isolated from the main trade as soon as the external "temperature" of the system is increased. The current approach adds an important tool for the analysis of socioeconomic networks in the real-world.

Annual Report of National Institute for Fusion Science, Feb 23, 2011

We propose to map the model of information diffusion on an online social network which one of the... more We propose to map the model of information diffusion on an online social network which one of the authors introduced previously to a non-hermitian quantum tight-binding model. By doing so, not only that we can interpret the diffusion process in the matrix form, but we also expect that many techniques developed in non-hermitian quantum mechanics can be applied.

Journal of the Physical Society of Japan, Feb 15, 1996

The ground state of the four-chain Heisenberg ladder model is numerically investigated. Hiddenord... more The ground state of the four-chain Heisenberg ladder model is numerically investigated. Hiddenorder correlations suitable for the system are introduced and calculated with an emphasis on the spatially isotropic point, where a corresponding material exists. The existence of a long-range hidden correlation indicates formation of a short-range RVB state in the case of the antiferromagnetic inter-chain coupling. A transition between the phase of the ferromagnetic inter-chain coupling and that of the antiferromagnetic one is discussed.

Journal of the Physical Society of Japan, Sep 15, 2007

We investigate the entanglement of the ferromagnetic XY model in a random magnetic field at zero ... more We investigate the entanglement of the ferromagnetic XY model in a random magnetic field at zero temperature and in the uniform magnetic field at finite temperatures. We use the concurrence to quantify the entanglement. We find that, in the ferromagnetic region of the uniform magnetic field h, all the concurrences are generated by the random magnetic field and by the thermal fluctuation. In one particular region of h, the next-nearest neighbor concurrence is generated by the random field but not at finite temperatures. We also find that the qualitative behavior of the maximum point of the entanglement in the random magnetic field depends on whether the variance of its distribution function is finite or not.

Physical review research, Jun 22, 2020

Many systems such as social networks and biological networks take the form of complex networks, w... more Many systems such as social networks and biological networks take the form of complex networks, which have a community structure. Community detection in complex networks is of great interest to many researchers in statistical physics and mathematical physics. There have been studies on community detection that use the classical random walk. The present study utilizes the discrete-time quantum walk instead. The quantum walk plays an important role in various fields, especially in research on quantum computers, and attracts much attention from mathematical physics too. The discrete-time quantum walk has two properties: it linearly spreads on a flat space, and it localizes in some cases because of quantum coherence. We demonstrate that these properties of the quantum walk are useful for community detection on complex networks. We define the discrete-time quantum walk on complex networks and utilize it for community detection. We numerically show that the quantum walk with a Fourier coin is localized in a community to which the initial node belongs. Meanwhile, the quantum walk with a Grover coin tends to be localized around the initial node, not over a community. The probability of a classical random walk on the same network converges to a uniform distribution with a relaxation time generally unknown a priori. We thus claim that the time average of the probability of a Fourier-coin quantum walk on complex networks reveals the community structure more explicitly than that of a Grover-coin quantum walk and a snapshot of the classical random walk. We first demonstrate our method of community detection for a prototypical three-community network, producing the correct grouping. We then apply our method to two real-world networks, namely, Zachary's karate club and the U.S. Airport network. We successfully reveal the community structure, the two communities of the instructor and the administrator in the former and major airline companies in the latter.

Physical Review E, Aug 8, 2008

We here present a method of clearly identifying multi-partite subgraphs in a network. The method ... more We here present a method of clearly identifying multi-partite subgraphs in a network. The method is based on a recently introduced concept of the communicability, which very clearly identifies communities in a complex network. We here show that, while the communicability at a positive temperature is useful in identifying communities, the communicability at a negative temperature is useful in idenfitying multi-partitite subgraphs; the latter quantity between two nodes is positive when the two nodes belong to the same subgraph and is negative when not. The method is able to discover `almost' multi-partite structures, where inter-community connections vastly outweigh intracommunity connections. We illustrate the relevance of this work to real-life food web and protein-protein interaction networks.

Solid State Communications, 2007

We argue that a pseudo-one-dimensional electron gas is magnetized when a voltage bias is applied ... more We argue that a pseudo-one-dimensional electron gas is magnetized when a voltage bias is applied with the Fermi level tuned to be in the energy gap generated by a spin-orbit interaction. The magnetization is an indication of spin-carrying currents due to the spin-orbit interaction. The origin of the magnetization, however, is essentially different from the "spin accumulation" in two-dimensional systems with spin-orbit interactions.

Annals of Physics, Dec 1, 2021

Delocalization transition is numerically found in a non-Hermitian extension of a discrete-time qu... more 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.

Physical review, Mar 31, 2017

Many studies of quantum-size heat engines assume that the dynamics of an internal system is unita... more Many studies of quantum-size heat engines assume that the dynamics of an internal system is unitary and that the extracted work is equal to the energy loss of the internal system. Both assumptions, however, should be under scrutiny. In the present paper, we analyze quantum-scale heat engines, employing the measurement-based formulation of the work extraction recently introduced by Hayashi and Tajima [M. Hayashi and H. Tajima, arXiv:1504.06150]. We first demonstrate the inappropriateness of the unitary time evolution of the internal system (namely the first assumption above) using a simple two-level system; we show that the variance of the energy transferred to an external system diverges when the dynamics of the internal system is approximated to a unitary time evolution. We second derive the quantum Jarzynski equality based on the formulation of Hayashi and Tajima as a relation for the work measured by an external macroscopic apparatus. The righthand side of the equality reduces to unity for "natural" cyclic processes, but fluctuates wildly for non-cyclic ones, exceeding unity often. This fluctuation should be detectable in experiments and provide evidence for the present formulation.

Solid State Communications, Aug 1, 2005

It is theoretically predicted that the Nernst coefficient is strongly suppressed and the thermal ... more It is theoretically predicted that the Nernst coefficient is strongly suppressed and the thermal conductance is quantized in the quantum Hall regime of the twodimensional electron gas. The Nernst effect is the induction of a thermomagnetic electromotive force in the y direction under a temperature bias in the x direction and a magnetic field in the z direction. The quantum nature of the Nernst effect is analyzed with the use of a circulating edge current and is demonstrated numerically. The present system is a physical realization of the non-equilibrium steady state.

Journal of Complex Networks, Oct 3, 2017

We develop a model for a random walker with long-range hops on general graphs. This random multi-... more We develop a model for a random walker with long-range hops on general graphs. This random multi-hopper jumps from a node to any other node in the graph with a probability that decays as a function of the shortest-path distance between the two nodes. We consider here two decaying functions in the form of the Laplace and Mellin transforms of the shortest-path distances. Remarkably, when the parameters of these transforms approach zero asymptotically, the multihopper's hitting times between any two nodes in the graph converge to their minimum possible value, given by the hitting times of a normal random walker on a complete graph. Stated differently, for small parameter values the multi-hopper explores a general graph as fast as possible when compared to a random walker on a full graph. Using computational experiments we show that compared to the normal random walker, the multi-hopper indeed explores graphs with clusters or skewed degree distributions more efficiently for a large parameter range. We provide further computational evidence of the speed-up attained by the random multi-hopper model with respect to the normal random walker by studying deterministic, random and real-world networks.

arXiv (Cornell University), Dec 22, 2014

We introduce the concept of communicability angle between a pair of nodes in a graph. We provide ... more We introduce the concept of communicability angle between a pair of nodes in a graph. We provide strong analytical and empirical evidence that the average communicability angle for a given network accounts for its spatial efficiency on the basis of the communications among the nodes in a network. We determine characteristics of the spatial efficiency of more than a hundred real-world complex networks that represent complex systems arising in a diverse set of scenarios. In particular, we find that the communicability angle correlates very well with the experimentally measured value of the relative packing efficiency of proteins that are represented as residue networks. We finally show how we can modulate the spatial efficiency of a network by tuning the weights of the edges of the networks. This allows us to predict effects of external stresses on the spatial efficiency of a network as well as to design strategies to improve important parameters in real-world complex systems.

Progress of Theoretical and Experimental Physics, Mar 1, 1991

The fractal decomposition of exponential operators proposed by Suzuki, which is a new category of... more The fractal decomposition of exponential operators proposed by Suzuki, which is a new category of the generalized Trotter decomposition valid up to higher orders, is examined with transfer-matrix calculations of the spin 1/2 antiferromagnetic XXZ model on the 4 x 2 triangular lattice. The dependence of correction terms on the Trotter number and temperature are studied. This dependence confirms rapid convergence of the fractal decomposition. The negative-sign problem arising in quantum Monte Carlo simulations is also discussed •from the present new point of view. § 1. Introduction

arXiv (Cornell University), Jun 28, 2021

The article reviews the theory of open quantum system from a perspective of the non-Hermiticity t... more 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.

Physical Review Letters, May 31, 2018

We investigate a heating phenomenon in periodically driven integrable systems that can be mapped ... more We investigate a heating phenomenon in periodically driven integrable systems that can be mapped to free-fermion models. We find that heating to the high-temperature state, which is a typical scenario in non-integrable systems, can also appear in integrable time-periodic systems; the amount of energy absorption rises drastically near a frequency threshold where the Floquet-Magnus expansion diverges. As the driving period increases, we also observe that the effective temperatures of the generalized Gibbs ensemble for conserved quantities go to infinity. By the use of the scaling analysis, we reveal that in the limit of infinite system size and driving period, the steady state after a long time is equivalent to the infinite-temperature state. We obtain the asymptotic behavior L −1 and T −2 as to how the steady state approaches the infinite-temperature state as the system size L and the driving period T increase.

Progress of theoretical and experimental physics, Dec 1, 2020

We all learn in elementary quantum mechanics class that all measurable physical quantities, and s... more We all learn in elementary quantum mechanics class that all measurable physical quantities, and specifically the Hamiltonian operator, must be Hermitian, because the eigenvalues must be real. This is perhaps von Neumann's mathematical dogma, to which two main physical counterarguements exist. Presumably the first attempt to extend the Hamiltonian to a non-Hermitian operator was made to explain nuclear decay. Alpha or beta particles emitted from a radioactive nuclide in an experimental apparatus travel through free space outside the nuclide and, theoretically, are lost to infinite space, or experimentally, are absorbed by detectors that surround the free space. In either case, the emitted particles never come back to the nuclide, and therefore the energy of the nuclide is not conserved. In the present terminology, the radioactive nuclide is an open quantum system; it is not closed but open to the environment of infinite free space for alpha and beta particles or macroscopic detectors. The same situation can emerge at a mesoscopic scale; in a typical experimental setup, a quantum dot is open to quantum wires, which are terminated outside by electrodes. The Hamiltonian of the whole universe may be Hermitian according to von Neumann, but a part of it, for example, a radioactive nuclide, a quantum dot, or whatever is connected to the rest of the macroscopic universe, does not conserve energy, and hence can be described by an effective non-Hermitian Hamiltonian after eliminating the environmental degrees of freedom [1]. The non-Hermitian Hamiltonian obtained in this way produces complex eigenvalues of resonant states. It is somewhat infamous that the eigenfunction of a resonant state diverges spatially, and hence is unnormalizable, but it in fact means that the environment is macroscopic. The other counterargument to von Neumann's dogma is more ambitious. The celebrated theory of parity-time (PT) symmetry [2] assumed, at least originally, that the Hamiltonian of the whole universe is non-Hermitian but in a parameter regime of real eigenvalues. The symmetry under the combination of time-reversal and parity operations, or more generally an antilinear operation combined with linear operations, produces either real or conjugate pairs of complex eigenvalues, which may be made exclusively real if the parameters are so tuned. The simplest example would be the Hamiltonian for a two-site tight-binding model, H = iγ −t hop −t hop −iγ , (1) where both γ and t hop are real parameters. This non-Hermitian Hamiltonian is PT symmetric in the sense that the combination of the antilinear complex conjugation operation T = * and the linear

Annals of Physics, Jul 1, 2021

We show how, given a non-Hermitian Hamiltonian H, we can generate new non-Hermitian operators seq... more We show how, given a non-Hermitian Hamiltonian H, we can generate new non-Hermitian operators sequentially, producing a virtually infinite chain of non-Hermitian Hamiltonians which are isospectral to H and H † and whose eigenvectors we can easily deduce in an almost automatic way; no ingredients are necessary other than H and its eigensystem. To set off the chain and keep it running, we use, for the first time in our knowledge, a series of maps all connected to different metric operators. We show how the procedure works in several physically relevant systems. In particular, we apply our method to various versions of the Hatano-Nelson model and to some PT-symmetric Hamiltonians.

Progress of Theoretical and Experimental Physics, Jun 1, 2009

We study the heat transfer between two finite quantum systems initially at different temperatures... more We study the heat transfer between two finite quantum systems initially at different temperatures. We find that a recently proposed fluctuation theorem for heat exchange, namely the exchange fluctuation theorem [C. Jarzynski and D. K. Wójcik, Phys. Rev. Lett. 92 (2004), 230602], does not generally hold in the presence of a finite heat transfer as in the original form proved for weak coupling. As the coupling is weakened, the deviation from the theorem and the heat transfer vanish in the same order of the coupling. We then discover a condition for the exchange fluctuation theorem to hold in the presence of a finite heat transfer, namely the commutable-coupling condition. We explicitly calculate the deviation from the exchange fluctuation theorem as well as the heat transfer for simple models. We confirm for the models that the deviation indeed has a finite value as far as the coupling between the two systems is finite except for the special point of the commutable-coupling condition. We also confirm analytically that the commutable-coupling condition indeed lets the exchange fluctuation theorem hold exactly under a finite heat transfer.