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Naomichi Hatano

Publications and source records attributed to Naomichi Hatano.

At least 91 records · Page 5Linked to original sources
arXiv2009

Probabilistic Interpretation of Resonant States

We provide probabilistic interpretation of resonant states. This we do by showing that the integral of the modulus square of resonance wave functions (i.e., the conventional norm) over a properly expanding spatial domain is independent of time, and therefore leads to probability conservation. This is in contrast with the conventional employment of a bi-orthogonal basis that precludes probabilistic interpretation, since wave functions of resonant states diverge exponentially in space. On the other hand, resonant states decay exponentially in time, because momentum leaks out of the central scattering area. This momentum leakage is also the reason for the spatial exponential divergence of resonant state. It is by combining the opposite temporal and spatial behaviors of resonant states that we arrive at our probabilistic interpretation of these states. The physical need to normalize resonant wave functions over an expanding spatial domain arises because particles leak out of the region which contains the potential range and escape to infinity, and one has to include them in the total count of particle number.

quant-ph↗
arXiv2009

The exchange fluctuation theorem in quantum mechanics

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. Wojcik, Phys. Rev. Lett. 92, 230602 (2004)], 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.

cond-mat.stat-mech↗
arXiv2008

Quantum Nernst effect in a bismuth single crystal

We report a theoretical calculation explaining the quantum Nernst effect observed experimentally in a bismuth single crystal. Generalizing the edge-current picture in two dimensions, we show that the peaks of the Nernst coefficient survive in three dimensions due to a van Hove singularity. We also evaluate the phonon-drag effect on the Nernst coefficient numerically. Our result agrees with the experimental result for a bismuth single crystal.

cond-mat.mes-hall↗
arXiv2008

Vortex generation in the RSP game on the triangular lattice

A new model of population dynamics on lattices is proposed. The model consists of players on lattice points, each of which plays the RSP game with neighboring players. Each player copies the next hand from the hand of the neighbouring player with the maximum point. The model exhibits a steady pattern with pairs of vortices and sinks on the triangular lattice. It is shown that the stationary vortex is due to the frustrations on the triangular lattice. A frustration is the three-sided situation where each of the three players around a triangle chooses the rock, the scissors and the paper, respectively.

cond-mat.stat-mech↗
arXiv2007

Transient Oscillation of Currents in Quantum Hall Effect of Bloch Electrons

We consider the quantum Hall effect of two-dimensional electrons with a periodic potential and study the time dependence of the Hall and longitudinal currents when the electric field is applied abruptly. We find that the currents oscillate in time with very large frequencies because of quantum fluctuation and the oscillations eventually vanish, for their amplitudes decay as 1/t.

cond-mat.mes-hall↗
arXiv2007

Quasi-bound states in continuum

We report the prediction of quasi-bound states (resonant states with very long lifetimes) that occur in the eigenvalue continuum of propagating states for a wide region of parameter space. These quasi-bound states are generated in a quantum wire with two channels and an adatom, when the energy bands of the two channels overlap. A would-be bound state that lays just below the upper energy band is slightly destabilized by the lower energy band and thereby becomes a resonant state with a very long lifetime (a second QBIC lays above the lower energy band).

quant-ph↗
arXiv2007

Some properties of the resonant state in quantum mechanics and its computation

The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take account of the outgoing momentum flux; the number of particles would decay exponentially in a fixed volume of integration. Moreover, we introduce new numerical methods of treating the resonant state with the use of the effective potential. We first give a numerical method of finding a resonance pole in the complex energy plane. The method seeks an energy eigenvalue iteratively. We found that our method leads to a super-convergence, the convergence exponential with respect to the iteration step. The present method is completely independent of commonly used complex scaling. We also give a numerical trick for computing the time evolution of the resonant state in a limited spatial area. Since the wave function of the resonant state is diverging away from the scattering potential, it has been previously difficult to follow its time evolution numerically in a finite area.

quant-ph↗
arXiv2007

Communicability in complex networks

Many topological and dynamical properties of complex networks are defined by assuming that most of the transport on the network flows along the shortest paths. However, there are different scenarios in which non-shortest paths are used to reach the network destination. Thus the consideration of the shortest paths only does not account for the global communicability of a complex network. Here we propose a new measure of the communicability of a complex network, which is a broad generalization of the concept of the shortest path. According to the new measure, most of real-world networks display the largest communicability between the most connected (popular) nodes of the network (assortative communicability). There are also several networks with the disassortative communicability, where the most "popular" nodes communicate very poorly to each other. Using this information we classify a diverse set of real-world complex systems into a small number of universality classes based on their structure-dynamic correlation. In addition, the new communicability measure is able to distinguish finer structures of networks, such as communities into which a network is divided. A community is unambiguously defined here as a set of nodes displaying larger communicability among them than to the rest of nodes in the network.

physics.soc-ph↗
arXiv2007

The entanglement of the XY spin chain in a random magnetic field

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 \textit{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.

quant-ph↗
arXiv2007

Resonance in an open quantum dot system with a Coulomb interaction: a Bethe-ansatz approach

An open quantum system consisting of a quantum dot with a Coulomb interaction and two leads without interactions is studied. The many-body scattering states are constructed with the Bethe-ansatz approach. The expectation value of the electric current is exactly calculated for the scattering states to observe resonance peaks due to many-body scattering.

cond-mat.str-el↗
arXiv2007

Non-Abelian gauge field theory of the spin-orbit interaction and a perfect spin filter

We point out that the Rashba and Dresselhaus spin-orbit interactions in two dimensions can be regarded as a Yang-Mills non-Abelian gauge field. The physical field generated by the gauge field gives the electron wave function a spin-dependent phase which is frequently called the Aharonov-Casher phase. Applying on an AB ring this non-Abelian field together with the usual vector potential, we can make the interference condition completely destructive for one component of the spin while completely constructive for the other component of the spin over the entire energy range. This enables us to construct a perfect spin filter.

quant-ph↗
arXiv2006

Gap-mediated magnetization of a pseudo-one-dimensional system with a spin-orbit interaction

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.

cond-mat.mes-hall↗
arXiv2006

A non-Hermitian critical point and the correlation length of strongly correlated quantum systems

We study a non-Hermitian generalization of quantum systems in which an imaginary vector potential is added to the momentum operator. In the tight-binding approximation, we make the hopping energy asymmetric in the Hermitian Hamiltonian. In a previous article, we conjectured that the non-Hermitian critical point where the energy gap vanishes is equal to the inverse correlation length of the Hermitian system and we confirmed the conjecture for two exactly solvable systems. In this article, we present more evidence for the conjecture. We also argue the basis of our conjecture by noting the dispersion relation of the elementary excitation.

cond-mat.str-el↗
arXiv2006

A non-Hermitian analysis of strongly correlated quantum systems

We study a non-Hermitian generalization of strongly correlated quantum systems in which the transfer energy of electrons is asymmetric. It is known that a non-Hermitian critical point is equal to the inverse localization length of a Hermitian non-interacting random electron system. We here conjecture that we can obtain in the same way the correlation length of a Hermitian interacting non-random system. We confirm the conjecture using exact solutions and numerical finite-size data of the Hubbard model and the antiferromagnetic XXZ model in one dimension.

cond-mat.str-el↗
arXiv2005

Quantum Nernst Effect

We report our recent predictions on the quantum Nernst effect, a novel thermomagnetic effect in the quantum Hall regime. We assume that, when the chemical potential is located between a pair of neighboring Landau levels, edge currents convect around the system. This yields theoretical predictions that the Nernst coefficient is strongly suppressed and the thermal conductance is quantized. The present system is a physical realization of the non-equilibrium steady state.

cond-mat.mes-hall↗
arXiv2005

Strong Resonance of Light in a Cantor Set

The propagation of an electromagnetic wave in a one-dimensional fractal object, the Cantor set, is studied. The transfer matrix of the wave amplitude is formulated and its renormalization transformation is analyzed. The focus is on resonant states in the Cantor set. In Cantor sets of higher generations, some of the resonant states closely approach the real axis of the wave number, leaving between them a wide region free of resonant states. As a result, wide regions of nearly total reflection appear with sharp peaks of the transmission coefficient beside them. It is also revealed that the electromagnetic wave is strongly enhanced and localized in the cavity of the Cantor set near the resonant frequency. The enhancement factor of the wave amplitude at the resonant frequency is approximately $6/|η_\mathrm{r}|$, where $η_\mathrm{r}$ is the imaginary part of the corresponding resonant eigenvalue. For example, a resonant state of the lifetime $τ_\mathrm{r}=4.3$ms and of the enhancement factor $M=7.8\times10^7$ is found at the resonant frequency $ω_\mathrm{r}=367$GHz for the Cantor set of the fourth generation of length L=10cm made of a medium of the dielectric constant $ε=10$.

cond-mat.mtrl-sci↗