Language：English   Publishing type：Research paper (scientific journal)  

A generalization of the standard spin-boson model is considered. The HamiltonianH(α) of the model with a coupling parameterα∈Racts in the tensor product H⊕F_bof a Hilbert space H and the boson (symmetric) Fock space F_boverL²(R^ν). The existence and uniqueness of ground states ofH(α) are investigated. The degeneracy of the ground states is also discussed. The results obtained arenonperturbative. The methods used are those of constructive quantum field theory and the min-max principle. An exact asymptotic formula for the ground state energy ofH(α) as |α|→∞ is also established.

DOI： 10.1006/jfan.1997.3140

Authorship：Last author,　Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：International Conference on Electrical, Computer and Energy Technologies, ICECET 2023  

Our concealing-restoring system (CRS) is for the security of the data on the physical layer of the open-systems-interconnection reference model. CRS is primarily for the security of the digital data on that physical layer. It conceals the data by disturbance with some random noises, and moreover, it restores the concealed data by the noise elimination with the proper stochastic filtering. We have lately been studying CRS for analog signals. We introduce some types of mean errors and evaluate its ability in this study. Through the evaluation, we consider the application of CRS to the analog, pictorial image in this paper.

DOI： 10.1109/ICECET61485.2024.10698034

DOI： 10.1109/ICECET61485.2024.10698034

Scopus

Other Link： https://doi.org/10.1109/ICECET61485.2024.10698034

Language：Japanese   Publisher：The Institute of Electrical Engineers of Japan  

<p>1．はじめに：量子コンピュータ？</p><p>現代社会はさまざまな場面でコンピュータの利便性を享受している。この利便性はコンピュータの計算能力に支えられ，計算能力は大規模集積回路（LSI）技術の進展に依存する。LSIの半導体微細加工に基づく集積度の進歩はMooreの法則^（1）という経験則に従うとされるが，ミクロな</p>

DOI： 10.1541/ieejjournal.144.217

CiNii Research

Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：International Conference on Electrical, Computer and Energy Technologies, ICECET 2023  

Our concealing-restoring system (CRS) is for the security of the data on the physical layer of the open-systems-interconnection reference model. CRS is primarily for the security of the digital data on that physical layer. It conceals the data by disturbance with some random noises, and moreover, it restores the concealed data by the noise elimination with the proper stochastic filtering. We have lately been studying CRS for analog signals. We introduce some types of mean errors and evaluate its ability in this study. Through the evaluation, we consider the application of CRS to the analog, pictorial image in this paper.

DOI： 10.1109/ICECET58911.2023.10389575

DOI： 10.1109/ICECET58911.2023.10389575

Scopus

Other Link： https://doi.org/10.1109/ICECET58911.2023.10389575

Language：English   Publishing type：Research paper (international conference proceedings)  

DOI： 10.1109/ICECET52533.2021.9698502

Other Link： https://ieeexplore.ieee.org/document/9698502

Publisher：International Conference on Electrical, Computer, and Energy Technologies, ICECET 2022  

We have proposed a concealing-restoring system (CRS), which is for the security of the digital data on the physical layer of the open-systems-interconnection reference model. Primarily, the main body (MB) of CRS shoulders the concealing and restoring of analog signals which should be transformed into the digital data on the physical layer. MB conceals an original, analog signal by the random-noise disturbance, and makes the concealed signals. MB also restores the analog signal from the concealed signals using the proper noise elimination based on the stochastic filtering theory. In this paper, thus, we apply the CRS to analog signals, and briefly report its performance of the restoration. Going through the results of those experiments, we give some mathematical conjectures.

DOI： 10.1109/ICECET55527.2022.9872933

Scopus

Language：English   Publishing type：Research paper (international conference proceedings)  

DOI： 10.1007/978-981-15-5191-8_11

Other Link： https://link.springer.com/chapter/10.1007/978-981-15-5191-8_11

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1016/j.physo.2020.100039

Other Link： https://www.sciencedirect.com/science/article/pii/S2666032620300260

Language：English   Publishing type：Research paper (international conference proceedings)  

DOI： 10.1109/ISVLSI49217.2020.00060

Other Link： https://ieeexplore.ieee.org/document/9155029

Language：English   Publishing type：Research paper (international conference proceedings)  

DOI： 10.1109/ISVLSI49217.2020.00059

Other Link： https://ieeexplore.ieee.org/document/9154928

Language：English   Publishing type：Research paper (scientific journal)  

We consider the generalized quantum Rabi model with the so-called A ²-term in the light of the Hepp-Lieb-Preparata quantum phase transition. We investigate the dressed photon in its ground state when the atom-light coupling strength is in the deep-strong coupling regime. This regime is introduced by Casanova et al (2010 Phys. Rev. Lett. 105 263603) as the coupling regime exceeding the ultra-strong one. We show how the dressed photon appears in the ground state.

DOI： 10.1088/1751-8121/aa677c

Language：English   Publishing type：Research paper (scientific journal)  

We study a physical system coupled with two one-mode Bose fields. The physical system is a two-level system or a harmonic oscillator. We prove that each dark and quasi-dark state appears under a proper condition, and then, we derive a duality between the dark state and the quasi-dark state. This duality induces the switch between the dark state and the quasi-dark state.

DOI： 10.1016/j.aop.2016.12.032

Language：English   Publishing type：Research paper (scientific journal)  

We consider the Dirac particle that lives in the 1-dimensional configuration space consisting of two quantum wires and a junction between the two. We regard the spin of a Dirac particle as spintronic qubit. We give concrete formulae explicitly expressing the one-to-one correspondence between every self-adjoint extension of the minimal Dirac operator and its corresponding boundary condition of the wave functions of the Dirac particle. We then show that all the boundary conditions can be classified into just two types. The two types are characterized by whether the electron passes through the junction or not. We also show how the tunneling produces its own phase factor and what is the relation between the phase factor and the spintronic qubit in the tunneling boundary condition.

DOI： 10.1016/j.jmaa.2014.03.061

Language：English   Publishing type：Research paper (scientific journal)  

We give a functional integral representation of the semigroup generated by the spin-boson Hamiltonian by making use of a Poisson point process and a Euclidean field. We present a method of constructing Gibbs path measures indexed by the full real line which can be applied also to more general stochastic processes with jump discontinuities. Using these tools we then show existence and uniqueness of the ground state of the spin-boson, and analyze ground state properties. In particular, we prove super-exponential decay of the number of bosons, Gaussian decay of the field operators, derive expressions for the positive integer, fractional and exponential moments of the field operator, and discuss the field fluctuations in the ground state.

DOI： 10.1007/s00209-014-1299-1

Language：English   Publishing type：Research paper (scientific journal)  

We handle all the self-adjoint extensions of the minimal Schrödinger operator for the nonrelativistic electron living in the one-dimensional configuration space with a junction. We are interested in every boundary condition corresponding to the individual self-adjoint extension. Thus, we clarify all the types of those boundary conditions of the wave functions of the nonrelativistic electron. We find concrete tunnel-junction formulae for the nonrelativistic electron passing through the junction, which reveals the phase factor caused by the tunneling through the junction. Using this tunnel-junction formula, we propose a mathematical possibility of a tunnel-junction device for qubit.

DOI： 10.1137/130929072

Language：English   Publishing type：Research paper (scientific journal)  

The tunneling effect is first characterized in quantum mechanics. However, the mathematical analysis for the tunneling effect is so complicated. In the conventional sense, the WKB analysis is useful to analyze such effect. Here, we consider the mathematical analysis for the tunneling effect in the one-dimensional Schrödinger system from the viewpoint of functional analysis. From the rigorous analysis, we obtain the interference pattern of the tunneling particle.

DOI： 10.1088/1742-6596/302/1/012044

Language：English   Publishing type：Research paper (scientific journal)  

One-dimensional quantum systems can be experimentally studied in recent nanotechnology like the carbon nanotube and the nanowire. We have considered the mathematical model of a one-dimensional Schrödinger particle with a junction and have analyzed the phase factor in the boundary condition of the junction. We have shown that the phase factor in the tunneling case appears in the situation of the non-adiabatic transition with the three energy levels in the exact Wentzel-Kramers-Brillouin analysis.

DOI： 10.1088/1751-8113/43/35/354010

Language：English   Publishing type：Research paper (scientific journal)  

We study the Dicke-type crossings among eigenvalues of a type of differential operators describing the noncommutative oscillator in a class. This class consists of some matrix-valued Schrödinger operators. We will show how the crossings occur for the differential operators in detail. In particular, we are interested in the crossing between the ground state energy and an excited state energy.

DOI： 10.1512/iumj.2009.58.3645

Language：English   Publishing type：Research paper (scientific journal)  

This paper is devoted to energy-spectral analysis for the system of a two-level atom coupled with photons in a cavity. It is shown that the Dicke-type energy level crossings take place when the atom-cavity interaction of the system undergoes changes between the weak-coupling regime and the strong one. Using the phenomenon of the crossings, we develop the idea of cavity-induced atom cooling proposed by Horak, and we lay mathematical foundations of a possible mechanism for another superradiant cooling in addition to that proposed by Domokos and Ritsch. The process of our superradiant cooling can function well by cavity decay and by control of the position of the atom, at least in (mathematical) theory, even if there is neither atomic absorption nor atomic emission of photons.

DOI： 10.1103/PhysRevA.79.043408

Language：English   Publishing type：Research paper (scientific journal)  

Regularities and higher order regularities of ground states of quantum field models are investigated through the fact that asymptotic annihilation operators vanish ground states. Moreover, a sufficient condition for the absence of a ground state is given.

DOI： 10.2206/kyushujm.61.321

Language：English   Publishing type：Research paper (scientific journal)  

In the Nelson model particles interact through a scalar massless field. For hydrogen-like atoms there is a nucleus of infinite mass and charge Ze, Z > 0, fixed at the origin and an electron of mass m and charge e. This system forms a bound state with binding energy E_bin =me⁴Z²/8π² to leading order in e. We investigate the radiative corrections to the binding energy and prove upper and lower bounds which imply that E_bin=me⁴ Z²/8π² + c₀e⁶ O(e⁷ ln e) with explicit coefficient c₀ and independent of the ultraviolet cutoff. c₀ can be computed by perturbation theory, which however is only formal since for the Nelson Hamiltonian the smallest eigenvalue sits exactly at the bottom of the continuous spectrum.

DOI： 10.1016/j.jfa.2004.07.009

Language：English   Publishing type：Research paper (scientific journal)  

We consider a simple model which is a caricature of a crystal interacting with a radiation field. The model has two bands of continuous spectrum and the particle can pass from the upper one to the lower by radiating a photon, the coupling between the excited and deexcited states being of a Friedrichs type. Under suitable regularity and analyticity assumptions we find the continued resolvent and show that for weak enough coupling it has a curve-type singularity in the lower halfplane which is a deformation of the upper-band spectral cut. We then find a formula for the decay amplitude and show that for a fixed energy it is approximately exponential at intermediate times, while the tail has a power-like behaviour.

DOI： 10.2969/jmsj/1191334085

Language：English   Publishing type：Research paper (scientific journal)  

For the two-level system coupled with a Bose field, we investigate the ground state transition and appearance of a non- perturbative ground state.

DOI： 10.1016/S0375-9601(02)00032-4

Language：English   Publishing type：Research paper (scientific journal)  

It is investigated that the structure of the kernel of the Dirac-Weyl operator D of a charged particle in the magnetic-field B = B₀ + B₁, given by the sum of a strongly singular magnetic field B₀ (·) = Σ_vγ^v δ(· - a_v with some singular points a_v and a magnetic-field B₁ with a bounded support. Here the magnetic field B₁ may have some singular points with the order of the singularity less than 2. At a glance, it seems that, following "Aharonov-Casher Theorem" [Phys. Rev. A 19, 2461 (1979)], the dimension of the kernel of D, dimker D, is a function of one variable of the total magnetic flux ( = Σ_vγ_v + ∫_R2B₁dxdy) of B. However, since the influence of the strongly singular points works, dim ker D indeed is a function of several variables of the total magnetic flux and each of y_v's.

DOI： 10.1063/1.1379312

Language：English   Publishing type：Research paper (scientific journal)  

We consider two kinds of stability (under a perturbation) of the ground state of a self-adjoint operator: the one is concerned with the sector to which the ground state belongs and the other is about the uniqueness of the ground state. As an application to the Wigner-Weisskopf model which describes one mode fermion coupled to a quantum scalar field, we prove in the massive case the following: (a) For a value of the coupling constant, the Wigner-Weisskopf model has degenerate ground states; (b) for a value of the coupling constant, the Wigner-Weisskopf model has a first excited state with energy level below the bottom of the essential spectrum. These phenomena are nonperturbative.

DOI： 10.1142/s0129055x01000740

Language：English   Publishing type：Research paper (scientific journal)  

For the ground state energy of the spin-boson (SB) model, we give a new upper bound in the case with infrared singularity condition (i.e. without infrared cutoff), and a new lower bound in the case of massless bosons with infrared regularity condition. We first investigate spectral properties of the Wigner-Weisskopf (WW) model, and apply them to SB model to achieve our purpose. Then, as an extra result of the spectral analysis for WW model, we show that a non-perturbative ground state appears, and its ground state energy is so low that we cannot conjecture it by using the regular perturbation theory.

DOI： 10.1142/S0129055X01000727

Language：English   Publishing type：Research paper (scientific journal)  

We consider a model of a quantum mechanical system coupled to a (massless) Bose field, called the generalized spin-boson model (A. Arai and M. Hirokawa, J. Funct. Anal. 151 (1997), 455-503), without infrared regularity condition. We define a regularized Hamiltonian H(ν) with a parameter ν ≥ 0 such that H = H(0) is the Hamiltonian of the original model. We clarify a relation between ground states of H(ν) and those of H by formulating sufficient conditions under which weak limits, as ν → 0, of the ground states of H(ν)'s are those of H. We also establish existence theorems on ground states of H(ν) and H under weaker conditions than in the previous paper mentioned above.

DOI： 10.1142/S0129055X00000393

Language：English   Publishing type：Research paper (scientific journal)  

We consider the canonical quantization (Schrödinger representation) on a doubly connected space Ω_R≡R²\{(x, y)x²+y²≤R²} (R>0). We show that, when we employ 2-dimensional orthogonal coordinates Ox₁x₂, there are uncountably many different self-adjoint extensions p_Uj of p_j≡-i∂/∂x_j (j=1, 2), and none of the pairs {p_j, q_j′}_{j, j′=1, 2} (q_j′≡x_j′·) satisfies the Weyl relation. Then, we construct a new canonical pair of canonical momentum and position operators so that the pair can satisfy the Weyl relation by using the streamline coordinates. As its application, in the Weyl relation with respect to the pair of the mv-momentum and position operators by the above new canonical pair, we find the Aharonov-Bohm phase.

DOI： 10.1006/jfan.2000.3591

Language：English   Publishing type：Research paper (scientific journal)  

A class of models of quantized, massless Bose fields, called the generalized spin-boson model (A. Arai and M. Hirokawa, J. Funct. Anal.151 (1997), 455-503) is considered. Theorems on the absence of ground states and the other eigenvectors of the model without infrared cutoff (but with ultraviolet cutoff) are established with conditions in terms of correlation functions for some operators.

DOI： 10.1006/jfan.1999.3472

Language：English   Publishing type：Research paper (scientific journal)  

We consider a two-dimensional electron with an anomalous magnetic moment, g > 2, interacting with a nonzero magnetic field B perpendicular to the plane which gives rise to a flux F. Recent results about the discrete spectrum of the Pauli operator are extended to fields with the O(r^-2-δ) decay at infinity: we show that if \F\ exceeds an integer N, there is at least N + 1 bound states. Furthermore, we prove that weakly coupled bound states exist under mild regularity assumptions also in the zero flux case.

DOI： 10.1023/A:1007679721268

Language：English   Publishing type：Research paper (scientific journal)  

An expression of the ground state energyE_SBof the spin-boson HamiltonianH_SBis considered. The expression in the cases of both massive and massless bosons is given by a nonperturbative method. By using the expression, we show a necessary and sufficient condition with respect to a parameterG∈[-1,0] such that a formula withGattains toE_SB.

DOI： 10.1006/jfan.1998.3369

Language：English   Publishing type：Research paper (scientific journal)  

In this paper, we treat a quantum harmonic oscillator in thermal equilibrium with any systems in certain classes of bosons with infinitely many degrees of freedom. We describe the following results: (i) when a canonical correlation function is given, we so reconstruct a Hamiltonian by the rotating wave approximation from it that the Hamiltonian restores it. Namely, we solve an inverse problem in the quantum field theory at finite temperature in a finite volume. (ii) Taking an infinite volume limit for the result in (i), we consider long-time behavior of the canonical correlation function in the finite volume limit.

DOI： 10.2969/jmsj/05120337

Language：English   Publishing type：Research paper (scientific journal)  

We consider a quantum particle in thermal equilibrium with any quantum system in a finite volume under some conditions. For the Heisenberg operator of the momentum operator of the quantum particle, we show that, on a partial *-algebra, the Heisenberg operator satisfies a quantum Langevin equation, which is similar to the work of Ford et al. [G. W. Ford, J. T. Lewis, and R. F. O'Connell, Phys. Rev. A 37, 4419 (1988)]. Through the Langevin equation, we show general and mathematical properties between the canonical correlation and the independent-oscillator model.

DOI： 10.1063/1.531379

Language：English   Publishing type：Research paper (scientific journal)  

For any observable in an equilibrium quantum system in a finite volume, we show a method of deriving Mori′s memory kernel equation, which consists of three components, Mori′s frequency, memory function, and fluctuation, i.e., we give a concrete mathematical expression for the three components in terms of an autocorrelation function of the observable.

DOI： 10.1006/aphy.1994.1011

Language：English   Publishing type：Research paper (scientific journal)  

We show a mathematical relation between the potential of the rotating wave approximation and an estimation of the fluctuation in Mori′s theory of generalized Brownian motion. We use this relation to prove that, when an autocorrelation function R_A(t), t ∈ R concerning the Bogoliubov scalar product is given for a certain quantum observable A in an equilibrium quantum system in finite volume, we can obtain a Hamiltonian H_RWA by making the rotating wave approximation from R_A(t) such that we reconstruct the autocorrelation function R_A(t) in the system governed by H_RWA.

DOI： 10.1006/aphy.1994.1078

Language：English   Publishing type：Research paper (scientific journal)  

For a quantum harmonic oscillator coupled to the RWA-oscillator, we actually derive Mori′s memory kernel equation, which consists of three components, Mori′s frequency, Mori′s memory function, and Mori;s fluctuation. Then we find the method of expressing the three components in terms of an autocorrelation function of an observable.

DOI： 10.1006/aphy.1993.1048

Language：English   Publishing type：Research paper (scientific journal)  

We clarify the mathematical difficulty when for bosonic systems (i.e., unbounded operators) we rigorously construct a Liouville space, in which a Liouville operator acts, associated with a Hamiltonian. Including unbounded and non-quasi-free cases. We give thermo field dynamics as an expression equivalent to the Liouville space and operator. We investigate the mathematical properties of them, and thus we clarify the mathematical properties of the thermal state.

DOI： 10.1006/aphy.1993.1025

Event date： 2020.1

Language：Japanese  

Venue：理化学研究所鈴木梅太郎記念ホール   Country：Japan  

Event date： 2019.9 - 2020.6

Language：English   Presentation type：Oral presentation (general)  

Venue：Kyushu University   Country：Japan  

We are interested in a mathematical method and a technology for its implementation for securing data on physical layer of our developing quantum-sensing device because the device detects and handles some ultimate personal information. I talk about the joint research with my student, Tomohiro Fujii. In the joint research, we use a noise-disturbance instead of using cryptograph.

Event date： 2019.6 - 2020.6

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：指宿温泉休暇村指宿   Country：Japan  

Event date： 2019.5

Language：Japanese  

Venue：東京大学   Country：Japan  

Event date： 2019.1

Language：English   Presentation type：Oral presentation (general)  

Venue：Washington, DC   Country：United States  

We report on the numerical results for the edge effect in the finite length of the ferromagnetic nanowires with a domain wall. The Majorana bound states (MBS) emerges at the edge of the topological superconductor (TSC) region for sufficiently large value of the effective strong spin-orbit interaction (SOI). From the local spin density, we obtain the result that the MBS with exponential decay forms a pair at the both edges of the TSC region and the decay length become smaller with larger effective SOI.

Event date： 2018.9

Language：Japanese   Presentation type：Oral presentation (general)  

Venue：名古屋国際会議場   Country：Japan  

磁壁を有する強磁性ナノワイヤにおけるトポロジカル超伝導体に関する数値計算結果

Event date： 2018.7

Language：English  

Venue：Lanzhou University   Country：China  

We give a procedure to approximate eigenstates of
the generalized quantum Rabi Hamiltonian both
without and with a quadratic interaction for
the deep-strong coupling regime.
Based on it, in the case without the quadratic interaction,
we show that whether each approximated bare eigenstate
forms a Schroedinger-cat-like entangled state or
a separate state depends on whether the bias energy
in the atom Hamiltonian is zero or non-zero,
and then, the effect of the atom is ignored in the approximation.
On the other hand, in the case with the quadratic interaction,
we consider its renormalization, and show that all the approximated
physical eigenstates form individual Schroedinger-cat-like entangled
states for every bias energy, and this fact comes from the effect of
the atom.

Event date： 1994.1

Language：English  

Venue：Wailea, HI, USA   Country：Other  

We are developing a new problem-solving methodology based on a self-organization paradigm. To realize our future goal of self-organizing computational systems, we have to study computation based on local information and its emergent behavior, which are considered essential in self-organizing systems. This paper presents a stochastic (or nondeterministic) problem solving method using local operations and local evaluation functions. Several constraint satisfaction problems are solved and approximate solutions of several optimization problem are found by this method in polynomial order time in average. Major features of this method are as follows. Problems can be solved using one or a few simple production rules and evaluation functions, both of which work locally, i.e., on a small number of objects. Local maxima of the sum of evaluation function values can sometimes be avoided. Limit cycles of execution can also be avoided. There are two methods for changing the locality of rules. The efficiency of searches and the possibility of falling into local maxima can be controlled by changing the locality.

Type：Competition, symposium, etc. 

Type：Competition, symposium, etc. 

Type：Competition, symposium, etc. 

Type：Competition, symposium, etc. 

Type：Competition, symposium, etc.