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Masao Hirokawa Last modified date：2023.11.27

Professor / Department of I&E Visionaries / Faculty of Information Science and Electrical Engineering


Papers
1. T. Fujii, M. Hirokawa, On Performance of Concealing-Restoring System for Analog Signals on Physical Layer, IEEE Xplore (2022 International Conference on Electrical, Computer and Energy Technologies (ICECET), 20-22 July 2022), 20-22 July 2022, 2022.09.
2. T. Fujii and M. Hirokawa , Concealing-Restoring System for Physical Layer Data: Based on Stochastic Filtering Theory, Physical Communication, 10.1016/j.phycom.2022.101602, 52, 101602 (21 pages), 2022.06, [URL].
3. M. Hirokawa, On Accuracy of Restoration of Concealing-Restoring System for Physical Layer, IEEE Xplore (International Conference on Electrical, Computer and Energy Technologies (ICECET2021), Cape Town, South Africa, 09-10 Dec., 2021), 10.1109/ICECET52533.2021.9698502, 2022.02, [URL].
4. T. Fujii and M. Hirokawa, A Data Concealing Technique with Random Noise Disturbance and A Restoring Technique for the Concealed Data by Stochastic Process Estimation, Mathematics for Industry, 10.1007/978-981-15-5191-8_11, 33, 103-124, 2021.01, [URL].
5. Masao Hirokawa, Schrödinger-Cat-Like States with Dressed Photons in Renormalized Adiabatic Approximation for Generalized Quantum Rabi Hamiltonian with Quadratic Interaction, Physics Open, 10.1016/j.physo.2020.100039, 5, 100039, 2020.12, [URL].
6. T. Tanimoto, S. Matsuo, S. Kawakami, Y. Tabuchi, M. Hirokawa, and K. Inoue, How Many Trials Do We Need for Reliable NISQ Computing?, 2020 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), 10.1109/ISVLSI49217.2020.00059, 2020.08, [URL].
7. T. Tanimoto, S. Matsuo, S. Kawakami, Y. Tabuchi, M. Hirokawa, and K. Inoue, Practical Error Modeling Toward Realistic NISQ Simulation, 2020 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), 10.1109/ISVLSI49217.2020.00060, 2020.08, [URL].
8. Masao Hirokawa, Jacob S. Moller, Itaru Sasaki, A mathematical analysis of dressed photon in ground state of generalized quantum Rabi model using pair theory, Journal of Physics A: Mathematical and Theoretical, 10.1088/1751-8121/aa677c, 50, 18, 2017.04, 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..
9. Masao Hirokawa, Duality between a dark state and a quasi-dark state, Annals of Physics, 10.1016/j.aop.2016.12.032, 377, 229-242, 2017.02, 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..
10. Masao Hirokawa, Takuya Kosaka, A mathematical aspect of a tunnel-junction for spintronic qubit, Journal of Mathematical Analysis and Applications, 10.1016/j.jmaa.2014.03.061, 417, 2, 856-872, 2014.09, 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..
11. Masao Hirokawa, Fumio Hiroshima, József Lőrinczi, Spin-boson model through a Poisson-driven stochastic process, Mathematische Zeitschrift, 10.1007/s00209-014-1299-1, 277, 3-4, 1165-1198, 2014.04, 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..
12. Masao Hirokawa, Takuya Kosaka, One-dimensional tunnel-junction formula for the schrödinger particle, SIAM Journal on Applied Mathematics, 10.1137/130929072, 73, 6, 2247-2261, 2013.12, 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..
13. Yutaka Shikano, Masao Hirokawa, Boundary conditions in one-dimensional tunneling junction, Journal of Physics: Conference Series, 10.1088/1742-6596/302/1/012044, 302, 1, 2011.01, 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..
14. Yoshiyuki Furuhashi, Masao Hirokawa, Kazumitsu Nakahara, Yutaka Shikano, Role of a phase factor in the boundary condition of a One-dimensional junction, Journal of Physics A: Mathematical and Theoretical, 10.1088/1751-8113/43/35/354010, 43, 35, 2010.09, 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..
15. Masao Hirokawa, The Dicke-type crossings among eigenvalues of differential operators in a class of non-commutative oscillators, Indiana University Mathematics Journal, 10.1512/iumj.2009.58.3645, 58, 4, 1493-1535, 2009.10, 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..
16. Masao Hirokawa, Dicke-type energy level crossings in cavity-induced atom cooling
Another superradiant cooling, Physical Review A - Atomic, Molecular, and Optical Physics, 10.1103/PhysRevA.79.043408, 79, 4, 2009.04, 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..
17. Asao Arai, Masao Hirokawa, Fumio Hiroshima, Regularities of ground states of quantum field models, Kyushu Journal of Mathematics, 10.2206/kyushujm.61.321, 61, 2, 321-372, 2007.01, 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..
18. Masao Hirokawa, Infrared catastrophe for Nelson's model - Non-existence of ground state and soft-boson divergence, Publications of the Research Institute for Mathematical Sciences, 10.2977/prims/1166642191, 42, 4, 897-922, 2006.12, We mathematically study the infrared catastrophe for the Hamiltonian of Nelson's model when it has the external potential in a general class. For the model, we prove the pull-through formula on ground states in operator theory first. Based on this formula, we show both non-existence of any ground state and divergence of the total number of soft bosons..
19. Christian Hainzl, Masao Hirokawa, Herbert Spohn, Binding energy for hydrogen-like atoms in the Nelson model without cutoffs, Journal of Functional Analysis, 10.1016/j.jfa.2004.07.009, 220, 2, 424-459, 2005.03, 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 Ebin =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 Ebin=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..
20. Masao Hirokawa, Fumio Hiroshima, Herbert Spohn, Ground state for point particles interacting through a massless scalar Bose field, Advances in Mathematics, 10.1016/j.aim.2004.03.011, 191, 2, 339-392, 2005.03, We consider a massless scalar Bose field interacting with two particles, one of them infinitely heavy. Neither an infrared nor an ultraviolet cutoff is imposed. In case the charge of the particles is of the same sign and sufficiently small, we prove the existence of a ground state..
21. Jaroslav Dittrich, Pavel Exner, Masao Hirokawa, A model of interband radiative transition, Journal of the Mathematical Society of Japan, 10.2969/jmsj/1191334085, 56, 3, 753-786, 2004.01, 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..
22. Masao Hirokawa, Ground state transition for two-level system coupled with Bose field, Physics Letters, Section A: General, Atomic and Solid State Physics, 10.1016/S0375-9601(02)00032-4, 294, 1, 13-18, 2002.02, For the two-level system coupled with a Bose field, we investigate the ground state transition and appearance of a non- perturbative ground state..
23. Masao Hirokawa, Osamu Ogurisu, Ground state of a spin-1/2 charged particle in a two-dimensional magnetic field, Journal of Mathematical Physics, 10.1063/1.1379312, 42, 8, 3334-3343, 2001.08, 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 (·) = Σvγv δ(· - av with some singular points av 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 ( = Σvγv + ∫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 yv's..
24. Asao Arai, Masao Hirokawa, Stability of ground states in sectors and its application to the Wigner-Weisskopf model, Reviews in Mathematical Physics, 10.1142/s0129055x01000740, 13, 4, 513-527, 2001.04, 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..
25. Masao Hirokawa, Remarks on the ground state energy of the spin-boson model. An application of the Wigner-Weisskopf model, Reviews in Mathematical Physics, 10.1142/S0129055X01000727, 13, 2, 221-251, 2001.02, 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..
26. Asao Arai, Masao Hirokawa, Ground states of a general class of quantum field Hamiltonians, Reviews in Mathematical Physics, 10.1142/S0129055X00000393, 12, 8, 1085-1135, 2000.08, 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..
27. Masao Hirokawa, Canonical Quantization on a Doubly Connected Space and the Aharonov-Bohm Phase, Journal of Functional Analysis, 10.1006/jfan.2000.3591, 174, 2, 322-363, 2000.07, We consider the canonical quantization (Schrödinger representation) on a doubly connected space ΩR≡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 pUj of pj≡-i∂/∂xj (j=1, 2), and none of the pairs {pj, qj′}j, j′=1, 2 (qj′≡xj′·) 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..
28. Asao Arai, Masao Hirokawa, Fumio Hiroshima, On the Absence of Eigenvectors of Hamiltonians in a Class of Massless Quantum Field Models without Infrared Cutoff, Journal of Functional Analysis, 10.1006/jfan.1999.3472, 168, 2, 470-497, 1999.11, 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..
29. P. Exner, M. Hirokawa, O. Ogurisu, Anomalous Pauli electron states for magnetic fields with tails, Letters in Mathematical Physics, 10.1023/A:1007679721268, 50, 2, 103-114, 1999.10, 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..
30. Masao Hirokawa, An Expression of the Ground State Energy of the Spin-Boson Model, Journal of Functional Analysis, 10.1006/jfan.1998.3369, 162, 1, 178-218, 1999.02, An expression of the ground state energyESBof the spin-boson HamiltonianHSBis 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 toESB..
31. Masao Hirokawa, An inverse problem in quantum field theory and canonical correlation functions, Journal of the Mathematical Society of Japan, 10.2969/jmsj/05120337, 51, 2, 337-369, 1999.01, 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..
32. Asao Arai, Masao Hirokawa, On the existence and uniqueness of ground states of a generalized spin-boson model, Journal of Functional Analysis, 10.1006/jfan.1997.3140, 151, 2, 455-503, 1997.12, 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⊕Fbof a Hilbert space H and the boson (symmetric) Fock space FboverL2(Rν). 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..
33. Masao Hirokawa, General properties between the canonical correlation and the independent-oscillator model on a partial *-algebra, Journal of Mathematical Physics, 10.1063/1.531379, 37, 1, 121-146, 1996.01, 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..
34. Masao Hirokawa, Mori′s memory kernel equation in equilibrium quantum systems in finite volumes, Annals of Physics, 10.1006/aphy.1994.1011, 229, 2, 354-383, 1994.02, 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..
35. Masao Hirokawa, A mathematical relation between the potential of the rotating wave approximation and an estimation of the fluctuation in mori′s theory, Annals of Physics, 10.1006/aphy.1994.1078, 234, 2, 185-210, 1994.01, 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 RA(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 HRWA by making the rotating wave approximation from RA(t) such that we reconstruct the autocorrelation function RA(t) in the system governed by HRWA..
36. Masao Hirokawa, Mori′s memory kernel equation for a quantum harmonic oscillator coupled to RWA-oscillator, Annals of Physics, 10.1006/aphy.1993.1048, 224, 2, 301-341, 1993.06, 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..
37. Masao Hirokawa, Rigorous construction of liouville spaces and thermo field dynamics for bosonic systems in mathematics, Annals of Physics, 10.1006/aphy.1993.1025, 223, 1, 1-36, 1993.04, 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..


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