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The optic vesicle in the developing embryonic eye contains a multitude of neuroepithelial progenitors that subsequently differentiate into functionally distinct domains of the optic cup, such as the neural retina, pigment epithelium, and optic stalk. To investigate cell-type diversity across early optic vesicles before regionalization of the optic cup, we performed single-cell RNA-sequencing (scRNA-seq) using 7989 cells from the presumptive eye area in mouse embryos at the 12–26-somite stages at five developmental time points. We demonstrated the presence of seven optic vesicle populations. Moreover, the four populations of retinal progenitor cells could be classified according to their stage-dependent time point, and these cells exhibited altered expression of several structural and metabolic key genes, such as Col9a1 and Ckb, just before regionalization of the optic cup. From these data, we provide the first report on stage-dependent transcriptional profiles during initial retinal specification at single-cell resolution and highlight the unexpected developmental heterogeneity of the murine optic vesicle structure.

We present a complete microscopic Fermi-liquid description for next-to-leading order transport through an Anderson impurity under a finite bias voltage $V$. It is applicable to multilevel quantum dots without particle-hole or time-reversal symmetry, and is constructed based on the nonequilibrium Keldysh formalism, taking into account the current conservation between electrons in the impurity levels and the conduction bands. Specifically, we derive the formula for the current noise generated in the steady flow up to terms of order $(eV)^3$ at zero temperature $T=0$. To this end, we calculate the Keldysh vertex functions $\Gamma_{\sigma\sigma';\sigma'\sigma}^{ \nu_1\nu_2;\nu_3\nu_4} (\omega,\omega'; \omega',\omega)$, which depend on branches $\nu_1, \nu_2, \nu_3$ and $\nu_4$ of the time-loop contour and on spin degrees of freedom $\sigma$ and $\sigma'$, up to linear-order terms with respect to $eV$, $T$, and frequencies $\omega$ and $\omega'$. The coefficients of these linear-order terms are determined by a set of the parameters, defined with respect to the equilibrium ground state: the phase shift, static susceptibilities, and nonlinear three-body susceptibilities of the impurity electrons. The low-energy expressions of the vertex components are shown to satisfy the Ward identities with the Keldysh Green's functions expanded up to terms of order $\omega^2$, $(eV)^2$, and $T^2$. We also find that the imaginary part of the Ward identities can be described in terms of the $eV$-dependent collision integrals for a single-quasiparticle excitation and that for a single quasiparticle-quasihole pair excitation. These collision integrals ensure the current conservation of the next-to-leading order Fermi-liquid transport due to the quasiparticles with a finite damping rate., Comment: 43 pages, 10 figures, typos have been corrected

We study the nonlinear conductance through a quantum dot, specifically its dependence on the asymmetries in the tunnel couplings and bias voltages $V$, at low energies. Extending the microscopic Fermi-liquid theory for the Anderson impurity model, we obtain an exact formula for the steady current $I$ up to terms of order $V^3$ in the presence of these asymmetries. The coefficients for the nonlinear terms are described in terms of a set of the Fermi-liquid parameters: the phase shift, static susceptibilities, and three-body correlation functions of electrons in the quantum dots, defined with respect to the equilibrium ground state. We calculate these correlation functions, using the numerical renormalization group approach (NRG), over a wide range of impurity-electron filling that can be controlled by a gate voltage in real systems. The NRG results show that the order $V^2$ nonlinear current is enhanced significantly in the valence fluctuation regime. It is caused by the order $V$ energy shift of the impurity level, induced in the presence of the tunneling or bias asymmetry. Furthermore, in the valence fluctuation regime, we also find that the order $V^3$ nonlinear current exhibits a shoulder structure, for which the three-body correlations that evolve for large asymmetries play an essential role., 18 pages, 27 figures. Typos have been corrected

Behavior of quantum liquids is a fascinating topic in physics. Even in a strongly correlated case, the linear response of a given system to an external field is described by the fluctuation-dissipation relations based on the two-body correlations in the equilibrium. However, to explore nonlinear non-equilibrium behaviors of the system beyond this well-established regime, the role of higher order correlations starting from the three-body correlations must be revealed. In this work, we experimentally investigate a controllable quantum liquid realized in a Kondo-correlated quantum dot and prove the relevance of the three-body correlations in the nonlinear conductance at finite magnetic field, which validates the recent Fermi liquid theory extended to the non-equilibrium regime., Recent theory has shown that the non-equilibrium response of a Kondo model can be described by the Fermi liquid theory with three-body correlations. Here, the authors experimentally measure such correlations in the nonlinear conductance of a Kondo-correlated quantum dot.

The Mab-21 gene family is crucial for animal development. A deficiency in the Mab-21 genes associates with several defects, including skeletal malformation in mice and humans. In this study, we observed that mice lacking Mab21l1 displayed an unclosed fontanelle, suggesting impaired calvarial bone development. Cells isolated from the calvaria of these mice showed a greater osteoblast differentiation potential as evidenced by the abundance of mineralized bone nodules and higher expression levels of osteogenic markers than wild-type cells. Mab21l1-/- osteoblasts also expressed higher levels of adipocyte genes and interferon-regulated genes at early stages of osteogenesis. Rankl/Opg expression levels were also higher in Mab21l1-/- osteoblasts than in wild-type cells. These data suggest that Mab21l1 is involved in either the regulation of mesenchymal cell proliferation and differentiation or the balance between bone formation and resorption. An alteration in these regulatory machineries, therefore, may lead to insufficient bone formation, causing the bone phenotype in Mab21l1-/- mice.

We present a microscopic Fermi-liquid view on the low-energy transport through an Anderson impurity with $N$ discrete levels, at arbitrary electron filling $N_d$. It is applied to nonequilibrium current fluctuations, for which the two-quasiparticle collision integral and the three-body correlations that determine the quasiparticle energy shift play important roles. Using the numerical renormalization group up to $N=6$, we find that for strong interactions the three-body fluctuations are determined by a single parameter other than the Kondo energy scale in a wide filling range $1 \lesssim N_d \lesssim N-1$. It significantly affects the current noise for $N>2$ and the behavior of noise in magnetic fields., 5 pages, 8 figures, supplemental material containing 8 figures

We study Bell-state correlations for quasiparticle pairs excited in nonlinear current through a double quantum dot in the Kondo regime. Exploiting the renormalized perturbation expansion in the residual interactions of the local Fermi liquid and Bell's inequality for cross correlation of spin currents through distinct conduction channels, we derive an asymptotically exact form of Bell's correlation for the double dot at low bias voltages. We find that pairs of quasiparticles and holes excited by the residual exchange interaction violate Bell's inequality for the spin currents.

We study finite-temperature properties of the Kondo effect in a carbon nanotube (CNT) quantum dot using the Wilson numerical renormalization group (NRG). In the absence of magnetic fields, four degenerate energy levels of the CNT consisting of spin and orbital degrees of freedom give rise to the SU(4) Kondo effect. We revisit the universal scaling behavior of the SU(4) conductance for quarter- and half-filling in a wide temperature range. We find that the filling dependence of the universal scaling behavior at low temperatures $T$ can be explained clearly with an extended Fermi-liquid theory. This theory clarifies that a $T^{2}$ coefficient of conductance becomes zero at quarter-filling whereas the coefficient at half-filling is finite. We also study a field-induced crossover from the SU(4) to SU(2) Kondo state observed at the half-filled CNT dot. The crossover is caused by the matching of the spin and orbital Zeeman splittings, which lock two levels among the four at the Fermi level even in magnetic fields $B$. We find that the conductance shows the SU($4$) scaling behavior at $\mu_{B}B, Comment: 27 pages, 14 figures

We study spin-entanglement of the quasiparticles of the local Fermi liquid excited in nonlinear current through a quantum dot described by the Anderson impurity model with two degenerate orbitals coupled to each other via an exchange interaction. Applying the renormalized perturbation theory, we obtain the precise form of the cumulant generating function and cross-correlations for the currents with spin angled to arbitrary directions, up to third order in the applied bias voltage. It is found that the exchange interaction gives rise to spin-angle dependency in the cross-correlation between the currents through the two different orbitals, and also brings an intrinsic cross-correlation of currents with three different angular momenta.

Universal properties of entangled many-body states are controlled by their symmetry and quantum fluctuations. By magnetic-field tuning of the spin-orbital degeneracy in a Kondo-correlated quantum dot, we have modified quantum fluctuations to directly measure their influence on the many-body properties along the crossover from $SU(4)$ to $SU(2)$ symmetry of the ground state. High-sensitive current noise measurements combined with the non-equilibrium Fermi liquid theory clarify that the Kondo resonance and electron correlations are enhanced as the fluctuations, measured by the Wilson ratio, increase along the symmetry crossover. Our achievement demonstrates that non-linear noise constitutes a measure of quantum fluctuations that can be used to tackle quantum phase transitions., Comment: 5 pages, 4 figures

We study the higher-order Fermi-liquid relations of Kondo systems for arbitrary impurity-electron fillings, extending the many-body quantum theoretical approach of Yamada-Yosida. It includes partly a microscopic clarification of the related achievements based on Nozi\`{e}res' phenomenological description: Filippone, Moca, von Delft, and Mora [Phys.\ Rev.\ B {\bf 95}, 165404 (2017)]. In our formulation, the Fermi-liquid parameters such as the quasi-particle energy, damping, and transport coefficients are related to each other through the total vertex $\Gamma_{\sigma\sigma';\sigma'\sigma} (\omega, \omega'; \omega', \omega)$, which may be regarded as a generalized Landau quasi-particle interaction. We obtain exactly this function up to linear order with respect to the frequencies $\omega$ and $\omega'$ using the anti-symmetry and analytic properties. The coefficients acquire additional contributions of three-body fluctuations away from half-filling through the non-linear susceptibilities. We also apply the formulation to non-equilibrium transport through a quantum dot, and clarify how the zero-bias peak evolves in a magnetic field., Comment: 5 pages, 2 figures, Introduction has been revised

We study the low-energy behavior of the vertex function of a single Anderson impurity away from half-filling for finite magnetic fields, using the Ward identities with careful consideration of the anti-symmetry and analytic properties. The asymptotic form of the vertex function $\Gamma_{\sigma\sigma';\sigma'\sigma}^{}(i\omega,i\omega';i\omega',i\omega)$ is determined up to terms of linear order with respect to the two frequencies $\omega$ and $\omega'$, as well as the $\omega^2$ contribution for anti-parallel spins $\sigma'\neq \sigma$ at $\omega'=0$. From these results, we also obtain a series of the Fermi-liquid relations beyond those of Yamada-Yosida. The $\omega^2$ real part of the self-energy $\Sigma_{\sigma}^{}(i\omega)$ is shown to be expressed in terms of the double derivative $\partial^2\Sigma_{\sigma}^{}(0)/\partial \epsilon_{d\sigma}^{2}$ with respect to the impurity energy level $\epsilon_{d\sigma}^{}$, and agrees with the formula obtained recently by Filippone, Moca, von Delft, and Mora in the Nozi\`{e}res phenomenological Fermi-liquid theory [Phys.\ Rev.\ B {\bf 95}, 165404 (2017)]. We also calculate the $T^2$ correction of the self-energy, and find that the real part can be expressed in terms of the three-body correlation function $\chi_{\uparrow\downarrow,-\sigma}^{[3]} = \partial \chi_{\uparrow\downarrow}/\partial \epsilon_{d,-\sigma}^{}$. We also provide an alternative derivation of the asymptotic form of the vertex function. Specifically, we calculate the skeleton diagrams for the vertex function $\Gamma_{\sigma\sigma;\sigma\sigma}^{}(i\omega,0;0,i\omega)$ for parallel spins up to order $U^4$ in the Coulomb repulsion $U$. It directly clarifies the fact that the analytic components of order $\omega$ vanish as a result of the cancellation of four related Feynman diagrams which are related to each other through the anti-symmetry operation., Comment: 15 figures, 19pages, and supplemental material (15 pages), typo found in (6.15) has been corrected

We theoretically study an emergent SU(2) symmetry which is suggested by recent magneto-transport measurements, carried out near two electrons filling of a carbon nanotube quantum dot. It emerges in the case where the spin and orbital Zeeman splittings cancel each other out for two of the one-particle dot levels among four. Using the Wilson numerical renormalization group, we show that a crossover from the SU(4) to SU(2) Fermi-liquid behavior occurs at two impurity-electrons filling as magnetic field increases. We also find that the quasiparticles are significantly renormalized as the remaining two one-particle levels move away from the Fermi level and are frozen at high magnetic fields. In order to clarify how the ground state evolves during such a crossover, we also reexamine the SU(N) Kondo singlet state for M impurity-electrons filling in the limit of strong exchange interactions. We show that the nondegenerate Fermi-liquid fixed point of Nozi\`{e}es and Blandin can be described as a bosonic Perron-Frobenius vector for M hard-core bosons, each of which consists of one impurity-electron and one conduction hole. This interpretation can also be applied to the Fermi-liquid fixed-point without the SU(N) symmetry., Comment: 20 pages, 10 figures, Sec.III B. has been revised. J.Phys.Soc.Jpn.in press

We describe a formulation to deduce the phase shifts, which determine the ground-state properties of interacting quantum-dot systems with the inversion symmetry, from the fixed-point eigenvalues of the numerical renormalization group (NRG). Our approach does not assume the specific form of the Hamiltonian nor the electron-hole symmetry, and it is applicable to a wide class of quantum impurities connected to noninteracting leads. We apply the method to a triple dot which is described by a three-site Hubbard chain connected to two noninteracting leads, and calculate the dc conductance away from half-filling. The conductance shows the typical Kondo plateaus of Unitary limit in some regions of the gate voltages, at which the total number of electrons N_el in the three dots is odd, i.e., N_el =1, 3 and 5. In contrast, the conductance shows a wide minimum in the gate voltages corresponding to even number of electrons, N_el = 2 and 4. We also discuss the parallel conductance of the triple dot connected transversely to four leads, and show that it can be deduced from the two phase shifts defined in the two-lead case., Comment: 9 pages, 12 figures: Fig. 12 has been added to discuss T_K

We derive an exact expression for the differential conductance for a quantum dot in an arbitrary magnetic field for small bias voltage. The derivation is based on the symmetric Anderson model using renormalized perturbation theory and is valid for all values of the on-site interaction $U$ including the Kondo regime. We calculate the critical magnetic field for the splitting of the Kondo resonance to be seen in the differential conductivity as function of bias voltage. Our calculations for small field show that the peak position of the component resonances in the differential conductance are reduced substantially from estimates using the equilibrium Green's function. We conclude that it is important to take the voltage dependence of the local retarded Green's function into account in interpreting experimental results, Comment: 8 pages, 4 figures; Replaced by a fully revised version with minor corrections in the text

We study the low-energy properties of a Hubbard chain of finite size N_C connected to two noninteracting leads using the numerical renormalization group (NRG) method. The results obtained for N_C = 3 and 4 show that the low-lying eigenstates have one-to-one correspondence with the free quasi-particle excitations of a local Fermi liquid. It enables us to determine the transport coefficients from the fixed-point Hamiltonian. At half-filling, the conductance for even N_C decreases exponentially with increasing U showing a tendency towards the development of a Mott-Hubbard gap. In contrast, for odd N_C, the Fermi-liquid nature of the low-energy states assures perfect transmission through the Kondo resonance. Our formulation to deduce the conductance from the fixed-point energy levels can be applied to various types of interacting systems., Comment: One typo found in Eq.(3) in previous version has been corrected

We show that the low energy behaviour of quite diverse impurity systems can be described by a single renormalized Anderson model, with three parameters, an effective level $\tilde\epsilon_d$, an effective hybridization $\tilde V$, and a quasiparticle interaction $\tilde U$. The renormalized parameters are calculated as a function of the bare parameters for a number of impurity models, including those with coupling to phonons and a Falikov-Kimball interaction term. In the model with a coupling to phonons we determine where the interaction of the quasiparticles changes sign as a function of the electron-phonon coupling. In the model with a Falikov-Kimball interaction we show that to a good approximation the low energy behaviour corresponds to that of a bare Anderson model with a shifted impurity level., Comment: 14 pages, 12 figures; Revised Sec. 2 and 4

Interacting quantum many-body systems constitute a fascinating playground for researchers since they form quantum liquids with correlated ground states and low-lying excitations, which exhibit universal behaviour. In fermionic systems, such quantum liquids are realized in helium-3 liquid, heavy fermion systems, neutron stars and cold gases. Their properties in the linear-response regime have been successfully described by the theory of Fermi liquids. However, non-equilibrium properties beyond this regime have still to be established and remain a key issue of many-body physics. Here, we show a precise experimental demonstration of Landau Fermi-liquid theory extended to the non-equilibrium regime in a 0-D system. Combining transport and ultra-sensitive current noise measurements, we have unambiguously identified the SU(2) and SU(4) symmetries of quantum liquid in a carbon nanotube tuned in the universal Kondo regime. We find that, while the electronic transport is well described by the free quasi-particle picture around equilibrium, a two-particle scattering process due to residual interaction shows up in the non-equilibrium regime. By using the extended Fermi-liquid theory, we obtain the interaction parameter "Wilson ratio" $R=1.9 \pm 0.1$ for SU(2) and $R=1.35 \pm 0.1$ for SU(4) as well as the corresponding effective charges, characterizing the quantum liquid behaviour. This result, in perfect agreement with theory, provides a strong quantitative experimental background for further developments of the many-body physics. Moreover, we discovered a new scaling law for the effective charge, signalling as-yet-unknown universality in the non-equilibrium regime. Our method to address quantum liquids through their non-equilibrium noise paves a new road to tackle the exotic nature of quantum liquids out-of-equilibrium in various physical systems., Comment: accepted for publication in Nature Physics

The Anderson impurity model is studied under a finite bias voltage V applying a microscopic theory of the local Fermi-liquid by Yamada and Yosida to the Keldysh diagrammatic formalism. Using the Ward identities for the nonequilibrium Green's functions, the low-energy behavior of the self-energy has been deduced exactly up to terms of order ω 2 , T 2 and V 2 . The coefficients are defined with respect to the equilibrium ground state, and contain all contributions of the Coulomb interaction U . In this report, we examine the U dependence of the spectral function and differential conductance in the vicinity of the equilibrium by computing the coefficients explicitly with the Bethe ansatz solution in the electron–hole symmetric case.

We study the nonequilibrium Keldysh Green's function for an N-orbital Anderson model at high bias voltages, extending a previous work, which for the case only with the spin degrees of freedom N=2, to arbitrary N. Our approach uses an effective non-Hermitian Hamiltonian that is defined with respect to a Liouville-Fock space in the context of a thermal field theory. The result correctly captures the relaxation processes at high energies, and is asymptotically exact not only in the high-bias limit but also in the high-temperature limit at thermal equilibrium. We also present an explicit continued-fraction representation of the Green's function. It clearly shows that the imaginary part is recursively determined by the decay rate of intermediate states with at most N-1 particle-hole-pair excitations. These high-bias properties follow from the conservations of a generalized charge and current in the Liouville-Fock space. We also examine temperature dependence of the spectral function in equilibrium, comparing the exact results with both the finite-T and infinite-T results of the non-crossing approximation (NCA)., 16 pages, 6 figures, typos have been corrected and DOI has been provided

Transport through small interacting systems connected to noninteracting leads is studied based on the Kubo formalism using a Eliashberg theory of the analytic properties of the vertex part. The transmission probability, by which the conductance is expressed as $g = (2e^2/h) \int d\epsilon (- \partial f / \partial \epsilon) {\cal T}(\epsilon)$, is introduced for interacting electrons. Here $f(\epsilon)$ is the Fermi function, and the transmission probability ${\cal T}(\epsilon)$ is defined in terms of a current vertex or a three-point correlation function. We apply this formulation to a series of Anderson impurities of size N (=1,2,3,4), and calculate ${\cal T}(\epsilon)$ using the order $U^2$ self-energy and current vertex which satisfy a generalized Ward identity. The results show that ${\cal T}(\epsilon)$ has much information about the excitation spectrum: ${\cal T}(\epsilon)$ has two broad peaks of the upper and lower Hubbard bands in addition to N resonant peaks which have direct correspondence with the noninteracting spectrum. The peak structures disappear at high temperatures., Comment: 18 pages, 16 figures

We calculate nonlinear I – V characteristics in the system comprising a tunnel junction and a rectangle barrier to study the quantum interference effect using the lattice Green's function method ba...

The spatial distribution of the nonequilibrium current and charge distributions in a series of two point contacts are studied in the presence of a magnetic field making use of a recursive Green function method based on the Keldysh formalism. Numerical results show that the structure of vortices appearing in between two barriers depends strongly on the applied bias voltage. The chemical potential dependence of the total current is also investigated.

Based on the Quantum Monte Carlo (QMC) technique, we developed a method to calculate the tunneling conductance of the quantum dot systems for which the Kondo effect becomes important. The method computes the conductance directly from the current correlation function, and is applicable to the cases in which the calculation is not reduced to the computation of single particle Green's function. We compare the calculated conductance with experiments, and found good qualitative agreement. The temperature in experiments seems to be not low enough compared with the Kondo temperature in the mid region of the two paired Coulomb oscillation peaks. We studied the Zeeman field effect, and showed that the conductance is strongly suppressed when it has been enhanced by the Kondo effect. The conductance of an Aharonov-Bhom circuit including dots was also studied.

We examine the response of the transport properties to the magnetic field and temperature gradient in the Hubbard model on the kagome lattice within the limit of U → ∞ , using the “retraceable-path” approximation. The layered cobalt oxides, Na x CoO 2 , involve the triangular lattice of the cobalt ions. However, the electron trajectory makes up the kagome lattice due to the orbital degeneracy of t 2 g states. It is shown that this kagome lattice hidden in the CoO 2 layer exhibits the anomalous high-temperature Hall effect recently observed by Wang et al.

We present renormalised perturbation theory calculations for the description of the dynamics of quasiparticles in the Anderson impurity model in magnetic field. Our calculations are compared with NRG spectra and good agreement is found for magnetic fields of the order of the Kondo temperature, when an appropriate perturbation series is chosen. We point out how this approach can be generalised to the non-equilibrium situation, where it is relevant for the description of quantum dots.

The electronic structure of CuGeO 3 in the spin-Peierls (SP) phase with the space group of Bbcm is calculated for the first time within the local-density approximation (LDA) and the LDA + U scheme where the local 3d–3d Coulomb interaction U is introduced on the Cu sites. Although the insulating antiferromagnetic solution is obtained in the LDA, the obtained bandgap of 0.19 eV and a magnetic moment of 0.39 μ B / Cu are much smaller than the experimental bandgap of 3.7 eV and the magnetic moment of 0.7 μ B / Cu , respectively. With the value of U = 6.7 eV determined using an electron spectroscopy, the LDA + U calculation yields a charge-transfer bandgap of 1.63 eV and gives a magnetic moment of 0.72 μ B / Cu . The essential electronic and magnetic properties of CuGeO 3 in the SP phase can be described by means of the LDA + U scheme.

The spatial distribution of the nonequilibrium current in a series of two point contacts under a finite bias voltage is investigated numerically making use of a recursive Green-function method based on the Keldysh formalism. The results of the current distribution show an interesting behavior such as the existence of vortices in between the two barriers. The temperature dependence of the nonlinear current-voltage characteristic is also studied.

A numerical analysis for evaluating the transport coefficient through a small interacting system is examined using the quantum Monte Carlo (QMC) method. To formulate the analysis, we consider a finite interacting system on a one-dimensional lattice that is connected to noninteracting leads, and investigate the expression of the dc conductance making use of the Kubo formula with the perturbation theory in the Coulomb interaction. At $T=0$ the dc conductance is written in terms of the transmission coefficient, which can be obtained numerically by extrapolating the QMC data for the Matsubara Green's function as $i{\ensuremath{\varepsilon}}_{n}\ensuremath{\rightarrow}{i0}^{+}$. We apply the analysis to the dc conductance through a region with a few resonance states.

自動車の排気ガスに含まれる窒素酸化物、硫黄酸化物、粒子状物質は光化学スモッグや酸性雨などを引き起こす大気汚染原因物質であるとともに、人間に健康被害をおよぼす恐れがある。特に二酸化 窒素( nitrogen dioxide : 以下 NO2と記述する)は顕著な健康被害を及ぼすとされている。呼吸によって空気に含まれるNO2が体内に入ると、容易に体内に吸収され、強い酸性を示すため粘膜の刺激、気管支炎、肺水腫などを引き起こす場合がある1)。 そのため、移動発生源である自動車に対してこれらの有害物質を低減させようとする取り組みが古くから実施されてきた。 窒素酸化物には一酸化窒素( nitric oxide:以下NO ) や三酸化二窒素( dinitrogen trioxide:N2O3 )も含まれるので、それら窒素の酸化物の総量に対して自動車排気ガス規制が行われている。窒素の酸化物の総称として窒素酸化物( nitrogen oxide : 以下NOx )と呼ばれることが多い。我が国におけるこのようなNOxの濃度に対する規制の変遷をガソリン乗用車とディーゼル重量貨物車に分けて図1.1(a)と図1.1(b)に示す。これらの図では、濃度規制値が暦年とともにどのように変化してきたかを、規制が始まる以前の濃度に対する削減率で示している。光化学スモッグによる事故への対応に起因した1973年の規制以来、アメリカでのマスキー法の提案を受けて、日本でも1975年、78年に規制強化が行われた。その後も、幾度も規制強化が繰り返されて現在に至っている。現状では、排気ガスに含まれるNOx濃度は規制が行なわれていなかった時期に比べて1 / 100 以下まで低減されている。その一方、ディーゼルエンジンを搭載した重量貨物車に対しては、それを利用した輸送・運搬が我が国の経済を支えているということもあり、1900年代では、ガソリンエンジンを搭載した乗用車に比べてやや緩めの対応になっていたことは否めない。しかし、1999年、「ディーゼル車からの排気ガスには、これほど多くのススが含まれているため、そのような車は都内を走れないようにする」と、ススが詰められたペットボトルを振りかざす都知事の主張に端を発した東京都の「ディーゼルNO(ノー)作戦」以来、ディーゼル自動車への風当たりが強まった。このため、粒子状物質( particulate matter:以下 PM )への対策も組み込まれた「新短期規制」が2003年に実施されることになった。 また、国内全地域でのNO2の環境基準達成は困難であることと、浮遊粒子状物質による健康被害が問題化していることを考慮して、2001年には、「自動車から排出される窒素酸化物及び粒子状物質の特定地域における総量の削減等に関する特別措置法(通称「自動車NOx・粒子状物質法」)」が成立している。この法律によって、首都圏、近畿圏、愛知・三重県などの大都市圏で使用できる車種が制限される厳しい規制が施行された。そして、2008年には「ポスト新長期規制」と呼ばれる世界で一番厳しい規制が実施され、現在に至っている。 「ポスト新長期規制」では、温度・湿度などが管理された実験室内のシャシダイナモメータ上で、都市走行を想定した運転モードに従って評価車両を走らせて、排気ガス中の成分と濃度を測定し、それが規制値を超えないことが新造車販売の条件になっている。この規制によって1台の自動車から排出される大気汚染物質の平均的な量は減少するであろうが、すでに市販、使用されている自動車からの排出量が減るわけではないので、大気汚染状況が急激に改善することはない。規制値は年々厳しくなっているので、旧型車ほど多くの大気汚染物質を排出している可能性がある。特に、整備不良の旧型車からの大気汚染物質を如何に削減するかが重要となろう自動車の車検の際に排気ガスの検査項目もあるが、一酸化炭素と炭化水素の濃度測定のみであり、 NOx の測定は行われない。つまり、新車の時よりも大気汚染物質を極めて多く排出するような自動車であっても車検は通るのである。自動車を使用していると、エンジン内での燃料の爆発燃焼時期などのバランスが次第に崩れて、大気汚染物質の濃度が高くなる可能性もある。この状態になれば整備が必要であり、この状態で道路を走行すれば整備不良車となる。黒煙を吐き出して走行する大型自動車を目にすることからすれば、現実的には、排気ガス濃度が規制値を超える自動車も道路を走行しているものと推測される。 走行中の自動車から排出される大気汚染物質の濃度を測定するための車載型の装置も市販されているが、道路に設置した装置で、自動車を特定しながらその濃度を測定することはできない。この点からすれば、走行中の自動車から排出される大気汚染物質を“その場"測定できる方法の開発が必要と思われる。 自動車や工場などから排出され NOxが高濃度になれば、光化学スモッグが発生したり、各種の健康被害を引き起こすことは明白である。このために、「大気汚染常時監視測定局」と呼ばれる大気汚染状態を常に監視する測定局が地方自治体などによって設置されている。測定局は以下の二つに分類される。一つは「一般環境大気測定局(以下、「一般局」)」であり、一般環境大気の汚染状況を監視する。さらに「自動車排出ガス測定局(以下、「自排局」)」が設けられ、自動車走行による大気汚染が憂慮される交差点、道路及び道路端付近の大気を対象にして汚染状況を監視している。測定局で測定された NO2 濃度の測定値は中央監視局に伝送され、1時間平均値として公表されている。NO2 濃度に関する大気環境基準は、大気汚染防止法に基づき1978年7月11日に告示された。「1時間値の1日平均値が 0.04 ppm から 0.06 ppm までのゾーン内又はそれ以下であること」と設定されている。この基準を満足しているかどうかを判断するために、上述の測定局において NO2 濃度が測定されている。 これらのように、道路近くの多くの地点でNO2 濃度などが測定され、公表されているが、その値は1時間平均値であり、大気汚染物質の濃度が急増しても早急な対応はできない。また、大量に排出する整備不良車の特定もできない。これらのことからも、大気汚染状況の常時監視、そして大気汚染物質の“その場"測定が必要と考えられる。

We describe some exact high-energy properties of a single Anderson impurity connected to two noninteracting leads in a nonequilibrium steady state. In the limit of high bias voltages, and also in the high-temperature limit at thermal equilibrium, the model can be mapped on to an effective non-Hermitian Hamiltonian consisting of two sites, which correspond to the original impurity and its image that is defined in a doubled Hilbert space referred to as Liouville-Fock space. For this, we provide a heuristic derivation using a path-integral representation of the Keldysh contour and the thermal field theory, in which the time evolution along the backward contour is replicated by extra degrees of freedom corresponding to the image. We find that the effective Hamiltonian can also be expressed in terms of charges and currents. From this, it can be deduced that the dynamic susceptibilities for the charges and the current fluctuations become independent of the Coulomb repulsion U in the high bias limit. Furthermore, the equation of motions for the Green's function and two other higher-order correlation functions constitute a closed system. The exact solution obtained from the three coupled equations extends the atomic-limit solution such that the self-energy correctly captures the imaginary part caused by the relaxation processes at high energies. The spectral weights of the upper and lower Hubbard levels depend sensitively on the asymmetry in the tunneling couplings to the left and right leads., Comment: 12 pages, 5 figures, typos have been corrected

We study the superconducting (SC) states with d x 2 - y 2 and extended s symmetry in the three-band Hubbard model on a CuO 2 plane using the variational Monte Carlo method in the limit U d →∞, where U d is the Coulomb repulsion between holes on a Cu site. By comparing the energy among the SC, paramagnetic (PM), and antiferromagnetic (AFM) states, we obtain a phase diagram and find that the d x 2 - y 2 -wave SC state becomes the lowest energy state near the phase boundary between the PM and AFM phases. In contrast to the d x 2 - y 2 -wave SC state, the energy of the extended s -wave SC state is always higher than that of the AFM state.

Low-energy properties of an SU(N) Anderson model are studied, using the \(1/(N - 1)\) expansion based on a perturbation theory in the Coulomb interaction U. This approach is different from conventional large N theories, such as from the usual 1 ∕ N expansion and the non-crossing approximation based on the expansion in the hybridization matrix element between the impurity orbital and conduction band. In our approach the scaling factor N − 1 appears as the total number of interacting orbitals excluding the one prohibited by the Pauli principle, and it captures the low-energy local Fermi-liquid behavior correctly. We find that the next-leading-order results of the renormalized parameters agree closely with the numerical renormalization group results in a wide range of electron fillings at N = 4, where the degeneracy is still not so large. This ensures the reliability of the next-leading order results for N > 4. Furthermore, we apply this approach to nonequilibrium current through a quantum dot in the Kondo regime.

In the Van Vleck metals such as Pr, an indirect interaction arises between the conduction electrons through the virtual excitation of the crystal-field singlet ground state. By solving the Eliashberg equations, it is shown that this effective interaction can bring about superconductivity in a way similar to the spin-fluctuation-mediated pairing due to the repulsive short-range interaction. For the free-electron band the triplet {ital p}-wave pairing is formed. Spin degeneracy of the triplet states is lifted by the crystal-field anisotropy to choose the highest {ital T}{sub {ital c}}. The retardation effect brought by the effective interaction and the depairing effects due to the scattering of the conduction electrons by the crystal-field states are analyzed in detail. Of all these effects, it is the mass renormalization effect that strongly depresses {ital T}{sub {ital c}}.

The effect of on-site Coulomb repulsion on the process of resonant tunneling through a small interacting region is studied in the presence of a magnetic field by using the recursive Green's function method within a mean field approximation. The conductance is calculated as a function of the chemical potential µ making use of the Kubo formula, and calculations are performed for single- and double-mode quasi-one-dimensional quantum wires. In a magnetic field, some resonance levels close each other to form a single Landau level, so that the electron correlation in the small region is enhanced, and the µ-dependence of the conductance is changed by rather small value of the Coulomb repulsion. For the double-mode wire a collinear-type electronic state, in which spins in the small region are aligned antiferromagnetically in the x -direction and ferromagnetically in the y -direction, is found to be stable over a wide range of the chemical potential.

Effects of Coulomb repulsion on the process of resonant tunneling through a single quantum level are studied by applying the quantum Monte Carlo method and the maximum-entropy method to the Wolf model on a one-dimensional chain. In the calculated spectral function there is a sharp Kondo peak near the chemical potential \ensuremath{\mu}, which contributes to the resonance tunneling. Correspondingly, the conductance calculated by using the Friedel sum rule shows the expected transparency, i.e., the transmission probability is almost unity when \ensuremath{\mu} is in the range ${\mathrm{\ensuremath{\epsilon}}}_{0}$${\mathrm{\ensuremath{\epsilon}}}_{0}$+U, where ${\mathrm{\ensuremath{\epsilon}}}_{0}$ is the on-site energy of the single quantum level and U is the Coulomb repulsion.

We study the antiferromagnetic (AFM) state in the three-band Hubbard model on the CuO 2 plane by using the variational Monte Carlo method (VMC) and the Gutzwiller approximation (GA). Near half-filling, the VMC energy is significantly reduced in the AFM state, and is much lower than the GA energy. By comparing the energy of the paramagnetic state with that of the AFM state, the phase diagram is determined as a function of the hole concentration and the charge-transfer energy. The AFM state is stable against doping in a wide range, and this tendency is more pronounced in the hole-doped case than that in the electron-doped case. We also study effects of the direct OO hopping, and find that the direct hopping suppresses the AFM phase especially in the hole-doped case.

We study non-equilibrium current fluctuations through a quantum dot, which includes a ferromagnetic Hund's rule coupling $J$, in the low-energy Fermi liquid regime using the renormalized perturbation theory. The resulting cumulant for the current distribution in the particle-hole symmetric case, shows that spin-triplet and spin-singlet pairs of quasiparticles are formed in the current due to the Hund's rule coupling and these pairs enhance the current fluctuations. In the fully screened higher-spin Kondo limit, the Fano factor takes a value $F_b = (9M+6)/ (5M+4)$ determined by the orbital degeneracy $M$. We also investigate crossover between the small and large $J$ limits in the two-orbital case M=2, using the numerical renormalization group approach., Comment: 5 pages, 3 figures

We study the Kondo effect in side-coupled double quantum dots with particular focus on the crossover between two distinct singlet ground states, using the numerical renormalization group. The crossover occurs as the quantized energy level of the embedded dot, which is connected directly to the leads, is varied. In the parameter region where the embedded dot becomes almost empty or doubly occupied, the local moment emerging in the other dot at the side of the path for the current is screened via a superexchange process by the conduction electrons tunneling through the embedded dot. In contrast, in the other region where the embedded dot is occupied by a single electron, the local moment emerges also in the embedded dot, and forms a singlet bond with the moment in the side dot. Furthermore, we derive two different Kondo Hamiltonians for these limits carrying out the Schrieffer-Wolff transformation, and show that they describe the essential feature of the screening for each case., 9 pages, 9 figures

We apply recently developed 1/(N-1) expansion to a particle-hole asymmetric SU(N) Anderson model with finite Coulomb interaction U. To leading order in 1/(N-1) it describes the Hartree-Fock random phase approximation (HF-RPA), and the higher-order corrections describe systematically the fluctuations beyond the HF-RPA. We show that the next-leading order results of the renormalized parameters for the local Fermi-liquid state agree closely with the numerical renormalization group results at N=4. It ensures the reliability of the next-leading order results for N>4, and we examine the N dependence of the local Fermi-liquid parameters. Our expansion scheme uses the standard Feynman diagrams, and has wide potential applications.

We study low-energy transport through a quantum dot coupled to one normal and two superconducting (SC) leads in a junction of Y-shape. In this geometry a crossover between Kondo dominated and Cooper-pairing dominated states occurs by tuning the parameters such as the quantized energy level of the dot and the Josephson phase, which induces a supercurrent flowing between the two SC leads through the dot. Furthermore, Andreev scattering takes place at the interface between the dot and normal lead. The low-lying energy states of this system can be described by a local Fermi-liquid theory for interacting Bogoliubov particles. In a description based on an Anderson impurity model we calculate transport coefficients, renormalized parameters and spectral function, using Wilson's numerical renormalization group (NRG) approach, in the limit of large SC gap. Our results demonstrate how the Andreev resonance level approaches the Fermi level in the crossover region between Cooper-pairing singlet state and strong coupling situation as the impurity level or Josephson phase are varied. The strong coupling situation shows a Kondo effect with a significantly renormalized resonance width. The crossover is smeared when the coupling between the dot and normal lead is large. Furthermore, asymmetry in the Josephson junction suppresses the cancellations of the SC proximity for finite Josephson phase, and it favors the SC singlet state rather than the Kondo singlet., Comment: 12 pages, 11 figures, some brief explanations are added

We apply a recently developed 1/(N-1) expansion to the full counting statistics for the N-fold degenerate Anderson impurity model in the Kondo regime. This approach is based on the perturbation theory in the Coulomb interaction U and is different from the conventional large N theories, such as the usual 1/N expansion and non-crossing approximation. We have confirmed that the calculations carried out up to order 1/(N-1)^2 agree closely with those of the numerical renormalization group at N=4, where the degeneracy is still not so large. This ensures the applicability of our approach for N>4. We present the results of the cumulants of the probability distribution function for a nonequilibrium current through a quantum dot in the particle-hole symmetric case., 4 pages, 6 figures, typos have been corrected