Papers by Akinori Nishino
27aBG-7 並列二重量子ドットの同時占有率 : 多電子散乱状態による解析(27aBG 電子系(第一原理計算・非平衡系・電子相関),領域11(統計力学,物性基礎論,応用数学,力学,流体物理))
Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2012
Ising-like spectrum of the superintegrable chiral Potts model through the L(sl_2) symmetry of an XXZ-type spin chain(Fundamental Problems and Applications of Quantum Field Theory)
素粒子論研究, Apr 20, 2006
Exact scattering eigenstates in double quantum-dot systems with an interdot Coulomb interaction
Journal of Physics: Conference Series, 2016
We study a double quantum-dot system which consists of two leads of noninteracting electrons and ... more We study a double quantum-dot system which consists of two leads of noninteracting electrons and two quantum dots with an interdot Coulomb interaction. We assume spinless electrons and consider arbitrary complex values of all lead-dot couplings and an interdot coupling. We construct exact many-electron scattering eigenstates whose incident states are free-electronic plane waves in the leads. Due to the interaction, some of the incident plane waves are scattered to two-body and three-body bound states. The binding strength of the many-body bound states is affected by the arrangement of the two quantum dots, by which we observe an interplay of the Coulomb interaction and quantum interference. We can understand the many-body bound states in terms of many-body resonances.
We study the correspondence between the Ising-like spectra of superintegrable N-state chiral Pott... more We study the correspondence between the Ising-like spectra of superintegrable N-state chiral Potts (SCP) model [1,2] and the energy degenerate subspaces of XXZ-type spin chain, called nilpotent Bazhanov-Stroganov (NBS) model [3], whose transfer matrix commutes with the SCP transfer matrix. We show that, if the number of sites is a multiple of N, the NBS model has a loop algebra
Journal of Statistical Physics, 2001
We study in an algebraic manner the symmetric basis of the Calogero model and the non-symmetric b... more We study in an algebraic manner the symmetric basis of the Calogero model and the non-symmetric basis of the corresponding Calogero model with distinguishable particles. The Rodrigues formulas are presented for the polynomial parts of both bases. The square norm of the non-symmetric basis is evaluated. Symmetrization of the non-symmetric basis reproduces the symmetric basis and enables us to calculate
Integrability of the Calogero Model: Conserved Quantities, the Classical General Solution and the Quantum Orthogonal Basis
Integrable Quantum Field Theories and Their Applications, 2001
The Lax formulation and the projection method, which provide a construction of involutive conserv... more The Lax formulation and the projection method, which provide a construction of involutive conserved quantities and the general solution for the initial value problem of the classical Calogero model, is reviewed. Through the Dunkl-Cherednik operator formulation, we present a construction of the set of commutative conserved operators for the quantum Calogero model. Further, we study in an algebraic manner the
Nuclear Physics B, 2004
For the one-dimensional Hubbard model with Aharonov-Bohm-type magnetic flux, we study the relatio... more For the one-dimensional Hubbard model with Aharonov-Bohm-type magnetic flux, we study the relation between its symmetry and the number of Bethe states. First we show the existence of solutions for Lieb-Wu equations with an arbitrary number of up-spins and one down-spin, and exactly count the number of the Bethe states. The results are consistent with Takahashi's string hypothesis if the system has the so(4) symmetry. With the Aharonov-Bohm-type magnetic flux, however, the number of Bethe states increases and the standard string hypothesis does not hold. In fact, the so(4) symmetry reduces to the direct sum of charge-u(1) and spin-sl(2) symmetry through the change of ABflux strength. Next, extending Kirillov's approach [12, 13], we derive two combinatorial formulas from the relation among the characters of so(4)-or u(1) ⊕ sl(2) -modules. One formula reproduces Essler-Korepin-Schoutens' combinatorial formula for counting the number of Bethe states in the so(4)-case. From the exact analysis of the Lieb-Wu equations, we find that another formula corresponds to the spin-sl(2) case.
Nuclear Physics B, 1999
In terms of the raising and lowering operators, we algebraically construct the non-symmetric Macd... more In terms of the raising and lowering operators, we algebraically construct the non-symmetric Macdonald polynomials which are simultaneous eigenfunctions of the commuting Cherednik operators. We also calculate Cherednik's scalar product of them.
Physical Review B, 2003
Motivated by Heilmann and Lieb's work , we discuss energy level crossings for the one-dimensional... more Motivated by Heilmann and Lieb's work , we discuss energy level crossings for the one-dimensional Hubbard model through the Bethe ansatz, constructing explicitly the degenerate eigenstates at the crossing points. After showing the existence of solutions for the Lieb-Wu equations with one-down spin, we solve them numerically and construct Bethe ansatz eigenstates. We thus verify all the level crossings in the spectral flows observed by the numerical diagonalization method with one down-spin. For each of the solutions we obtain its energy spectral flow along the interaction parameter U . Then, we observe that some of the energy level crossings can not be explained in terms of Uindependent symmetries. Dynamical symmetries of the Hubbard model are fundamental for identifying each of the spectral lines at the level crossing points. We show that the Bethe ansatz eigenstates which degenerate at the points have distinct sets of eigenvalues of the higher conserved operators. We also show a twofold permanent degeneracy in terms of the Bethe ansatz wavefunction.
Physical Review B, 2011
Through an extension of the Landauer formula, we study the electron transport in an open quantum ... more Through an extension of the Landauer formula, we study the electron transport in an open quantum dot system under a finite bias voltage. The system that we study is an interacting resonant-level model equipped with infinite two leads of a linearized dispersion relation. We explicitly construct many-electron scattering eigenstates whose incident states are free-fermionic. A remarkable feature of the scattering state is the appearance of many-body bound states after the scattering. Extending Landauer's idea, we calculate the average electric current flowing through the quantum dot. We use a renormalization-group technique to deal with the divergences that appear in the limit of the large bandwidth of the leads. As a result, the average electric current is brought to a universal form.
Physical Review B, 2015
We study the electron transport in open quantum-dot systems described by the interacting resonant... more We study the electron transport in open quantum-dot systems described by the interacting resonant-level models with Coulomb interactions. We consider the situation in which the quantum dot is connected to the left and right leads asymmetrically. We exactly construct many-electron scattering eigenstates for the two-lead system, where two-body bound states appear as a consequence of one-body resonances and the Coulomb interactions. By using an extension of the Landauer formula, we calculate the average electric current for the system under bias voltages in the first order of the interaction parameters. Through a renormalization-group technique, we arrive at the universal electric current, where we observe the suppression of the electric current for large bias voltages, i.e., negative differential conductance. We find that the suppressed electric current is restored by the asymmetry of the system parameters.
Studies in Applied Mathematics, 2002
We study the Macdonald polynomials that give eigenstates of some quantum many-body system with lo... more We study the Macdonald polynomials that give eigenstates of some quantum many-body system with long-range interactions. Scalar products of the nonsymmetric Macdonald polynomials are algebraically evaluated through their Rodrigues-type formulas. We present a new proof of Macdonald's inner product identities without recourse to the shift operators; that is, we calculate square norms of the Macdonald polynomials through Weyl-symmetrization of those of the nonsymmetric Macdonald polynomials.
Physics Letters A, 2006
The loop algebra L(sl 2 ) symmetry is found in a sector of the nilpotent Bazhanov-Stroganov model... more The loop algebra L(sl 2 ) symmetry is found in a sector of the nilpotent Bazhanov-Stroganov model. The Drinfeld polynomial of a L(sl 2 )-degenerate eigenspace of the model is equivalent to the polynomial which characterizes a subspace with the Isinglike spectrum of the superintegrable chiral Potts model.
Physics Letters A, 1998
We demonstrate an algebraic construction of all the simultaneous eigenfunctions of the conserved ... more We demonstrate an algebraic construction of all the simultaneous eigenfunctions of the conserved operators for distinguishable particles governed by the Calogero Hamiltonian. Our construction is completely parallel to the construction of the Fock space for decoupled quantum harmonic oscillators. The simultaneous eigenfunction does not coincide with the non-symmetric Hi-Jack polynomial, which shows that the conserved operators derived from the number operators of the decoupled quantum harmonic oscillators are algebraically different from the known ones derived by the Dunkl operator formulation.
Physical Review Letters, 2009
We obtain an exact many-body scattering eigenstate in an open quantum dot system. The scattering ... more We obtain an exact many-body scattering eigenstate in an open quantum dot system. The scattering state is not in the form of the Bethe eigenstate in the sense that the wave-number set of the incoming plane wave is not conserved during the scattering and many-body bound states appear. By using the scattering state, we study the average nonequilibrium current through the quantum dot under a finite bias voltage. The current-voltage characteristics that we obtained by taking the two-body bound state into account is qualitatively similar to several known results.
Nuclear Physics B, 2000
The non-symmetric Macdonald-Koornwinder polynomials are joint eigenfunctions of the commuting Che... more The non-symmetric Macdonald-Koornwinder polynomials are joint eigenfunctions of the commuting Cherednik operators which are constructed from the representation theory for the affine Hecke algebra corresponding to the BC -type root system. We present the Rodrigues N formula for the non-symmetric Macdonald-Koornwinder polynomials. The raising operators are derived from the realizations of the corresponding double affine Hecke algebra. In the quasiclassical limit, the above theory reduces to that of the BC -type Sutherland model which describes N many particles with inverse-square long-range interactions on a circle with one impurity. We also present the Rodrigues formula for the non-symmetric Jacobi polynomials of type BC which are N eigenstates of the BC -type Sutherland model.
Fock Spaces for the Calogero Models with Distinguishable Particles
Journal of the Physical Society of Japan, 1998
We present the creation, annihilation and number operators for theAN-1- and BN-Calogero models wi... more We present the creation, annihilation and number operators for theAN-1- and BN-Calogero models with distinguishable particles.In a parallel way to the construction of the Fock space of the quantumharmonic oscillators, we construct the Fock spaces as the simultaneouseigenfunctions of the number operators for the Calogero models.Relationships between the Fock spaces and the knownnonsymmetric orthogonal bases, which are spanned by the
Journal of the Physical Society of Japan, 2007
An open quantum system consisting of a quantum dot with a Coulomb interaction and two leads witho... more An open quantum system consisting of a quantum dot with a Coulomb interaction and two leads without interactions is studied. The many-body scattering states are constructed with the Bethe-ansatz approach. The expectation value of the electric current is exactly calculated for the scattering states to observe resonance peaks due to many-body scattering.
Journal of the Physical Society of Japan, 1999
Applying a method developed by Takamura and Takano for the nonsymmetric Jack polynomial, we prese... more Applying a method developed by Takamura and Takano for the nonsymmetric Jack polynomial, we present the Rodrigues formula for the nonsymmetric multivariable Hermite polynomial.
Rodrigues Formula for the Nonsymmetric Macdonald Polynomial
Journal of the Physical Society of Japan, 1999
Through the q-deformation of the method developed by Takamura and Takano for the nonsymmetric Jac... more Through the q-deformation of the method developed by Takamura and Takano for the nonsymmetric Jack polynomials, we present the Rodrigues formula for the nonsymmetric Macdonald polynomials.
Uploads
Papers by Akinori Nishino