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J. Suzuki

Publications and source records attributed to J. Suzuki.

54 records · Page 3Linked to original sources
arXiv2000

Stokes Multipliers, Spectral Determinants and T-Q relations

Recently, a remarkable correspondence has been unveiled between a certain class of ordinary linear differential equations (ODE) and integrable models. In the first part of the report, we survey the results concerning the 2nd order differential equations, the Schroedinger equation with a polynomial potential. We will observe that fundamental objects in the study of the solvable models, e.g., Baxter's Q- operator, fusion transfer matrices come into play in the analyses on ODE. The second part of the talk is devoted to the generalization to higher order linear differential equations. The correspondence found in the case of the 2nd order ODE is naturally lifted up. We also mention a connection to the discrete soliton theory.

nlin.SI↗
arXiv2000

Functional relations in Stokes multipliers - Fun with $x^6 + αx^2$ potential-

We consider eigenvalue problems in quantum mechanics in one dimension. Hamiltonians contain a class of double well potential terms, x^6 + αx^2, for example . The space coordinate is continued to a complex plane and the connection problem of fundamental system of solutions is considered. A hidden U_q(\hat{gl}(2|1)) structure arises in "fusion relations" of Stokes multipliers. With this observation, we derive coupled nonlinear integral equations which characterize the spectral properties of both \pm αpotentials simultaneously. equations.

quant-ph↗
arXiv2000

Precise Measurement of Cosmic-Ray Proton and Helium Spectra with the BESS Spectrometer

We report cosmic-ray proton and helium spectra in energy ranges of 1 to 120 GeV and 1 to 54 GeV/nucleon, respectively, measured by a balloon flight of the BESS spectrometer in 1998. The magnetic-rigidity of the cosmic-rays was reliably determined by highly precise measurement of the circular track in a uniform solenoidal magnetic field of 1 Tesla. Those spectra were determined within overall uncertainties of +-5 % for protons and +- 10 % for helium nuclei including statistical and systematic errors.

astro-ph↗
arXiv1999

Hidden E type structures in dilute A models

The hidden E_{7} (E_{6}) structure has been conjectured for the minimal model ${\cal M}_{4,5} ({\cal M}_{6,7}$) perturbed by $Φ_{1,2}$ in the context of conformal field theory(CFT). Motivated by this, we examine the dilute A_{4, 6} models, which are expected to be corresponding lattice models. Thermodynamics of the equivalent one dimensional quantum systems is analyzed via the quantum transfer matrix approach. Appropriate auxiliary functions, related to kinks in the theory, play a role in constructing functional relations among transfer matrices. We successfully recover the universal Y- systems and thereby Thermodynamic Bethe Ansatz equations for E_{6,7} from the dilute A_{6,4} model, respectively.

hep-th↗
arXiv1999

Precision Measurement of Cosmic-Ray Antiproton Spectrum

The energy spectrum of cosmic-ray antiprotons has been measured in the range 0.18 to 3.56 GeV, based on 458 antiprotons collected by BESS in recent solar-minimum period. We have detected for the first time a distinctive peak at 2 GeV of antiprotons originating from cosmic-ray interactions with the interstellar gas. The peak spectrum is reproduced by theoretical calculations, implying that the propagation models are basically correct and that different cosmic-ray species undergo a universal propagation. Future BESS flights toward the solar maximum will help us to study the solar modulation and the propagation in detail and to search for primary antiproton components.

astro-ph↗
arXiv1999

Spinons in Magnetic Chains of Arbitrary Spins at Finite Temperatures

The thermodynamics of solvable isotropic chains with arbitrary spins is addressed by the recently developed quantum transfer matrix (QTM) approach. The set of nonlinear equations which exactly characterize the free energy is derived by respecting the physical excitations at T=0, spinons and RSOS kinks. We argue the implication of the present formulation to spinon character formula of level k=2S SU(2) WZWN model .

cond-mat.stat-mech↗
arXiv1998

Measurement of Low-Energy Cosmic-Ray Antiprotons at Solar Minimum

The absolute fluxes of the cosmic-ray antiprotons at solar minimum are measured in the energy range 0.18 to 1.4 GeV, based on 43 events unambiguously detected in BESS '95 data. The resultant energy spectrum appears to be flat below 1 GeV, compatible with a possible admixture of primary antiproton component with a soft energy spectrum, while the possibility of secondary antiprotons alone explaining the data cannot be excluded with the present accuracy. Further improvement of statistical accuracy and extension of the energy range are planned in future BESS flights.

astro-ph↗
arXiv1998

Quantum Jacobi-Trudi Formula and $E_8$ Structure in the Ising Model in a Field

We investigate a 1D quantum system associated with the Ising model in a field(the dilute $A_3$ model) by the recently developed quantum transfer matrix (QTM) approach. A closed set of functional relations is found among variants of fusion QTMs which are characterized by skew Young tableaux. These relations are proved by using a quantum analogue of Jacobi-Trudi formula, together with special features at "root of unity" . The numerical analysis on their eigenvalues shows a remarkable coincidence with exponents characteristic to $E_8$. From these findings, we have successfully recovered the $E_8$ Thermodynamic Bethe ansatz equation by Bazhanov et al, however, without specific choice of strings solutions.

cond-mat.stat-mech↗
arXiv1998

Characters for $\hat{sl(n)}_{k=1}$ from a novel Thermodynamic Bethe Ansatz

Motivated by the recent development on the exact thermodynamics of 1D quantum systems, we propose quasi-particle like formulas for $\hat{\mathfrak{sl}(n)}_{k=1}$ characters. The $\hat{\mathfrak{sl}(2)}_{k=1}$ case is re-examined first. The novel formulation yields a direct connection to the fractional statistics in the short range interacting model, and provides a clear description of the spinon character formula. Generalizing the observation, we find formulas for $\hat{\mathfrak{sl}(n)}_{k=1}$, which can be proved by the Durfee rectangle formula.

cond-mat.stat-mech↗
arXiv1997

The Hubbard chain at finite temperatures: ab initio calculations of Tomonaga-Luttinger liquid properties

We present a novel treatment of finite temperature properties of the one-dimensional Hubbard model. Our approach is based on a Trotter-Suzuki mapping utilizing Shastry's classical model and a subsequent investigation of the quantum transfer matrix. We derive non-linear integral equations for three auxiliary functions which have a clear physical interpretation of elementary excitations of spin type and charge excitations in lower and upper Hubbard bands. This allows for a transparent analytical study of certain limiting cases as well as for precise numerical investigations. We present data for the specific heat, magnetic and charge susceptibilities for various particle densities and coupling strengths U. The structure exposed by these curves is discussed in terms of the elementary charge and spin excitations. Special emphasis is placed on the study of the low-temperature behavior within our ab initio approach confirming the scaling predictions by Tomonaga-Luttinger liquid theory. In addition we make contact with the ``dressed energy'' formalism established for the analysis of ground state properties.

cond-mat.str-el↗
arXiv1997

A New Limit on the Flux of Cosmic Antihelium

A very sensitive search for cosmic-ray antihelium was performed using data obtained from three scientific flights of BESS magnetic rigidity spectrometer. We have not observed any antihelium; this places a model-independent upper limit (95 % C.L.) on the antihelium flux of 6*10**(-4) m**(-2)sr**(-1)s**(-1) at the top of the atmosphere in the rigidity region 1 to 16 GV, after correcting for the estimated interaction loss of antihelium in the air and in the instrument. The corresponding upper limit on the Hebar/He flux ratio is 3.1*10**(-6), 30 times more stringent than the limits obtained in similar rigidity regions with magnetic spectrometers previous to BESS.

astro-ph↗
arXiv1997

From Fusion Hierarchy to Excited State TBA

Functional relations among the fusion hierarchy of quantum transfer matrices give a novel derivation of the TBA equations, namely without string hypothesis. This is demonstrated for two important models of 1D highly correlated electron systems, the supersymmetric $t-J$ model and the supersymmetric extended Hubbard model. As a consequence, "the excited state TBA" equations, which characterize correlation lengths, are explicitly derived for the $t-J$ model. To the authors' knowledge, this is the first explicit derivation of excited state TBA equations for 1D lattice electron systems.

hep-th↗
arXiv1996

Exact thermodynamics and Luttinger liquid properties of the integrable t-J model

A Trotter-Suzuki mapping is used to calculate the finite-temperature properties of the one-dimensional supersymmetric $t-J$ model. This approach allows for the exact calculation of various thermodynamical properties by means of the quantum transfer matrix (QTM). The free energy and other interesting quantities are obtained such as the specific heat and compressibility. For the largest eigenvalue of the QTM leading to the free energy a set of just two non-linear integral equations is presented. These equations are studied analytically and numerically for different particle densities and temperatures. The structure of the specific heat is discussed in terms of the elementary charge as well as spin excitations. Special emphasis is placed on the study of the low-temperature behavior confirming scaling predictions by conformal field theory and Luttinger liquid theory. To our knowledge this is the first complete investigation of a strongly correlated electron system on a lattice at finite temperature.

cond-mat.str-el↗
arXiv1994

Exact Results for Hamiltonian Walks from the Solution of the Fully Packed Loop Model on the Honeycomb Lattice

We derive the nested Bethe Ansatz solution of the fully packed O($n$) loop model on the honeycomb lattice. From this solution we derive the bulk free energy per site along with the central charge and geometric scaling dimensions describing the critical behaviour. In the $n=0$ limit we obtain the exact compact exponents $γ=1$ and $ν=1/2$ for Hamiltonian walks, along with the exact value $κ^2 = 3 \sqrt 3 /4$ for the connective constant (entropy). Although having sets of scaling dimensions in common, our results indicate that Hamiltonian walks on the honeycomb and Manhattan lattices lie in different universality classes.

cond-mat↗
arXiv1994

Functional Relations in Solvable Lattice Models I: Functional Relations and Representation Theory

We study a system of functional relations among a commuting family of row-to-row transfer matrices in solvable lattice models. The role of exact sequences of the finite dimensional quantum group modules is clarified. We find a curious phenomenon that the solutions of those functional relations also solve the so-called thermodynamic Bethe ansatz equations in the high temperature limit for $sl(r+1)$ models. Based on this observation, we propose possible functional relations for models associated with all the simple Lie algebras. We show that these functional relations certainly fulfill strong constraints coming from the fusion procedure analysis. The application to the calculations of physical quantities will be presented in the subsequent publication.

hep-th↗