arXiv subjects

Yasuhiro Hieida

Publications and source records attributed to Yasuhiro Hieida.

17 recordsLinked to original sources

arXiv2018

Study on Origins of Reverse Lane Usage using Nagel-Schreckenberg Model

On highways with two lanes, cars are requested to run on the slow lane and are allowed to run on the fast lane for overtaking. However, on real two-lane highways, we daily observe a phenomenon called "reverse lane usage", in which the flow on the fast lane exceeds that on the slow lane. The origins of the phenomenon have not been discussed clearly. In this paper, we study a two-lane extension of the Nagel-Schreckenberg model. We employ two types of lane-changing rules: a German and a Japanese type. The German type suppresses overtaking slow cars on the fast lane through the slow lane. The Japanese type, on the contrary, allows overtaking through both lanes. If two lanes allow the same maximum speed, the suppression of overtaking through the slow lane is the key for the reverse lane usage. If the maximum speed on the fast lane is faster than that on the slow lane, the reverse lane usage is observed in the Japanese type. The effects of stochasticity in lane changing, and mixing trucks and passenger cars are also discussed.

physics.soc-ph↗

arXiv2013

Fluctuation in e-mail sizes weakens power-law correlations in e-mail flow

Power-law correlations have been observed in packet flow over the Internet. The possible origin of these correlations includes demand for Internet services. We observe the demand for e-mail services in an organization, and analyze correlations in the flow and the sequence of send requests using a Detrended Fluctuation Analysis (DFA). The correlation in the flow is found to be weaker than that in the send requests. Four types of artificial flow are constructed to investigate the effects of fluctuations in e-mail sizes. As a result, we find that the correlation in the flow originates from that in the sequence of send requests. The strength of the power-law correlation decreases as a function of the ratio of the standard deviation of e-mail sizes to their average.

physics.soc-ph↗

arXiv2011

A systematic way to find and construct exact finite dimensional matrix product stationary states

We explain how to construct matrix product stationary states which are composed of finite-dimensional matrices. Our construction explained in this article was first presented in a part of [Hieida and Sasamoto:J. Phys. A: Math. Gen. 37 (2004) 9873] for general models. In this article, we give more details on the treatment than in the above-mentioned reference, for one-dimensional asymmetric simple exclusion process(ASEP).

cond-mat.stat-mech↗

arXiv2006

Least Action Principle for the Real-Time Density Matrix Renormalization Group

A kind of least action principle is introduced for the discrete time evolution of one-dimensional quantum lattice models. Based on this principle, we obtain an optimal condition for the matrix product states on succeeding time slices generated by the real-time density matrix renormalization group method. This optimization can also be applied to classical simulations of quantum circuits. We discuss the time reversal symmetry in the fully optimized MPS.

cond-mat.stat-mech↗

arXiv2006

Effects of Bottlenecks on Vehicle Traffic

Traffic congestion is usually observed at the upper streams of bottlenecks such as tunnels. Congestion appears as stop-and-go waves and high density uniform flow. We perform simulations of traffic flow with a bottleneck using the coupled map optimal velocity model. The bottleneck is expressed as a road segment with speed reduction. The speed reduction in the bottleneck controls the emergence of stop-and-go waves. A phenomenological theory of bottleneck effects is constructed.

physics.soc-ph↗

arXiv2005

Product Wave Function Renormalization Group: construction from the matrix product point of view

We present a construction of a matrix product state (MPS) that approximates the largest-eigenvalue eigenvector of a transfer matrix T, for the purpose of rapidly performing the infinite system density matrix renormalization group (DMRG) method applied to two-dimensional classical lattice models. We use the fact that the largest-eigenvalue eigenvector of T can be approximated by a state vector created from the upper or lower half of a finite size cluster. Decomposition of the obtained state vector into the MPS gives a way of extending the MPS, at the system size increment process in the infinite system DMRG algorithm. As a result, we successfully give the physical interpretation of the product wave function renormalization group (PWFRG) method, and obtain its appropriate initial condition.

cond-mat.stat-mech↗

arXiv2004

Construction of a matrix product stationary state from solutions of finite size system

Stationary states of stochastic models, which have $N$ states per site, in matrix product form are considered. First we give a necessary condition for the existence of a finite $M$-dimensional matrix product state for any ${N,M}$. Second, we give a method to construct the matrices from the stationary states of small size system when the above condition and $N\le M$ are satisfied. Third, the method by which one can check that the obtained matrices are valid for any system size is presented for the case where $M=N$ is satisfied. The application of our methods is explained using three examples: the asymmetric exclusion process, a model studied in [F. H. Jafarpour: J. Phys. A: Math. Gen. 36 (2003) 7497] and a hybrid of both of the models.

cond-mat.stat-mech↗

arXiv2001

Anisotropic Antiferromagnetic Spin Chains in a Transverse Field: Reentrant Behavior of the Staggered Magnetization

We investigate one-dimensional S=1/2 and S=1 antiferromagnetic quantum spin chains with easy-axis anisotropies in a transverse field. We calculate both the uniform magnetization and the staggered magnetization, using a variant of the density matrix renormalization group method. We find that the staggered magnetizations exhibit reentrant behavior as functions of the transverse field, where the competition between the classical Neel order and the quantum fluctuations plays an important role. We also discuss the critical behavior associated with the staggered magnetizations.

cond-mat.stat-mech↗

arXiv2001

Vertical Density Matrix Algorithm: A Higher-Dimensional Numerical Renormalization Scheme based on the Tensor Product State Ansatz

We present a new algorithm to calculate the thermodynamic quantities of three-dimensional (3D) classical statistical systems, based on the ideas of the tensor product state and the density matrix renormalization group. We represent the maximum-eigenvalue eigenstate of the transfer matrix as the product of local tensors which are iteratively optimized by the use of the ``vertical density matrix'' formed by cutting the system along the transfer direction. This algorithm, which we call vertical density matrix algorithm (VDMA), is successfully applied to the 3D Ising model. Using the Suzuki-Trotter transformation, we can also apply the VDMA to two-dimensional (2D) quantum systems, which we demonstrate for the 2D transverse field Ising model.

cond-mat.stat-mech↗

arXiv2000

Phase Diagram of a 2D Vertex Model

Phase diagram of a symmetric vertex model which allows 7 vertex configurations is obtained by use of the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). The critical indices of this model are identified as $β= 1/8$ and $α= 0$.

cond-mat.stat-mech↗

arXiv2000

Two-Dimensional Tensor Product Variational Formulation

We propose a numerical self-consistent method for 3D classical lattice models, which optimizes the variational state written as two-dimensional product of tensors. The variational partition function is calculated by the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). Numerical efficiency of the method is observed via its application to the 3D Ising model.

cond-mat.stat-mech↗

arXiv1999

Middle-Field Cusp Singularities in the Magnetization Process of One-Dimensional Quantum Antiferromagnets

We study the zero-temperature magnetization process (M-H curve) of one-dimensional quantum antiferromagnets using a variant of the density-matrix renormalization group method. For both the S=1/2 zig-zag spin ladder and the S=1 bilinear-biquadratic chain, we find clear cusp-type singularities in the middle-field region of the M-H curve. These singularities are successfully explained in terms of the double-minimum shape of the energy dispersion of the low-lying excitations. For the S=1/2 zig-zag spin ladder, we find that the cusp formation accompanies the Fermi-liquid to non-Fermi-liquid transition.

cond-mat.stat-mech↗

arXiv1999

Numerical Renormalization Approach to Two-Dimensional Quantum Antiferromagnets with Valence-Bond-Solid Type Ground State

We study the ground-state properties of the two-dimensional quantum spin systems having the valence-bond-solid (VBS) type ground states. The ``product-of-tensors'' form of the ground-state wavefunction of the system is utilized to associate it with an equivalent classical lattice statistical model which can be treated by the transfer-matrix method. For diagonalization of the transfer matrix, we employ the product-wavefunction renormalization group method which is a variant of the density-matrix renormalization group method. We obtain the correlation length and the sublattice magnetization accurately. For the anisotropically ``deformed'' S=3/2 VBS model on the honeycomb lattice, we find that the correlation length as a function of the deformation parameter behaves very much alike as that in the S=3/2 VBS chain.

cond-mat.stat-mech↗

arXiv1998

Universal Asymptotic Eigenvalue Distribution of Density Matrices and the Corner Transfer Matrices in the Thermodynamic Limit

We study the asymptotic behavior of the eigenvalue distribution of the Baxter's corner transfer matrix (CTM) and the density matrix (DM) in the White's density-matrix renormalization group (DMRG), for one-dimensional quantum and two-dimensional classical statistical systems. We utilize the relationship ${\rm DM}={\rm CTM}^4$ which holds for non-critical systems in the thermodynamic limit. Using the known diagonal form of CTM, we derive exact asymptotic form of the DM eigenvalue distribution for the integrable $S=1/2$ XXZ chain (and its related integrable models) in the massive regime. The result is then recast into a ``universal'' form without model-specific quantities, which leads to $ω_{m}\sim \exp[-{\rm const.}(\log m)^2]$ for $m$-th DM eigenvalue at larg $m$. We perform numerical renormalization group calculations (using the corner-transfer-matrix RG and the product-wavefunction RG) for non-integrable models, verifying the ``universal asymptotic form'' for them. Our results strongly suggest the universality of the asymptotic eigenvalue distribution of DM and CTM for a wide class of systems.

cond-mat.stat-mech↗

arXiv1998

Delta-Function Bose Gas Picture of S=1 Antiferromagnetic Quantum Spin Chains Near Critical Fields

We study the zero-temperature magnetization curve (M-H curve) of the S=1 bilinear-biquadratic spin chain, whose Hamiltonian is given by $H=\sum_{i} S_i S_{i+1}+β(S_iS_{i+1})^2 with $0 \leq β<1$. We focus on validity of the delta-function bose-gas picture near the two critical fields: the saturation field $H_s$ and the lower critical field $H_c$ associated with the Haldane gap. Near $H_s$, we take ``low-energy effective S-matrix'' approach, which gives correct effective bose-gas coupling constant $c$, different from the spin-wave value. Comparing the M-H curve of the bose gas with the product-wavefunction renormalization group (PWFRG) calculation, excellent agreement is seen. Near $H_c$, comparing the PWFRG result with the bose-gas prediction, we find that there are two distinct regions of $β$ separated by a critical value $β_c(\approx 0.41)$. In the region $0<β<β_c$, the effective coupling $c$ is positive but rather small. The small value of $c$ makes the ``critical region'' of the square-root behavior $M\sim \sqrt{H-H_c}$ very narrow. Further, we find that in the $β\to β_c-0$, the square-root behavior transmutes to a different one, $M\sim (H-H_c)^{1/4}$. In the region $β_c<β<1$, the square-root behavior is rather distinct, but the effective coupling $c$ becomes negative.

cond-mat.stat-mech↗

arXiv1997

Application of the Density Matrix Renormalization Group Method to a Non-Equilibrium Problem

We apply the density matrix renormalization group (DMRG) method to a non-equilibrium problem: the asymmetric exclusion process in one dimension. We study the stationary state of the process to calculate the particle density profile (one-point function). We show that, even with a small number of retained bases, the DMRG calculation is in excellent agreement with the exact solution obtained by the matrix-product-ansatz approach.

cond-mat.stat-mech↗

arXiv1997

Magnetization Process of One-Dimensional Quantum Antiferromagnet: The Product Wavefunction Renormalization Group Approach

The product-wavefunction renormalization group method, which is a novel numerical renormalization group scheme proposed recently,is applied to one-dimensional quantum spin chains in a magnetic field. We draw the zero-temperature magnetization curve of the spin chains, which excellently agrees with the exact solution in the whole range of the field.

cond-mat.stat-mech↗