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Ken-Ichi Aoki

Publications and source records attributed to Ken-Ichi Aoki.

At least 19 recordsLinked to original sources
arXiv2023

The International Linear Collider: Report to Snowmass 2021

The International Linear Collider (ILC) is on the table now as a new global energy-frontier accelerator laboratory taking data in the 2030s. The ILC addresses key questions for our current understanding of particle physics. It is based on a proven accelerator technology. Its experiments will challenge the Standard Model of particle physics and will provide a new window to look beyond it. This document brings the story of the ILC up to date, emphasizing its strong physics motivation, its readiness for construction, and the opportunity it presents to the US and the global particle physics community.

physics.acc-ph↗
arXiv2019

Logical Reasoning for Revealing the Critical Temperature through Deep Learning of Configuration Ensemble of Statistical Systems

Recently, there have been many works on the deep learning of statistical ensembles to determine the critical temperature of a possible phase transition. We analyze the detailed structure of an optimized deep learning machine and prove the basic equalities among the optimized machine parameters and the physical quantities of the statistical system. According to these equalities, we conclude that the bias parameters of the final full connection layer record the free energy of the statistical system as a function of temperature. We confirm these equalities in one- and two-dimensional Ising spin models and actually demonstrate that the deep learning machine reveals the critical temperature of the phase transition through the second difference of bias parameters, which is equivalent to the specific heat. Our results disprove the previous works claiming that the weight parameters of the full connection might play a role of the order parameter such as the spin expectation.

cond-mat.stat-mech↗
arXiv2019

Singularity Free Direct Calculation of Spontaneous Mass Generation

We propose a new iterative method to directly calculate the spontaneous mass generation. It is regarded as a new regularization method resembling the finite volume calculation which assures non-negative fluctuation property at every stage. We work with the Nambu--Jona-Lasinio model and the strong coupling gauge theory where the dynamical chiral symmetry breaking occurs. We are able to conclude the physical mass definitely without encountering any singularity nor recourse to any additional consideration like the free energy comparison. However in special case of the 1st order phase transition, we find that the iterative method has a chance to go wrong.

hep-th↗
arXiv2018

Phase structure of NJL model with weak renormalization group

We analyze the chiral phase structure of the Nambu--Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential $V(σ;t)$ is given as a partial differential equation, where $σ:=\bar ψψ$ and $t$ is a dimensionless RG scale. When the dynamical chiral symmetry breaking (D$χ$SB) occurs at a certain scale $t_c$, $V(σ;t)$ has singularities originated from the phase transitions, and then one cannot follow RG flows after $t_c$. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the D$χ$SB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.

hep-th↗
arXiv2017

Restricted Boltzmann Machines for the Long Range Ising Models

We set up Restricted Boltzmann Machines (RBM) to reproduce the Long Range Ising (LRI) models of the Ohmic type in one dimension. The RBM parameters are tuned by using the standard machine learning procedure with an additional method of Configuration with Probability (CwP). The quality of resultant RBM are evaluated through the susceptibility with respect to the magnetic external field. We compare the results with those by Block Decimation Renormalization Group (BDRG) method, and our RBM clear the test with satisfactory precision.

cond-mat.stat-mech↗
arXiv2016

Dynamical chiral symmetry breaking and weak nonperturbative renormalization group equation in gauge theory

We analyze the dynamical chiral symmetry breaking in gauge theory with the nonperturbative renormalization group equation (NPRGE), which is a first order nonlinear partial differential equation (PDE). In case that the spontaneous chiral symmetry breaking occurs, the NPRGE encounters some non-analytic singularities at the finite critical scale even though the initial function is continuous and smooth. Therefore there is no usual solution of the PDE beyond the critical scale. In this paper, we newly introduce the notion of a weak solution which is the global solution of the weak NPRGE. We show how to evaluate the physical quantities with the weak solution.

physics.gen-ph↗
arXiv2016

Functional renormalization group study of the Nambu--Jona-Lasinio model at finite temperature and density in an external magnetic field

In this study, we investigate the Nambu--Jona-Lasinio (NJL) model at finite temperature and finite density in an external magnetic field using the functional renormalization group. We investigate the dependence of the position of the ultraviolet fixed point (UVFP) of the four-Fermi coupling constant on the temperature, density, and external magnetic field, and we obtain the chiral phase structure. The UVFP at low temperature and finite chemical potential oscillates in a small external magnetic field, which can be interpreted as the de Haas--van Alphen effect. We also obtain phase diagrams with complex structures, where the phase boundary moves back and forth as the external magnetic field increases in the low temperature and high density region.

hep-ph↗
arXiv2015

The RG flow of Nambu--Jona-Lasinio model at finite temperature and density

We study the Nambu--Jona-Lasinio model at finite temperature and finite density by using the functional renormalization group. The RG flows of the four-fermi coupling constant in the NJL model are investigated. We obtain the chiral phase boundary in cases of the large-$N$ leading approximation and an improved approximation. The large-$N$ non-leading term at the vanishing temperature has a singularity at the fermi surface. We show that the quantum corrections by the large-$N$ non-leading term largely influence the phase boundary at the low temperature and high density region.

hep-ph↗
arXiv2014

Analysis of the Dynamical Chiral Symmetry Breaking in QCD at Finite Temperature and Density using the Non-Perturbative Renormalization Group

We analyze the Nambu--Jona-Lasinio model which is a chiral effective model of QCD by using the non-perturbative renormalization group at finite temperature and finite density. We discuss the chiral phase diagram in the model. We include the large-$N$ non-leading contribution in the beta function and discuss its effects for the phase boundary.

hep-ph↗
arXiv2014

Weak solution of the non-perturbative renormalization group equation to describe the dynamical chiral symmetry breaking

We analyze the dynamical chiral symmetry breaking (D$χ$SB) in the Nambu-Jona-Lasinio (NJL) model by using the non-perturbative renormalization group (NPRG) equation. The equation takes a form of two-dimensional partial differential equation for the multi-fermion effective interactions $V(x,t)$ where $x$ is $\barψψ$ operator and $t$ is the logarithm of the renormalization scale. The D$χ$SB occurs due to the quantum corrections, which means it emerges at some finite $t_{\rm c}$ in the mid of integrating the equation with respect to $t$. At $t_{\rm c}$ some singularities suddenly appear in $V$ which is compulsory in the spontaneous symmetry breakdown. Therefore there is no solution of the equation beyond $t_{\rm c}$. We newly introduce the notion of weak solution to get the global solution including the infrared limit $t\rightarrow \infty$ and investigate its properties. The obtained weak solution is global and unique, and it perfectly describes the physically correct vacuum even in case of the first order phase transition appearing in finite density medium. The key logic of deduction is that the weak solution we defined automatically convexifies the effective potential when treating the singularities.

hep-th↗
arXiv2013

Weak solution method of the non-perturbative renormalization group equation to describe dynamical chiral symmetry breaking and its application to beyond the ladder analysis in QCD

The method of non-perturbative renormalization group (NPRG) is applied to the analysis of dynamical chiral symmetry breaking (DCSB) in QCD. We show that the DCSB solution of the NPRG flow equation can be obtained without the bosonization. The solution, having the singular point, can be authorized as the weak solution of partial differential equation, and can be easily evaluated using the method of the characteristic curve. Also we show that our non-ladder extended approximation improves almost perfectly the gauge dependence of the chiral condensates.

hep-th↗
arXiv2013

Uniqueness and Significance of Weak Solution of Non-perturbative Renormalization Group Equation to Analyze Dynamical Chiral Symmetry Breaking

We propose quite a new method of analyzing the dynamical chiral symmetry breaking in gauge theories. Starting with the non-perturbative renormalization group equation for the Wilsonian fermion potential, we define the weak solution of it in order to mathematically authorize solutions with singularity. The weak solution is obtained uniquely and it successfully predicts the physically correct vacuum, chiral condensates, dynamical mass, through its auto-convexizing power for the effective potential. Thus it works perfectly even for the first order phase transition in the finite density QCD.

hep-th↗
arXiv2012

Solving the QCD non-perturbative flow equation as a partial differential equation and its application to the dynamical chiral symmetry breaking

Non-perturbative renormalization group approach to the dynamical chiral symmetry breaking is an effective method which can accommodate beyond the ladder (mean filed) approximation. The usual method relying on the field operator expansion suffers explosive behaviors of the 4-fermi coupling constant, which prevent us from evaluating the physical quantities in the broken phase. In order to overcome this difficulty, we solve the flow equation directly as a partial differential equation and calculate the dynamical mass and the chiral condensates. Also we formulate a beyond the ladder equation and it gives almost gauge independent results for the chiral condensates.

hep-th↗
arXiv2012

Phase transition of the dissipative double-well quantum mechanics

We investigate the critical dissipation of the double-well quantum mechanics. We adopt two-state approximation to define effective Ising models and apply the block decimation renormalization group and the finite range scaling method recently proposed for the long range Ising model. We briefly report the numerical results of the critical dissipation for various model parameters.

cond-mat.stat-mech↗
arXiv2011

Domain Wall Renormalization Group Analysis of 2-dimensional Ising Model

Using a recently proposed new renormalization group method (tensor renormalization group), we analyze the Ising model on the 2-dimensional square lattice. For the lowest order approximation with two domain wall states, it realizes the idea of coarse graining of domain walls. We write down explicit analytic renormalization transformation and prove that the picture of the coarse graining of the physical domain walls does hold for all physical renormalization group flows. We solve it to get the fixed point structure and obtain the critical exponents and the critical temperature. These results are very near to the exact values. We also briefly report the improvement using four domain wall states.

cond-mat.stat-mech↗
arXiv2009

Finite-Range Scaling Method to Analyze Systems with Infinite-Range Interactions

We propose a new practical method for evaluating the critical coupling constant in one-dimensional long-range interacting systems. We assume a finite-range scaling and define its exponent for the logarithm of the susceptibility. We find criticality in the form of a zeta function singularity. As an example, we present results for a long-range Ising model.

cond-mat.stat-mech↗
arXiv2003

Non-Perturbative Renormalization Group Analysis of the Ohmic Quantum Dissipation

We analyze quantum tunneling with the Ohmic dissipation by the non-perturbative renormalization group method. We calculate the localization susceptibility to evaluate the critical dissipation for the quantum-classical transition, and find considerably larger critical dissipation compared to the previous semi-classical arguments.

quant-ph↗