arXiv subjects

Yuta Ito

Publications and source records attributed to Yuta Ito.

At least 37 records · Page 2Linked to original sources

arXiv2020

Complex Langevin calculations in QCD at finite density

We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action with $β= 5.7$ and four-flavor staggered fermions with degenerate quark mass $m a = 0.01$ and nonzero quark chemical potential $μ$. We confirm that a sufficient condition for correct convergence is satisfied for $μ/T = 5.2 - 7.2$ on a $8^3 \times 16$ lattice and $μ/T = 1.6 - 9.6$ on a $16^3 \times 32$ lattice. In particular, the expectation value of the quark number is found to have a plateau with respect to $μ$ with the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color) $\times$ 4 (flavor) $\times$ 2 (spin) $=24$. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.

hep-lat↗

arXiv2020

Complex Langevin studies of the dynamical compactification of extra dimensions in the Euclidean IKKT matrix model

The type IIB matrix model, also known as the IKKT matrix model, is a promising candidate for a nonperturbative formulation of superstring theory. In this talk we study the Euclidean version of the IKKT matrix model, which has a "sign problem" due to the Pfaffian coming from integrating out the fermionic degrees of freedom. To study the spontaneous breaking of the SO(10) rotational symmetry, we apply the Complex Langevin Method (CLM) to the Euclidean IKKT matrix model. We conclude that the SO(10) symmetry is broken to SO(3), in agreement with the previous studies by the Gaussian Expansion Method (GEM). We also apply the GEM to the deformed model and find consistency with the CLM result. These are proceedings of Takehiro Azuma's talk at Asia-Pacific Symposium for Lattice Field Theory (APLAT 2020) on August 4-7, 2020, based on the paper arXiv:2002.07410.

hep-lat↗

arXiv2020

Dynamical Compactification of Extra Dimensions in the Euclidean IKKT Matrix Model via Spontaneous Symmetry Breaking

The IKKT matrix model has been conjectured to provide a promising nonperturbative formulation of superstring theory. In this model, spacetime emerges dynamically from the microscopic matrix degrees of freedom in the large-N limit, and Monte Carlo simulations of the Lorentzian version provide evidence of an emergent (3+1)-dimensional expanding space-time. In this talk, we discuss the Euclidean version of the IKKT matrix model and provide evidence of dynamical compactification of the extra dimensions via the spontaneous symmetry breaking (SSB) of the 10D rotational symmetry. We perform numerical simulations of a system with a severe complex action problem by using the complex Langevin method (CLM). The CLM suffers from the singular-drift problem and we deform the model in order to avoid it. We study the SSB pattern as we vary the deformation parameter and we conclude that the original model has an SO(3) symmetric vacuum, in agreement with previous calculations using the Gaussian expansion method (GEM). We employ the GEM to the deformed model and we obtain results consistent with the ones obtained by CLM.

hep-lat↗

arXiv2020

Self-similar orbit-averaged Fokker-Planck equation for isotropic spherical dense clusters (ii) physical properties and negative heat capacity of pre-collapse core

This is the second paper of a series of our works on the self-similar orbit-averaged Fokker-Planck (OAFP) equation and details physical properties of isotropic pre-collapse solution. The fundamental core collapse process at the late stage of relaxation evolution of spherical star clusters can be described by the self-similar OAFP equation. The accurate spectral solution was found recently in the first paper. The present work details the thermodynamic aspects of the model based on the stellar DF obtained from the solution. Our calculation shows the following local properties (i) Equation of state is $p=1.0ρ/χ_\text{esc}$ in the core where $p$ is the pressure, $ρ$ the density and $χ_\text{esc}$ the scaled escape energy, while it is $p=0.5ρ^{1.1}/χ_\text{esc}$ at large radii. (ii) If we consider the center of the core is polytropic, the polytropic index is 177. Also, as a global property we construct caloric curves of the model to discuss the heat capacity together with Virial. Special focus is the cause of negative heat capacity of the core; the well-relaxed core can be directly compared to the isothermal sphere with positive heat capacity. Comparing our results to the previous works, we conclude, in the self-similar evolution, the negative heat capacity in the core holds due to collisionless and high-temperature stars that experience a rapid change in mean field potential through stellar- and heat- flows, rather than due to the (quasi-)isolation of the core from surroundings.

astro-ph.GA↗

arXiv2020

Self-similar orbit-averaged Fokker-Planck equation for isotropic spherical dense clusters (i) accurate pre-collapse solution

This is the first paper of a series of our works on the self-similar orbit-averaged Fokker-Planck (OAFP) equation for distribution function of stars in dense isotropic star clusters. At the late stage of relaxation evolution of the clusters, standard stellar dynamics predicts that the clusters evolve in a self-similar fashion forming collapsing cores. However, the corresponding mathematical model, the self-similar OAFP equation, has never been solved on the whole energy domain $(-1< E < 0)$. The existing works based on kinds of finite difference methods provide solutions only on the truncated domain $-1< E<-0.2$. To broaden the range of the truncated domain, the present work resorts to a (highly accurate and efficient) Gauss-Chebyshev pseudo-spectral method. We provide a spectral solution, whose number of significant figures is four, on the whole domain. Also, the solution can reduce to a semi-analytical form whose degree of polynomials is only eighteen holding three significant figures. We also provide the new eigenvalues; $c_{1}=9.0925\times10^{-4}$, $c_{2}=1.1118\times10^{-4}$, $c_{3}=7.1975\times10^{-2}$ and $c_{4}=3.303\times10^{-2}$, corresponding to the core collapse rate $ξ=3.64\times10^{-3}$, scaled escape energy $χ_\text{esc}=13.881$ and power-law exponent $α=2.2305$. Since the solution on the whole domain is unstable against degree of Chebyshev polynomials, we also provide spectral solutions on truncated domains ( $-1< E<E_\text{max}$, where $-0.35<E_\text{max}<-0.03$) to explain how to handle the instability. By reformulating the OAFP equation in several ways, we improve the accuracy of the spectral solution and reproduce an existing self-similar solution, which infers that existing solutions have only one significant figure at best.

physics.comp-ph↗

arXiv2020

Self-similar orbit-averaged Fokker-Planck equation for isotropic spherical dense clusters (iii) application of pre-collapse solution to Galactic globular clusters

This is the third paper of a series of our works on the self-similar orbit-averaged Fokker-Planck (OAFP) equation. The first paper provided an accurate spectral solution of the equation for isotropic pre-collapse star clusters and the second detailed the physical feature of the model. Based on the works, the present work applies the solution to the observed structural profiles of Galactic globular clusters. For fitting to the profiles, the most fundamental (quasi-)stationary model, the King model, and the variants have shown successful results while they can not apply to core-collapsing and core-collapsed clusters at the late stage of the relaxation evolution. We propose an energy-truncated self-similar OAFP model that can apply to clusters at both the early and late stages of the evolution. This new model fits the structural profiles of at least half of Galactic globular clusters while it also applies to core-collapsed stars with resolved cores. As a main result, we provide the completion rate of core collapse against concentration for the clusters. Also, we show our new model can apply to the globular clusters even in a broad range of radii (0.01$\sim$10 arcminutes). However, since our model includes polytrope (elongated outer halo), the tidal radius of the model becomes unrealistically large for some clusters. To avoid the issue, we also propose an approximated form of the new model. Lastly, we report that Milky Way globular clusters with low concentrations have the same spatial structures as stellar polytropes and discuss whether such polytropic cluster is a reasonable concept.

astro-ph.GA↗

arXiv2020

Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model

The IKKT matrix model is a promising candidate for a nonperturbative formulation of superstring theory, in which spacetime is conjectured to emerge dynamically from the microscopic matrix degrees of freedom in the large-$N$ limit. Indeed in the Lorentzian version, Monte Carlo studies suggested the emergence of (3+1)-dimensional expanding space-time. Here we study the Euclidean version instead, and investigate an alternative scenario for dynamical compactification of extra dimensions via the spontaneous symmetry breaking (SSB) of 10D rotational symmetry. We perform numerical simulations based on the complex Langevin method (CLM) in order to avoid a severe sign problem. Furthermore, in order to avoid the singular-drift problem in the CLM, we deform the model and determine the SSB pattern as we vary the deformation parameter. From these results, we conclude that the original model has an SO(3) symmetric vacuum, which is consistent with previous results obtained by the Gaussian expansion method (GEM). We also apply the GEM to the deformed matrix model and find consistency with the results obtained by the CLM.

hep-th↗

arXiv2019

Exploring the QCD phase diagram at finite density by the complex Langevin method on a $16^3\times 32$ lattice

We explore the QCD phase diagram at finite density with four-flavor staggered fermions using the complex Langevin method, which is a promising approach to overcome the sign problem. In our previous work on an $8^3 \times 16$ lattice at $β= 5.7$ with the quark mass $m = 0.01$, we have found that the baryon number density has a clear plateau as a function of the chemical potential. In this study, we use a $16^3 \times 32$ lattice to reduce finite volume effects and find that the plateau structure survives. Moreover, the number of quarks in the plateau region turns out to be 24, which is exactly the same as the one obtained previously on the $8^3 \times 16$ lattice. We provide a simple interpretation of this number, which suggests that the Fermi sphere is starting to form.

hep-lat↗

arXiv2019

On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model

The emergence of (3+1)-dimensional expanding space-time in the Lorentzian type IIB matrix model is an intriguing phenomenon which was observed in Monte Carlo studies of this model. In particular, this may be taken as a support to the conjecture that the model is a nonperturbative formulation of superstring theory in (9+1) dimensions. In this paper we investigate the space-time structure of the matrices generated by simulating this model and its simplified versions, and find that the expanding part of the space is described essentially by the Pauli matrices. We argue that this is due to an approximation used in the simulation to avoid the sign problem, which actually amounts to replacing $e^{iS_{\rm b}}$ by $e^{βS_{\rm b}}$ ($β>0$) in the partition function, where $S_{\rm b}$ is the bosonic part of the action. We also discuss the possibility of obtaining a regular space-time with the (3+1)-dimensional expanding behavior in the original model with the correct $e^{iS_{\rm b}}$ factor.

hep-th↗

arXiv2019

Dynamical compactification of extra dimensions in the Euclidean type IIB matrix model: A numerical study using the complex Langevin method

The type IIB matrix model is conjectured to be a nonperturbative definition of type IIB superstring theory. In this model, spacetime is a dynamical quantity and compactification of extra dimensions can be realized via spontaneous symmetry breaking(SSB). In this work, we consider a simpler, related, six dimensional model in its Euclidean version and study it numerically. Our calculations provide evidence that the SO(6) rotational symmetry of the model breaks down to SO(3), which means that the theory lives in a vacuum where 3 out of the 6 dimensions are large compared to the other 3. Our results show the same SSB pattern predicted by the Gaussian expansion method and that they are in quantitative agreement. The Monte Carlo simulations are hindered by a severe complex action problem which is addressed by applying the complex Langevin method.

hep-th↗

arXiv2019

Ionization age of iron ejecta in the Galactic Type Ia supernova remnant G306.3-0.9

We present a 190 ks observation of the Galactic supernova remnant (SNR) G306.3-0.9 with Suzaku. To study ejecta properties of this possible Type Ia SNR, the absolute energy scale at the Fe-K band was calibrated to a level of uncertainty less than 10 eV by a cross-calibration with the Hitomi microcalorimeter using the Perseus cluster spectra. This enabled us for the first time to accurately determine the ionization state of the Fe K$α$ line of this SNR. The ionization timescale ($τ$) of the Fe ejecta was measured to be $\log_{10} τ$ (cm$^{-3}$ s) $=10.24\pm0.03$, significantly smaller than previous measurements. Marginally detected K$α$ lines of Cr and Mn have consistent ionization timescales with Fe. The global spectrum was well fitted with shocked interstellar matter (ISM) and at least two ejecta components with different ionization timescales for Fe and intermediate mass elements (IME) such as S and Ar. One plausible interpretation of the one-order-of-magnitude shorter timescale of Fe than that of IME ($\log_{10} τ= 11.17\pm0.07$) is a chemically stratified structure of ejecta. By comparing the X-ray absorption column to the HI distribution decomposed along the line of sight, we refined the distance to be $\sim$20 kpc. The large ISM-to-ejecta shocked mass ratio of $\sim$100 and dynamical timescale of $\sim$6 kyr place the SNR in the late Sedov phase. These properties are consistent with a stratified ejecta structure that has survived the mixing processes expected in an evolved supernova remnant.

astro-ph.HE↗

arXiv2018

Exploring the phase diagram of finite density QCD at low temperature by the complex Langevin method

Monte Carlo studies of QCD at finite density suffer from the sign problem, which becomes easily uncontrollable as the chemical potential $μ$ is increased even for a moderate lattice size. In this work we make an attempt to approach the high density low temperature region by the complex Langevin method (CLM) using four-flavor staggered fermions with reasonably small quark mass on a $8^3 \times 16$ lattice. Unlike the previous work on a $4^3 \times 8$ lattice, the criterion for correct convergence is satisfied within a wide range of $μ$ without using the deformation technique. In particular, the baryon number density exhibits a plateau behavior consistent with the formation of eight baryons, and it starts to grow gradually at some $μ$.

hep-lat↗

arXiv2018

Can the complex Langevin method see the deconfinement phase transition in QCD at finite density?

Exploring the phase diagram of QCD at finite density is a challenging problem since first-principle calculations based on standard Monte Carlo methods suffer from the sign problem. As a promising approach to this issue, the complex Langevin method (CLM) has been pursued intensively.In this work, we investigate the applicability of the CLM in the vicinity of the deconfinement phase transition using the four-flavor staggered fermions. In particular, we look for a signal of the expected first order phase transition within the validity region of the CLM.

hep-lat↗

arXiv2018

A generalized Landau kinetic equation for weakly-coupled probability distribution of N-stars in dense star cluster

The secular evolution of a collisional star cluster of $N$-'point' stars have been conventionally discussed based on cumulative two-body relaxation process. The relaxation process requires a cut-off on the range of two-body encounter between stars in physical space and the relaxation time is characterized by Coulomb logarithm $\ln[N]$; the conventional cut-off on the encounter distance in the literature gives "dominant" effect. In addition, incorrect cut-offs exposed a mathematical "infinite-density" problem in the late stage of core-collapse. The present paper shows these are merely the results due to incorrect cut-off process. If one correctly constrains the cut-off on interaction range between stars based on truncated BBGKY hierarchy, one must introduce a self-consistent 'truncated' Newtonian mean-field (m.f.) acceleration of star. The present paper shows the effect of total number on the structure of finite star cluster (in which stars undergo only two-body encounters) for the first time after establishing a mathematical formulation of a generalized Landau kinetic equation that includes the cut-off effect on both of collision term and m.f. potential by employing a BBGKY hierarchy for truncated DF stars. The cut-off effect increases the typical relaxation time by a few of percentage, which means the effect of cut-off itself is "non-dominant" on the relaxation time. On the other hand, the cut-off on m.f. acceleration is necessary to avoid "infinite-density" problem at the center of the system; the effect of total number $N$ on density profile and m.f. acceleration are shown by applying the truncated-DF BBGKY hierarchy to a toy model (a quasi-static modified Hubble density profile) for a core-halo structure of a star cluster at the late stage of evolution.

astro-ph.GA↗

arXiv2018

A convergent kinetic theory of collisional star clusters (i) a self-consistent 'truncated' mean-field acceleration of stars

Fundamental relaxation processes in the secular evolution of a collisional star cluster of $N$-'point' stars have been conventionally discussed based on either of collision kinetic theory (for strong two-body encounters) and wave one (for statistical acceleration and gravitational polarization). If combining the both theories together, one must introduce a self-consistent 'truncated' Newtonian mean-field (m.f.) acceleration of star at position $r$ and time $t$ due to a phase-space distribution function $f\left(r', p',t\right)$ for stars $A^{\triangle}(r,t)=-Gm\left(1-\frac{1}{N}\right)\int_{\mid r-r' \mid > \triangle}\frac{r-r'}{\mid r-r' \mid^{3}} f\left(r',p',t\right)\text{d}^{3}{r'}\text{d}^{3}{p'},$ where $G$ is the gravitational constant and $m$ the mass of stars. The lower limit $\triangle$ of the distance between two stars is order of the Landau distance. The truncated m.f. acceleration is a necessary consequence due to the strong encounters and m.f. acceleration being not able to 'coexist' at specific distance between stars. The present paper aims at initiating a star-cluster convergent kinetic theory to self-consistently derive kinetic equations of star clusters, mathematically non-divergent in distance- and wavenumber- spaces based on the truncated m.f. acceleration, correct at time scales of the secular evolution. This will be achieved by focusing on mathematical formulations of the Kandrup's generalised-Landau equation including the effect of the strong encounters and by extending the Grad's truncated distribution function and Klimontovich's theory of non-ideal systems.

astro-ph.GA↗

arXiv2018

Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models

In recent years the complex Langevin method (CLM) has proven a powerful method in studying statistical systems which suffer from the sign problem. Here we show that it can also be applied to an important problem concerning why we live in four-dimensional spacetime. Our target system is the type IIB matrix model, which is conjectured to be a nonperturbative definition of type IIB superstring theory in ten dimensions. The fermion determinant of the model becomes complex upon Euclideanization, which causes a severe sign problem in its Monte Carlo studies. It is speculated that the phase of the fermion determinant actually induces the spontaneous breaking of the SO(10) rotational symmetry, which has direct consequences on the aforementioned question. In this paper, we apply the CLM to the 6D version of the type IIB matrix model and show clear evidence that the SO(6) symmetry is broken down to SO(3). Our results are consistent with those obtained previously by the Gaussian expansion method.

hep-lat↗

arXiv2017

Comparative studies of the deformation techniques for the singular-drift problem in the complex Langevin method

In application of the complex Langevin method to QCD at high density and low temperature, the singular-drift problem occurs due to the appearance of near-zero eigenvalues of the Dirac operator. In order to avoid this problem, we proposed to deform the Dirac operator in such a way that the near-zero eigenvalues do not appear and to extrapolate the deformation parameter to zero from the available data points. Here we test three different types of deformation in a simple large-$N$ matrix model, which undergoes an SSB due to the phase of the fermion determinant, and compare them to see the consistency with one another.

hep-lat↗

arXiv2017

A new method for probing the late-time dynamics in the Lorentzian type IIB matrix model

The type IIB matrix model has been investigated as a possible nonperturbative formulation of superstring theory. In particular, it was found by Monte Carlo simulation of the Lorentzian version that the 9-dimensional rotational symmetry of the spatial matrices is broken spontaneously to the 3-dimensional one after some "critical time". In this paper we develop a new simulation method based on the effective theory for the submatrices corresponding to the late time. Using this method, one can obtain the results for $N\times N$ matrices by simulating matrices typically of the size $O(\sqrt{N})$. We confirm the validity of this method and demonstrate its usefulness in simplified models.

hep-th↗