arXiv subjects

Teiji Kunihiro

Publications and source records attributed to Teiji Kunihiro.

At least 37 records · Page 2Linked to original sources

arXiv2017

Tachyonic instability of the scalar mode prior to QCD critical point based on Functional renormalization-group method

We establish and elucidate the physical meaning of the appearance of an acausal mode in the sigma mesonic channel, found in the previous work by the present authors, when the system approaches the $\mathrm{Z}_{2}$ critical point. The functional renormalization group method is applied to the two--flavor quark--meson model with varying current quark mass $m_q$ even away from the physical value at which the pion mass is reproduced. We first determine the whole phase structure in the three-dimensional space $(T, μ, m_q)$ consisting of temperature $T$, quark chemical potential $μ$ and $m_q$, with the tricritical point, $\mathrm{O}(4)$ and $\mathrm{Z}_{2}$ critical lines being located; they altogether make a wing-like shape quite reminiscent of those known in the condensed matters with a tricritical point. We then calculate the spectral functions $ρ_{σ, π}(ω, p)$ in the scalar and pseudoscalar channel around the critical points. We find that the sigma mesonic mode becomes tachyonic with a superluminal velocity at finite momenta before the system reaches the $\mathrm{Z}_{2}$ point from the lower density, even for $m_q$ smaller than the physical value. One of the possible implications of the appearance of such a tachyonic mode at finite momenta is that the assumed equilibrium state with a uniform chiral condensate is unstable toward a state with an inhomogeneous $σ$ condensate. No such an anomalous behavior is found in the pseudoscalar channel. We find that the $σ$-to-$2σ$ coupling due to finite $m_q$ play an essential role for the drastic modification of the spectral function.

hep-ph↗

arXiv2017

A novel probe of chiral restoration in nuclear medium

We propose measuring the mass shift and width broadening of the $f_1(1285)$ meson together with those of the $ω$ from a nuclear target as a means to experimentally probe the partial restoration of chiral symmetry inside the nuclear matter. The relation between the order parameter of chiral symmetry and the difference in the correlation functions of the $f_1(1285)$ current and the $ω$ current is discussed in the limit where the disconnected diagrams are neglected. A QCD sum rule analysis of the $f_1(1285)$ meson mass leads to about 100 MeV attraction in nuclear matter, which can be probed in future experiments.

nucl-th↗

arXiv2016

Spectral functions in functional renormalization group approach -- analysis of the collective soft modes at the QCD critical point --

We first review the method to calculate the spectral functions in the functional renormalization group (FRG) approach, which has been recently developed. We also provide the numerical stability conditions given by the present authors for a generic nonlinear evolution equation that are necessary for obtaining the accurate effective potential from the flow equation in the FRG. As an interesting example, we report the recent calculation of the spectral functions of the mesonic and particle-hole excitations using a chiral effective model of Quantum Chromodynamics (QCD); we extract the dispersion relations from them and try to reveal the nature of the soft modes at the QCD critical point (CP) where the phase transition is second order. Our result shows that a clear development and the softening of the phonon mode in the space-like region as the system approaches the CP; furthermore it turns out that the sigma mesonic mode once in the time-like region gets to merge with the phonon mode in the close vicinity of the CP, implying a novel possibility about the nature of the soft mode of the QCD CP.

hep-ph↗

arXiv2016

Novel picture of the soft modes at the QCD critical point based on the FRG method

We investigate the soft mode at the QCD critical point (CP) on the basis of the functional renormalization group. We calculate the spectral functions in the meson channels in the two-flavor quark--meson model. Our result shows that the energy of the peak position of the particle--hole mode in the sigma channel becomes vanishingly small as the system approaches the QCD CP, which is a manifestation of the softening of the phonon mode. We also extract the dispersion curves of the mesonic and the phonon mode, a hydrodynamic mode which leads to a finding that the dispersion curve of the sigma-mesonic mode crosses the light-cone into the space-like momentum region, and then eventually merges into the phonon mode as the system approaches further close to the CP. This may suggest that the sigma-mesonic mode forms the soft mode together with the hydrodynamic mode at the CP.

hep-ph↗

arXiv2016

Effective field theory and the scattering process for magnons in the ferromagnet, antiferromagnet, and ferrimagnet

We discuss that a low-energy effective Lagrangian relying on SO(3) $\rightarrow$ SO(2) is applicable for a ferrimagnet as well as a ferromagnet and an antiferromagnet. The analysis of the particle states shows that there exist not only massless modes with the dispersion relations $ω\propto |\bm{k}|,\, |\bm{k}|^2$, i.e., the so-called type-I and type-II Nambu-Goldstone modes, respectively, but also gapped modes with $ω\propto m^2+|\bm{k}|^2$. We clarify how the coefficients of the terms with one time derivative and those with two time derivatives in the effective Lagrangian determine the order parameters specifying whether the system is in a ferromagnetic, antiferromagnetic or ferrimagnetic state; we stress that the gapped mode related to the spontaneous symmetry breaking appears only in the ferrimagnetic system and not in the ferromagnetic and antiferromagnetic systems. We also establish the power counting scheme and calculate the scattering amplitudes and thereby the scattering lengths between the two Nambu-Goldstone bosons. We show that the scattering length of the gapped mode is finite and proportional to the gap. This characteristic property of the gapped NG mode can be used to discriminate it from gapped excitations which originate in other mechanisms. Finally, we study the effects of the explicit symmetry breaking that are given by an external magnetic field and a single-ion anisotropy, and show that the external magnetic fields do not have any effects on the scattering amplitudes in all the spin systems as was known for the ferromagnet system. In contrast, the anisotropy does affect the scattering amplitudes, the phase shift, and the scattering length except for spin 1/2 systems. This result supports the possibility of the Efimov effect in spin systems discussed in previous studies.

cond-mat.str-el↗

arXiv2016

Functional renormalization group analysis of the soft mode at the QCD critical point

We make an intensive investigation of the soft mode at the quantum chromodynamics (QCD) critical point on the basis of the functional renormalization group (FRG) method in the local potential approximation. We calculate the spectral functions $ρ_{σ, π}(ω,\, p)$ in the scalar ($σ$) and pseudoscalar ($π$) channels beyond the random phase approximation in the quark--meson model. At finite baryon chemical potential $μ$ with a finite quark mass, the baryon-number fluctuation is coupled to the scalar channel and the spectral function in the $σ$ channel has a support not only in the time-like ($ω\,>\,p$) but also in the space-like ($ω\,<\, p$) regions, which correspond to the mesonic and the particle--hole phonon excitations, respectively. We find that the energy of the peak position of the latter becomes vanishingly small with the height being enhanced as the system approaches the QCD critical point, which is a manifestation of the fact that the phonon mode is the {\em soft mode} associated with the second-order transition at the QCD critical point, as has been suggested by some authors. Moreover, our extensive calculation of the spectral function in the $(ω, p)$ plane enables us to see that the mesonic and phonon modes have the respective definite dispersion relations $ω_{σ.{\rm ph}}(p)$, and it turns out that $ω_σ(p)$ crosses the light-cone line into the space-like region, and then eventually merges into the phonon mode as the system approaches the critical point more closely. This implies that the sigma-mesonic mode also becomes soft at the critical point. We also provide numerical stability conditions that are necessary for obtaining the accurate effective potential from the flow equation.

hep-ph↗

arXiv2016

Possible relevance of the softening of the sigma meson to $η$ decay into 3$π$ in the nuclear medium

We investigate the role of the softening of the scalar-isoscalar (sigma) meson in the $η\rightarrowπ^+π^-π^0$ and $3π^0$ decay widths in the symmetric nuclear medium using a linear sigma model. Our calculation shows that these decay widths in the nuclear medium increase by up to a factor of four to ten compared with those in the free space mainly depending on the mass of the sigma meson in the free space, which is an input parameter of the model. The enhancements are considerable even at a half of the normal nuclear density. Thus, the $η$ decay into $3π$ could be a possible new probe for the chiral restoration in the nuclear medium. We find that the density dependence of the $η\rightarrow3π^0$ decay is moderate in comparison with that of $η\rightarrowπ^+π^-π^0$, although the former width is greater than the latter one at a given density. This is because the softening of the sigma meson causes cancellation of the terms appearing from the Bose symmetry in the $η\rightarrow3π^0$ decay. The difference between the density dependences should be helpful for experimental confirmation of the findings of the present study.

nucl-th↗

arXiv2016

Second-order hydrodynamics for fermionic cold atoms: Detailed analysis of transport coefficients and relaxation times

We give a detailed derivation of the second-order (local) hydrodynamics for Boltzmann equation with an external force by using the renormalization group method. In this method, we solve the Boltzmann equation faithfully to extract the hydrodynamics without recourse to any ansatz. Our method leads to microscopic expressions of not only all the transport coefficients that are of the same form as those in Chapman-Enskog method but also those of the viscous relaxation times $τ_i$ that admit physically natural interpretations. As an example, we apply our microscopic expressions to calculate the transport coefficients and the relaxation times of the cold fermionic atoms in a quantitative way, where the transition probability in the collision term is given explicitly in terms of the $s$-wave scattering length $a_s$. We thereby discuss the quantum statistical effects, temperature dependence, and scattering-length dependence of the first-order transport coefficients and the viscous relaxation times: It is shown that as the temperature is lowered, the transport coefficients and the relaxation times increase rapidly because Pauli principle acts effectively. On the other hand, as $a_s$ is increased, these quantities decrease and become vanishingly small at unitarity because of the strong coupling. The numerical calculation shows that the relation $τ_π=η/P$, which is derived in the relaxation-time approximation and used in most of literature without almost any foundation, turns out to be satisfied quite well, while the similar relation for the relaxation time $τ_J$ of the heat conductivity is satisfied only approximately with a considerable error.

cond-mat.quant-gas↗

arXiv2016

Mesoscopic dynamics of fermionic cold atoms ---Quantitative analysis of transport coefficients and relaxation times---

We give a quantitative analysis of the dynamical properties of fermionic cold atomic gases in normal phase, such as the shear viscosity, heat conductivity, and viscous relaxation times, using the novel microscopic expressions derived by the renormalization group (RG) method, where the Boltzmann equation is faithfully solved to extract the hydrodynamics without recourse to any ansatz. In particular, we examine the quantum statistical effects, temperature dependence, and scattering-length dependence of the transport coefficients and the viscous relaxation times. The numerical calculation shows that the relation $τ_π=η/P$, which is derived in the relaxation-time approximation (RTA) and is used in most of the literature, turns out to be satisfied quite well, while the similar relation for the viscous relaxation time $τ_J$ of the heat conductivity is satisfied only approximately with a considerable error.

cond-mat.quant-gas↗

arXiv2016

Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function

We investigate possible entropy production in Yang-Mills (YM) field theory by using a quantum distribution function called Husimi function $f_{\rm H}(A, E, t)$ for YM field, which is given by a coarse graining of Wigner function and non-negative. We calculate the Husimi-Wehrl (HW) entropy $S_{\rm HW}(t)=-{\rm Tr}f_H \log f_H$ defined as an integral over the phase-space, for which two adaptations of the test-particle method are used combined with Monte-Carlo method. We utilize the semiclassical approximation to obtain the time evolution of the distribution functions of the YM field, which is known to show a chaotic behavior in the classical limit. We also make a simplification of the multi-dimensional phase-space integrals by making a product ansatz for the Husimi function, which is found to give a 10-20 per cent over estimate of the HW entropy for a quantum system with a few degrees of freedom. We show that the quantum YM theory does exhibit the entropy production, and that the entropy production rate agrees with the sum of positive Lyapunov exponents or the Kolmogorov-Sinai entropy, suggesting that the chaoticity of the classical YM field causes the entropy production in the quantum YM theory.

hep-ph↗

arXiv2016

Combined chiral and diquark fluctuations along QCD critical line and enhanced baryon production with parity doubling

We argue that there should exist the large combined fluctuations of chiral and diquark condensates along the phase boundary of QCD at moderately high density and relatively low temperature. Such fluctuations might lead to anomalous production of nucleons and its parity partner, which we propose to detect at NICA.

hep-ph↗

arXiv2015

Relativistic Causal Hydrodynamics Derived from Boltzmann Equation: a novel reduction theoretical approach

We derive the second-order hydrodynamic equation and the microscopic formulae of the relaxation times as well as the transport coefficients systematically from the relativistic Boltzmann equation. Our derivation is based on a novel development of the renormalization-group method, a powerful reduction theory of dynamical systems, which has been applied successfully to derive the non-relativistic second-order hydrodynamic equation Our theory nicely gives a compact expression of the deviation of the distribution function in terms of the linearized collision operator, which is different from those used as an ansatz in the conventional fourteen-moment method. It is confirmed that the resultant microscopic expressions of the transport coefficients coincide with those derived in the Chapman-Enskog expansion method. Furthermore, we show that the microscopic expressions of the relaxation times have natural and physically plausible forms. We prove that the propagating velocities of the fluctuations of the hydrodynamical variables do not exceed the light velocity, and hence our seconder-order equation ensures the desired causality. It is also confirmed that the equilibrium state is stable for any perturbation described by our equation.

hep-ph↗

arXiv2015

Parametric Instability of Classical Yang-Mills Fields in an Expanding Geometry

We investigate the instability of classical Yang-Mills field in an expanding geometry under a color magnetic background field within the linear regime. We consider homogeneous, boost-invariant and time-dependent color magnetic fields simulating the glasma configuration. We introduce the conformal coordinates which enable us to map an expanding problem approximately into a nonexpanding problem. We find that the fluctuations with finite longitudinal momenta can grow exponentially due to parametric instability. Fluctuations with finite transverse momenta can also show parametric instability, but their momenta are restricted to be small. The most unstable modes start to grow exponentially in the early stage of the dynamics and they may affect the thermalization in heavy-ion collisions.

hep-ph↗

arXiv2015

Study of entropy production in Yang-Mills theory with use of Husimi function

Understanding the thermalization process in a pure quantum system is a challenge in theoretical physics. In this work, we explore possible thermalization mechanism in Yang-Mills(YM) theory by using a positive semi-definite quantum distribution function called a Husimi function which is given by a coarse graining of the Wigner function within the minimum uncertainty. Then entropy is defined in terms of the Husimi function, which is called the Husimi-Wehrl(HW) entropy. We propose two numerical methods to calculate the HW entropy. We find that it is feasible to apply the semi-classical approximation with the use of classical YM equation. It should be noted that the semi-classical approximation is valid in the systems of physical interest including the early stage of heavy-ion collisions. Using a product ansatz for the Husimi function, which is confirmed to reproduce the HW entropy within 20% error (overestimate) for a few-body quantum system, we succeed in a numerical evaluation of HW entropy of YM fields and show that it surely has a finite value and increases in time.

hep-ph↗

arXiv2015

Entropy production in quantum Yang-Mills mechanics in semi-classical approximation

We discuss thermalization of isolated quantum systems by using the Husimi-Wehrl entropy evaluated in the semiclassical treatment. The Husimi-Wehrl entropy is the Wehrl entropy obtained by using the Husimi function for the phase space distribution. The time evolution of the Husimi function is given by smearing the Wigner function, whose time evolution is obtained in the semiclassical approximation. We show the efficiency and usefullness of this semiclassical treatment in describing entropy production of a couple of quantum mechanical systems, whose classical counter systems are known to be chaotic. We propose two methods to evaluate the time evolution of the Husimi-Wehrl entropy, the test-particle method and the two-step Monte-Carlo method. We demonstrate the characteristics of the two methods by numerical calculations, and show that the simultaneous application of the two methods ensures the reliability of the results of the Husimi-Wehrl entropy at a given time.

hep-ph↗

arXiv2015

Causal hydrodynamics from kinetic theory by doublet scheme in renormalization-group method

We develop a general framework in the renormalization-group (RG) method for extracting a mesoscopic dynamics from an evolution equation by incorporating some excited (fast) modes as additional components to the invariant manifold spanned by zero modes. We call this framework the doublet scheme. The validity of the doublet scheme is first tested and demonstrated by taking the Lorenz model as a simple three-dimensional dynamical system; it is shown that the two-dimensional reduced dynamics on the attractive manifold composed of the would-be zero and a fast modes are successfully obtained in a natural way. We then apply the doublet scheme to construct causal hydrodynamics as a mesoscopic dynamics of kinetic theory, i.e., the Boltzmann equation, in a systematic manner with no ad-hoc assumption. It is found that our equation has the same form as thirteen-moment causal hydrodynamic equation, but the microscopic formulae of the transport coefficients and relaxation times are different. In fact, in contrast to the Grad equation, our equation leads to the same expressions for the transport coefficients as given by the Chapman-Enskog expansion method and suggests novel formulae of the relaxation times expressed in terms of relaxation functions which allow a natural physical interpretation of the relaxation times. Furthermore, our theory nicely gives the explicit forms of the distribution function and the thirteen hydrodynamic variables in terms of the linearized collision operator, which in turn clearly suggest the proper ansatz forms of them to be adopted in the method of moments.

physics.flu-dyn↗

arXiv2015

Derivation of second-order relativistic hydrodynamics for reactive multi-component systems

We derive the second-order hydrodynamic equation for reactive multi-component systems from the relativistic Boltzmann equation. In the reactive system, particles can change their species under the restriction of the imposed conservation laws during the collision process. Our derivation is based on the renormalization group (RG) method, in which the Boltzmann equation is solved in an organized perturbation method as faithfully as possible and possible secular terms are resummed away by a suitable setting of the initial value of the distribution function. The microscopic formulae of the relaxation times and the lengths are explicitly given as well as those of the transport coefficients for the reactive multi-component system. The resultant hydrodynamic equation with these formulae has nice properties that it satisfies the positivity of the entropy production rate and the Onsager's reciprocal theorem, which ensure the validity of our derivation.

hep-ph↗

arXiv2015

Lattice QCD study of four-quark components of the isosinglet scalar mesons: Significance of disconnected diagrams

We study the possible significance of four-quark states in the iso-singlet scalar mesons ($J^{PC}=0^{++}$, $I=0$) by performing two-flavor full lattice QCD simulations on an $8^3 \times 16$ lattice using the improved gauge action and the clover-improved Wilson quark action. In particular, we evaluate the propagators of molecular and tetra-quark operators together with singly disconnected diagrams. In the computation of the singly disconnected diagrams we employ the $Z_2$-noise method with the truncated eigenmode approach. We show that the quark loops given by the disconnected diagrams play an essential role in propagators of tetraquark and molecular operators.

hep-lat↗