arXiv subjects

Eiji Nakano

Publications and source records attributed to Eiji Nakano.

At least 37 records · Page 2Linked to original sources

arXiv2016

BEC-Polaron gas in a boson-fermion mixture : a many-body extension of Lee-Low-Pines theory

We investigate the ground state properties of the gaseous mixture of a single species of bosons and fermions at zero temperature, where bosons are major in population over fermions, and form the Bose-Einstein condensate (BEC). The boson-boson and boson-fermion interactions are assumed to be weakly repulsive and attractive respectively, while the fermion-fermion interaction is absent due to the Pauli exclusion for the low energy $s$-wave scattering. We treat fermions as a gas of polarons dressed with Bogoliubov phonons, which is an elementary excitation of the BEC, and evaluate the ground state properties with the method developed by Lemmens, Devreese, and Brosens (LDB) originally for the electron polaron gas, and also with a general extension of the Lee-Low-Pines theory for many-body systems (eLLP), which incorporates the phonon drag effects as in the original LLP theory. The formulation of eLLP is developed and discussed in the present paper. The binding (interaction) energy of the polaron gas is calculated in these methods, and shown to be finite (negative) for the dilute gas of heavy fermions with attractive boson-fermion interactions, though the suppression by the many-body effects exists.

cond-mat.quant-gas↗

arXiv2015

Landau-Peierls instability in a Fulde-Ferrell type inhomogeneous chiral condensed phase

We investigate the stability of an inhomogeneous chiral condensed phase against low energy fluctuations about a spatially modulated order parameter. This phase corresponds to the so-called dual chiral density wave in the context of quark matter, where the chiral condensate is spatially modulated with a finite wavevector in a single direction. From the symmetry viewpoint, the phase realizes a locking of flavor and translational symmetries. Starting with a Landau-Ginzburg-Wilson effective Lagrangian, we find that the associated Nambu-Goldstone modes, whose dispersion relations are spatially anisotropic and soft in the direction normal to the wavevector of the modulation, wash out the long-range order at finite temperatures, but support algebraically decaying long-range correlations. This implies that the phase can exhibit a quasi-one-dimensional order as in liquid crystals.

hep-ph↗

arXiv2014

Bose-Einstein condensation and density collapse in a weakly coupled boson-fermion mixture

We investigate the mechanical instability toward density collapse and the transition temperature of Bose-Einstein condensation in the weakly coupled boson-fermion many-body mixture of single-component boson and fermion gases, in the case of the repulsive boson-boson and attractive boson-fermion interactions; no fermion-fermion interaction is assumed due to the Pauli exclusion because of the diluteness of the mixture. The mechanical instability occurs in the part of bosonic gas in the case where the induced boson-boson attraction mediated by the fermion polarization overcomes the boson-boson repulsive interaction at low temperatures. We calculate the onset temperature of the mechanical instability and the BEC transition temperature for the interaction strength and the boson-fermion number ratio. We also discuss the relation between the mechanical instability and the BEC transition using a diagrammatic method.

cond-mat.quant-gas↗

arXiv2014

Color Magnetism in Non-Abelian Vortex Matter

We propose color magnetism as a generalization of the ordinary Heisenberg (anti-)ferro magnets on a triangular lattice. Vortex matter consisting of an Abrikosov lattice of non-Abelian vortices with color magnetic fluxes shows a color ferro or anti-ferro magnetism, depending on the interaction among the vortex sites. A prime example is a non-Abelian vortex lattice in rotating dense quark matter, showing a color ferromagnetism. We show that the low-energy effective theory for the vortex lattice system in the color ferromagnetic phase is described by a 3+1 dimensional $CP^{N-1}$ nonlinear sigma model with spatially anisotropic couplings. We identify gapless excitations independent from Tkachenko modes as color magnons, that is, Nambu-Goldstone modes propagating in the vortex lattice with an anisotropic linear dispersion relation $ω_p^2 = c_{xy}^2(p_x^2+p_y^2) + c_z^2 p_z^2$. We calculate the transition temperature between the ordered and disordered phases, and apply it to dense quark matter. We also identify the order parameter spaces for color anti-ferromagnets.

hep-ph↗

arXiv2012

Transport coefficients of O(N) scalar field theories close to the critical point

We investigate the critical dynamics of O(N)-symmetric scalar field theories to determine the critical exponents of transport coefficients as a second-order phase transition is approached from the symmetric phase. A set of stochastic equations of motion for the slow modes is formulated, and the long wavelength dynamics is examined for an arbitrary number of field components, $N$, in the framework of the dynamical renormalization group within the $ε$ expansion. We find that for a single component scalar field theory, N=1, the system reduces to the model C of critical dynamics, whereas for $N>1$ the model G is effectively restored owing to dominance of O(N)-symmetric charge fluctuations. In both cases, the shear viscosity remains finite in the critical region. On the other hand, we find that the bulk viscosity diverges as the correlation length squared, for N=1, while it remains finite for $N>1$.

hep-ph↗

arXiv2011

Analytical study of critical magnetic field in a holographic superconductor

We analytically sutdy the effect of external magnetic field in a Holographic superconductor by using Sturm-Liouville method. We estimate the coefficient of proportionality at critical temperature and find its denpendence on external magnetic field. By exploring phase diagrams of critical temperature and magnetic field for various condensates, we conclude that a Meissner-like effect is a general feature in Holographic superconductors. We also study the quantum phase transition at zero temperature and find that critical charge density increases linearly with the condensate dimension.

hep-th↗

arXiv2009

Color Magnetic Flux Tubes in Dense QCD. II: Effective World-Sheet Theory

Color magnetic flux tubes appear in the color-flavor locked phase of high density QCD, which exhibits color superconductivity as well as superfluidity. They are non-Abelian superfluid vortices and are accompanied by orientational zero modes in the internal space associated with the color-flavor locked symmetry spontaneously broken in the presence of the vortex. We show that those zero modes are localized around the vortex in spite of the logarithmic divergence of its tension, and derive the low-energy effective theory of them on the world-sheet of the vortex-string.

hep-ph↗

arXiv2009

Non-Abelian Global Vortices

We study topologically stable non-Abelian global vortices in the U(N) linear sigma model. The profile functions of the solutions are numerically obtained. We investigate the behaviour of vortices in two limits in which masses of traceless or trace parts of massive bosons are much larger than the others. In the limit that the traceless parts are much heavier, we find a somewhat bizarre vortex solution carrying a non-integer U(1) winding number 1/\sqrt{N} which is irrational in general.

hep-ph↗

arXiv2009

Interactions of Non-Abelian Global Strings

Non-Abelian global strings are expected to form during the chiral phase transition. They have orientational zero modes in the internal space, associated with the vector-like symmetry SU(N)_{L+R} broken in the presence of strings. The interaction among two parallel non-Abelian global strings is derived for general relative orientational zero modes, giving a non-Abelian generalization of the Magnus force. It is shown that when the orientations of the strings are the same, the repulsive force reaches the maximum, whereas when the relative orientation becomes the maximum, no force exists between the strings. For the Abelian case we find a finite volume correction to the known result. The marginal instability of the previously known Abelian eta' strings is discussed.

hep-ph↗

arXiv2008

Phase Transitions and the Perfectness of Fluids

We calculate the ratio eta/s, the shear viscosity (eta) to entropy density (s), which characterizes how perfect a fluid is, in weakly coupled real scalar field theories with different types of phase transitions. The mean-field results of the eta/s behaviors agree with the empirical observations in atomic and molecular systems such as water, He, N, and all the matters with data available in the NIST database. These behaviors are expected to be the same in N component scalar theories with an O(N) symmetry. We speculate these eta/s behaviors are general properties of fluid shared by QCD and cold atoms. Finally, we clarify some issues regarding counterexamples of the conjectured universal eta/s bound found in Refs.[16,17].

hep-ph↗

arXiv2008

Non-Abelian Strings in Hot or Dense QCD

Different types of non-Abelian vortex-strings appear in dense or hot QCD, both of which possess non-Abelian internal orientation zero modes. We calculate the interaction between them and find the universal repulsion for dense QCD (color superconductivity) and the dependence on the orientations for hot QCD (chirally broken phase). This is a review article based on our papers arXiv:0708.4092 and arXiv:0708.4096.

hep-ph↗

arXiv2008

Critical magnetic field in AdS/CFT superconductor

We have studied a holographically dual description of superconductor in (2+1)-dimensions in the presence of applied magnetic field, and observed that there exists a critical value of magnetic field, below which a charged condensate can form via a second order phase transition.

hep-th↗

arXiv2008

Drag Force, Jet Quenching, and AdS/QCD

In this note, two important transport observables in the RHIC experiment, relaxation time constant and jet quenching parameter, are calculated from an AdS/QCD model. A quark moving in the viscous medium such as the Quark-Gluon-Plasma is modelled by an open string whose end point travels on the boundary of a deformed AdS_5 black hole. The correction introduced via the deformed AdS_5 is believed to help us better understand the data which is expected to be measured in the RHIC.

hep-ph↗

arXiv2007

Non-Abelian Strings in High Density QCD: Zero Modes and Interactions

The most fundamental strings in high density color superconductivity are the non-Abelian semi-superfluid strings which have color gauge flux tube but behave as superfluid vortices in the energetic point of view. We show that in addition to the usual translational zero modes, these vortices have normalizable orientational zero modes in the internal space, associated with the color-flavor locking symmetry broken in the presence of the strings. The interaction among two parallel non-Abelian semi-superfluid strings is derived for general relative orientational zero modes to show the universal repulsion. This implies that the previously known superfluid vortices, formed by spontaneously broken U(1)_B, are unstable to decay. Moreover, our result proves the stability of color superconductors in the presence of external color gauge fields.

hep-ph↗

arXiv2007

QCD Viscosity to Entropy Density Ratio in the Hadronic Phase

Shear viscosity (eta) of QCD in the hadronic phase is computed by the coupled Boltzmann equations of pions and nucleons in low temperatures and low baryon number densities. The eta to entropy density ratio eta/s maps out the nuclear gas-liquid phase transition by forming a valley tracing the phase transition line in the temperature-chemical potential plane. When the phase transition turns into a crossover, the eta/s valley gradually disappears. We suspect the general feature for a first-order phase transition is that eta/s has a discontinuity in the bottom of the eta/s valley. The discontinuity coincides with the phase transition line and ends at the critical point. Beyond the critical point, a smooth eta/s valley is seen. However, the valley could disappear further away from the critical point. The eta/s measurements might provide an alternative to identify the critical points.

hep-ph↗

arXiv2007

Shear viscosity of pion gas

Using chiral perturbation theory we investigate the QCD shear viscosity ($η$) to entropy density ($s$) ratio below the deconfinement temperature ($\sim 170$ MeV) with zero baryon number density. It is found that $η/s$ of QCD is monotonically decreasing in temperature ($T$) and reaches 0.6 with estimated $\sim 50%$ uncertainty at T=120 MeV. A naive extrapolation of the leading order result shows that $η/s$ reaches the $1/4π$ minimum bound proposed by Kovtun, Son, and Starinets using string theory methods at $T\sim 210$ MeV. This suggests a phase transition or cross over might occur at $T\lesssim 210$ MeV in order for the bound to remain valid. Also, it is natural for $η/s$ to stay close to the minimum bound around the phase transition temperature as was recently found in heavy ion collisions.

hep-ph↗

arXiv2006

BEC-BCS Crossover in the Epsilon Expansion

The epsilon expansion (expansion around four spacial dimensions) developed by Nishida and Son for a cold fermi gas with infinite scattering length is extended to finite scattering length to study the BEC-BCS crossover. A resummation of higher order logarithms and a suitable extension of fermion coupling in d-dimensions are developed in order to apply the theory in the BCS regime. The ratio between the chemical potential and the Fermi energy, mu/eF, is computed to next-to-leading order in the epsilon expansion as a function of eta=1/(a kF), where a is the scattering length and kF is the Fermi momentum in a non-interacting system. Near the unitarity limit eta->0, we found mu/eF=0.475-0.707 eta-0.5 eta^2. Near the BEC limit eta->infinity, mu/eF=0.062/eta - eta^2, while near the BCS limit eta->-infinity, mu/eF=1+0.707/eta. Overall good agreement with Quantum Monte Carlo results is found.

cond-mat.other↗

arXiv2006

Shear Viscosity to Entropy Density Ratio of QCD below the Deconfinement Temperature

Using chiral perturbation theory we investigate the QCD shear viscosity to entropy density ratio below the deconfinement temperature (~170 MeV) with zero baryon number density. It is found that the viscosity to entropy density ratio of QCD is monotonically decreasing in temperature (T) and reaches 0.6 with estimated ~50% uncertainty at T=120 MeV. A naive extrapolation of the leading order result shows that the ratio reaches the 1/(4 pi) minimum bound proposed by Kovtun, Son, and Starinets using string theory methods at T~200 MeV. This suggests a phase transition or cross over might occur at T less than 200 MeV in order for the bound to remain valid. Also, it is natural for the ratio to stay close to the minimum bound around the phase transition temperature as was recently found in heavy ion collisions.

hep-ph↗