arXiv subjects

Yuta Kikuchi

Publications and source records attributed to Yuta Kikuchi.

47 records · Page 3Linked to original sources

arXiv2017

Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics

An 't Hooft anomaly is the obstruction for gauging symmetries, and it constrains possible low-energy behaviors of quantum field theories by excluding trivial infrared theories. Global inconsistency condition is recently proposed as a milder condition but is expected to play an almost same role by comparing high symmetry points in the theory space. In order to clarify the consequence coming from this new condition, we discuss several quantum mechanical models with topological angles and explicitly compute their energy spectra. It turns out that the global inconsistency can be saturated not only by the ground-state degeneracy at either of high symmetry points but also by the level crossing (phase transition) separating those high symmetry points.

hep-th↗

arXiv2017

Topological Properties of the Chiral Magnetic Effect in Multi-Weyl Semimetals

We compute the chiral magnetic effect (CME) in multi-Weyl semimetals (multi-WSMs) based on the chiral kinetic theory. Multi-WSMs are WSMs with multiple monopole charges that have nonlinear and anisotropic dispersion relations near Weyl points, and we need to extend conventional computation of CME in WSMs with linear dispersion relations. Topological properties of CME in multi-WSMs are investigated in details for not only static magnetic fields but also time-dependent (dynamic) ones. We propose an experimental setup to measure the multiple monopole charge via the topological nature hidden in the dynamic CME.

cond-mat.mes-hall↗

arXiv2017

Neural Sequence Model Training via $α$-divergence Minimization

We propose a new neural sequence model training method in which the objective function is defined by $α$-divergence. We demonstrate that the objective function generalizes the maximum-likelihood (ML)-based and reinforcement learning (RL)-based objective functions as special cases (i.e., ML corresponds to $α\to 0$ and RL to $α\to1$). We also show that the gradient of the objective function can be considered a mixture of ML- and RL-based objective gradients. The experimental results of a machine translation task show that minimizing the objective function with $α> 0$ outperforms $α\to 0$, which corresponds to ML-based methods.

stat.ML↗

arXiv2017

Vacuum structure of bifundamental gauge theories at finite topological angles

We discuss possible vacuum structures of $SU(n)\times SU(n)$ gauge theories with bifundamental matters at finite $θ$ angles. In order to give a precise constraint, a mixed 't Hooft anomaly is studied in detail by gauging the center $\mathbb{Z}_n$ one-form symmetry of the bifundamental gauge theory. We propose phase diagrams that are consistent with the constraints, and also give a heuristic explanation of the result based on the dual superconductor scenario of confinement.

hep-th↗

arXiv2016

Controlling Output Length in Neural Encoder-Decoders

Neural encoder-decoder models have shown great success in many sequence generation tasks. However, previous work has not investigated situations in which we would like to control the length of encoder-decoder outputs. This capability is crucial for applications such as text summarization, in which we have to generate concise summaries with a desired length. In this paper, we propose methods for controlling the output sequence length for neural encoder-decoder models: two decoding-based methods and two learning-based methods. Results show that our learning-based methods have the capability to control length without degrading summary quality in a summarization task.

cs.CL↗

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

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↗

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

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↗