arXiv subjects

Yoshiyuki Y. Yamaguchi

Publications and source records attributed to Yoshiyuki Y. Yamaguchi.

At least 37 records · Page 2Linked to original sources

arXiv2017

Nondivergent and negative susceptibilities around critical points of a long-range Hamiltonian system with two order parameters

The linear response is investigated in a long-range Hamiltonian system from the view point of dynamics, which is described by the Vlasov equation in the limit of large population. Due to existence of the Casimir invariants of the Vlasov dynamics, an external field does not drive the system to the forced thermal equilibrium in general, and the linear response is suppressed. With the aid of a linear response theory based on the Vlasov dynamics, we compute the suppressed linear response in a system having two order parameters, which introduce the conjugate two external fields and the susceptibility matrix of size two accordingly. Moreover, the two order parameters bring three phases and the three types of second-order phase transitions between two of them. For each type of the phase transitions, all the critical exponents for elements of the susceptibility matrix are computed. The critical exponents reveal that some elements of the matrices do not diverge even at critical points, while the mean-field theory predicts divergences. The linear response theory also suggests appearance of negative off-diagonal elements, in other words, an applied external field decreases the value of an order parameter. These theoretical predictions are confirmed by direct numerical simulations of the Vlasov equation.

cond-mat.stat-mech↗

arXiv2016

Absence of thermalization for systems with long-range interactions coupled to a thermal bath

We investigate the dynamics of a small long-range interacting system, in contact with a large long-range thermal bath. Our analysis reveals the existence of striking anomalies in the energy flux between the bath and the system. In particular, we find that the evolution of the system is not influenced by the kinetic temperature of the bath, as opposed to what happens for short-range collisional systems. As a consequence, the system may get hotter also when its initial temperature is larger than the bath temperature. This observation is explained quantitatively in the framework of the collisionless Vlasov description of toy models with long-range interactions and shown to be valid whenever the Vlasov picture applies, from cosmology to plasma physics.

cond-mat.stat-mech↗

arXiv2016

Nonstandard transitions in the Kuramoto model: A role of asymmetry in natural frequency distributions

We study transitions in the Kuramoto model by shedding light on asymmetry in the natural frequency distribution, which has been assumed to be symmetric in many previous studies. The asymmetry brings two nonstandard bifurcation diagrams, with the aid of bimodality. The first diagram consists of stationary states, and has the standard continuous synchronization transition and a subsequent discontinuous transition as the coupling strength increases. Such a bifurcation diagram has been also reported in a variant model, which breaks the odd symmetry of the coupling function by introducing the phase lag. The second diagram includes the oscillatory state emerging from the partially synchronized state and followed by a discontinuous transition. This diagram is firstly revealed in this study. The two bifurcation diagrams are obtained by employing the Ott-Antonsen ansatz, and are verified by direct $N$-body simulations. We conclude that the asymmetry in distribution, with the bimodality, plays a similar role to the phase lag, and diversifies the transitions.

nlin.AO↗

arXiv2016

Strange Scaling and Temporal Evolution of Finite-Size Fluctuation in Thermal Equilibrium

We numerically exhibit strange scaling and temporal evolution of finite-size fluctuation in thermal equilibrium of a simple long-range interacting system. These phenomena are explained from the view point of existence of the Casimirs and their nonexactness in finite-size systems, where the Casimirs are invariants in the Vlasov dynamics describing the long-range systems in the limit of large population. This explanation expects appearance of the reported phenomena in a wide class of isolated long-range systems. The scaling theory is also discussed as an application of the strange scaling.

cond-mat.stat-mech↗

arXiv2015

Conditions for predicting quasistationary states by rearrangement formula

Predicting the long-lasting quasistationary state for a given initial state is one of central issues in Hamiltonian systems having long-range interaction. A recently proposed method is based on the Vlasov description and uniformly redistributes the initial distribution along contours of the asymptotic effective Hamiltonian, which is defined by the obtained quasistationary state and is determined self-consistently. The method, to which we refer as the rearrangement formula, was suggested to give precise prediction under limited situations. Restricting initial states consisting of spatially homogeneous part and small perturbation, we numerically reveal two conditions that the rearrangement formula prefers: One is no Landau damping condition for unperturbed homogeneous part, and the other comes from the Casimir invariants. Mechanisms of these conditions are discussed. Clarifying these conditions, we inform validity to use the rearrangement formula as the response theory for an external field, and we shed light on improving the theory as a nonequilibrium statistical mechanics.

cond-mat.stat-mech↗

arXiv2015

Non-diagonalizable and non-divergent susceptibility tensor in the Hamiltonian mean-field model with asymmetric momentum distributions

We investigate response to an external magnetic field in the Hamiltonian mean-field model, which is a paradigmatic toy model of a ferromagnetic body and consists of plane rotators like the XY spins. Due to long-range interactions, the external field drives the system to a long-lasting quasistationary state before reaching thermal equilibrium, and the susceptibility tensor obtained in the quasista- tionary state is predicted by a linear response theory based on the Vlasov equation. For spatially homogeneous stable states, whose momentum distributions are asymmetric with zero-means, the theory reveals that the susceptibility tensor for an asymptotically constant external field is neither symmetric nor diagonalizable, and the predicted states are not stationary accordingly. Moreover, the tensor has no divergence even at the stability threshold. These theoretical findings are confirmed by direct numerical simulations of the Vlasov equation for the skew-normal distribution functions.

cond-mat.stat-mech↗

arXiv2015

Landau like theory for universality of critical exponents in quasistatioary states of isolated mean-field systems

An external force dynamically drives an isolated mean-field Hamiltonian system to a long-lasting quasistationary state, whose lifetime increases with population of the system. For second order phase transitions in quasistationary states, two non-classical critical exponents have been reported individually by using a linear and a nonlinear response theories in a toy model. We provide a simple way to compute the critical exponents all at once, which is an analog of the Landau theory. The present theory extends universality class of the non-classical exponents to spatially periodic one-dimensional systems, and shows that the exponents satisfy a classical scaling relation inevitably by using a key scaling of momentum.

cond-mat.stat-mech↗

arXiv2014

Nonlinear response for external field and perturbation in the Vlasov system

A nonlinear response theory is provided by use of the transient linearization method in the spatially one-dimensional Vlasov systems. The theory inclusively gives responses to external fields and to perturbations for initial stationary states, and is applicable even to the critical point of a second order phase transition. We apply the theory to the Hamiltonian mean-field model, a toy model of a ferromagnetic body, and investigate the critical exponent associated with the response to the external field at the critical point in particular. The obtained critical exponent is nonclassical value 3/2, while the classical value is 3. However, interestingly, one scaling relation holds with another nonclassical critical exponent of susceptibility in the isolated Vlasov systems. Validity of the theory is numerically confirmed by directly simulating temporal evolutions of the Vlasov equation.

cond-mat.stat-mech↗

arXiv2014

Non-mean-field Critical Exponent in a Mean-field Model : Dynamics versus Statistical Mechanics

The mean-field theory tells that the classical critical exponent of susceptibility is the twice of that of magnetization. However, the linear response theory based on the Vlasov equation, which is naturally introduced by the mean-field nature, makes the former exponent half of the latter for families of quasistationary states having second order phase transitions in the Hamiltonian mean-field model and its variances. We clarify that this strange exponent is due to existence of Casimir invariants which trap the system in a quasistationary state for a time scale diverging with the system size. The theoretical prediction is numerically confirmed by $N$-body simulations for the equilibrium states and a family of quasistationary states.

cond-mat.stat-mech↗

arXiv2014

Dynamical pattern formations in two dimensional fluid and Landau pole bifurcation

A phenomenological theory is proposed to analyze the asymptotic dynamics of perturbed inviscid Kolmogorov shear flows in two dimensions. The phase diagram provided by the theory is in qualitative agreement with numerical observations, which include three phases depending on the aspect ratio of the domain and the size of the perturbation: a steady shear flow, a stationary dipole, and four traveling vortices. The theory is based on a precise study of the inviscid damping of the linearized equation and on an analysis of nonlinear effects. In particular, we show that the dominant Landau pole controlling the inviscid damping undergoes a bifurcation, which has important consequences on the asymptotic fate of the perturbation.

physics.flu-dyn↗

arXiv2013

On the neighborhood of an inhomogeneous stable stationary solution of the Vlasov equation - Case of the Hamiltonian mean-field model

We consider the one-dimensional Vlasov equation with an attractive cosine potential, and its non homogeneous stationary states that are decreasing functions of the energy. We show that in the Sobolev space $W^{1,p}$ ($p>2$) neighborhood of such a state, all stationary states that are decreasing functions of the energy are stable. This is in sharp contrast with the situation for homogeneous stationary states of a Vlasov equation, where a control over strictly more than one derivative is needed to ensure the absence of unstable stationary states in a neighborhood of a reference stationary state [Z.Lin and C.Zeng, Comm.Math.Phys. {\bf 306}, 291-331 (2011)].

math-ph↗

arXiv2011

Algebraic damping in the one-dimensional Vlasov equation

We investigate the asymptotic behavior of a perturbation around a spatially non homogeneous stable stationary state of a one-dimensional Vlasov equation. Under general hypotheses, after transient exponential Landau damping, a perturbation evolving according to the linearized Vlasov equation decays algebraically with the exponent -2 and a well defined frequency. The theoretical results are successfully tested against numerical $N$-body simulations, corresponding to the full Vlasov dynamics in the large $N$ limit, in the case of the Hamiltonian mean-field model. For this purpose, we use a weighted particles code, which allows us to reduce finite size fluctuations and to observe the asymptotic decay in the $N$-body simulations.

math-ph↗

arXiv2007

Out-of-equilibrium tricritical point in a system with long-range interactions

Systems with long-range interactions display a short-time relaxation towards Quasi Stationary States (QSSs) whose lifetime increases with system size. With reference to the Hamiltonian Mean Field (HMF) model, we here show that a maximum entropy principle, based on Lynden-Bell's pioneering idea of "violent relaxation", predicts the presence of out-of-equilibrium phase transitions separating the relaxation towards homogeneous (zero magnetization) or inhomogeneous (non zero magnetization) QSSs. When varying the initial condition within a family of "water-bags" with different initial magnetization and energy, first and second order phase transition lines are found that merge at an out--of--equilibrium tricritical point. Metastability is theoretically predicted and numerically checked around the first-order phase transition line.

cond-mat.stat-mech↗

arXiv2005

Non-Universal Finite Size Effects with Universal Infinite-Size Free Energy for the $α$-XY model

We study finite size effects in a family of systems in which a parameter controls interaction-range. In the long-range regime where the infinite-size free energy is universal, we show that the finite size effects are not universal but depend on the interaction-range. The finite size effects are observed through discrepancies between time-averages of macroscopic variables in Hamiltonian dynamics and canonical averages of ones with infinite degrees of freedom. For a high energy regime, the relation to a pair of the discrepancies is theoretically predicted and numerically confirmed. We also numerically show that the finite-size effects of macroscopic variables in the canonical ensemble are close to ones in the dynamical systems.

cond-mat.stat-mech↗

arXiv2005

The Vlasov equation and the Hamiltonian Mean-Field model

We show that the quasi-stationary states observed in the $N$-particle dynamics of the Hamiltonian Mean-Field (HMF) model are nothing but Vlasov stable homogeneous (zero magnetization) states. There is an infinity of Vlasov stable homogeneous states corresponding to different initial momentum distributions. Tsallis $q$-exponentials in momentum, homogeneous in angle, distribution functions are possible, however, they are not special in any respect, among an infinity of others. All Vlasov stable homogeneous states lose their stability because of finite $N$ effects and, after a relaxation time diverging with a power-law of the number of particles, the system converges to the Boltzmann-Gibbs equilibrium.

cond-mat.stat-mech↗

arXiv2001

New renormalization procedure for perturbed ordinally differential equations with given initial condition and prescribed secular terms

For perturbed ordinally differential equations, a procedure of renormalization group method is proposed. To uniquely obtain renormalized solutions for given initial conditions, the procedure assumes that the extra integral constants yielded by perturbative expansion are determined as they cancel out all the prescribed secular terms. A sufficient condition for the renormalized solutions coinciding with exact solutions is also stated.

nlin.CD↗

arXiv1999

Renormalization of Long-wavelength Solution of Einstein Equation

Using the renormalization group method, we improved the first order solution of the long-wavelength expansion of the Einstein equation. By assuming that the renormalization group transformation has the property of Lie group, we can regularize the secular divergence caused by the spatial gradient terms and absorb it to the background seed metric. The solution of the renormalization group equation shows that the renormalized metric describes the behavior of gravitational collapse in the expanding universe qualitatively well.

gr-qc↗

arXiv1999

Renormalization group method and canonical perturbation theory

Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action variables. We show that the renormalization group method gives the same approximate solutions as canonical perturbation theory up to the second order of a small parameter with action-angle coordinates.

chao-dyn↗