arXiv subjects

Doochul Kim

Publications and source records attributed to Doochul Kim.

At least 19 recordsLinked to original sources

arXiv2014

Ground state energy of $q$-state Potts model: the minimum modularity

A wide range of interacting systems can be described by complex networks. A common feature of such networks is that they consist of several communities or modules, the degree of which may quantified as the \emph{modularity}. However, even a random uncorrelated network, which has no obvious modular structure, has a finite modularity due to the quenched disorder. For this reason, the modularity of a given network is meaningful only when it is compared with that of a randomized network with the same degree distribution. In this context, it is important to calculate the modularity of a random uncorrelated network with an arbitrary degree distribution. The modularity of a random network has been calculated [Phys. Rev. E \textbf{76}, 015102 (2007)]; however, this was limited to the case whereby the network was assumed to have only two communities, and it is evident that the modularity should be calculated in general with $q(\geq 2)$ communities. Here, we calculate the modularity for $q$ communities by evaluating the ground state energy of the $q$-state Potts Hamiltonian, based on replica symmetric solutions assuming that the mean degree is large. We found that the modularity is proportional to $\langle \sqrt{k} \rangle / \langle k \rangle$ regardless of $q$ and that only the coefficient depends on $q$. In particular, when the degree distribution follows a power law, the modularity is proportional to $\langle k \rangle^{-1/2}$. Our analytical results are confirmed by comparison with numerical simulations. Therefore, our results can be used as reference values for real-world networks.

cond-mat.stat-mech↗

arXiv2006

Universal fluctuation of the average height in the early-time regime of the one-dimensional Kardar-Parisi-Zhang-type growth

The statistics of the average height fluctuation of the one-dimensional Kardar-Parisi-Zhang(KPZ)-type surface is investigated. Guided by the idea of local stationarity, we derive the scaling form of the characteristic function in the early-time regime, $t\ll N^{3/2}$ with $t$ time and $N$ the system size, from the known characteristic function in the stationary state ($t\gg N^{3/2}$) of the single-step model derivable from a Bethe Ansatz solution, and thereby find the scaling properties of the cumulants and the large deviation function in the early-time regime. These results, combined with the scaling analysis of the KPZ equation, imply the existence of the universal scaling functions for the cumulants and an universal large deviation function. The analytic predictions are supported by the simulation results for two different models.

cond-mat.stat-mech↗

arXiv2005

Spontaneous Symmetry Breaking of Population between Two Dynamic Attractors in a Driven Atomic Trap: Ising-class Phase Transition

We have observed spontaneous symmetry breaking of atomic populations in the dynamic phase-space double-potential system, which is produced in the parametrically driven magneto-optical trap of atoms. We find that the system exhibits similar characteristics of the Ising-class phase transition and the critical value of the control parameter, which is the total atomic number, can be calculated. In particular, the collective effect of the laser shadow becomes dominant at large atomic number, which is responsible for the population asymmetry of the dynamic two-state system. This study may be useful for investigation of dynamic phase transition and temporal behaviour of critical phenomena.

physics.atom-ph↗

arXiv2004

Mechanical restriction versus human overreaction triggering congested traffic states

A new cellular automaton (CA) traffic model is presented. The focus is on mechanical restrictions of vehicles realized by limited acceleration and deceleration capabilities. These features are incorporated into the model in order to construct the condition of collision-free movement. The strict collision-free criterion imposed by the mechanical restrictions is softened in certain traffic situations, reflecting human overreaction. It is shown that the present model reliably reproduces most empirical findings including synchronized flow, the so-called {\it pinch effect}, and the time-headway distribution of free flow. The findings suggest that many free flow phenomena can be attributed to the platoon formation of vehicles ({\it platoon effect})

cond-mat.stat-mech↗

arXiv2002

Derivation of continuum stochastic equations for discrete growth models

We present a formalism to derive the stochastic differential equations (SDEs) for several solid-on-solid growth models. Our formalism begins with a mapping of the microscopic dynamics of growth models onto the particle systems with reactions and diffusion. We then write the master equations for these corresponding particle systems and find the SDEs for the particle densities. Finally, by connecting the particle densities with the growth heights, we derive the SDEs for the height variables. Applying this formalism to discrete growth models, we find the Edwards-Wilkinson equation for the symmetric body-centered solid-on-solid (BCSOS) model, the Kardar-Parisi-Zhang equation for the asymmetric BCSOS model and the generalized restricted solid-on-solid (RSOS) model, and the Villain--Lai--Das Sarma equation for the conserved RSOS model. In addition to the consistent forms of equations for growth models, we also obtain the coefficients associated with the SDEs.

cond-mat.stat-mech↗

arXiv2002

Universality class of the restricted solid-on-solid model with hopping

We study the restricted solid-on-solid (RSOS) model with finite hopping distance $l_{0}$, using both analytical and numerical methods. Analytically, we use the hard-core bosonic field theory developed by the authors [Phys. Rev. E {\bf 62}, 7642 (2000)] and derive the Villain-Lai-Das Sarma (VLD) equation for the $l_{0}=\infty$ case which corresponds to the conserved RSOS (CRSOS) model and the Kardar-Parisi-Zhang (KPZ) equation for all finite values of $l_{0}$. Consequently, we find that the CRSOS model belongs to the VLD universality class and the RSOS models with any finite hopping distance belong to the KPZ universality class. There is no phase transition at a certain finite hopping distance contrary to the previous result. We confirm the analytic results using the Monte Carlo simulations for several values of the finite hopping distance.

cond-mat.stat-mech↗

arXiv2001

Phase diagram of a Disordered Boson Hubbard Model in Two Dimensions

We study the zero-temperature phase transition of a two-dimensional disordered boson Hubbard model. The phase diagram of this model is constructed in terms of the disorder strength and the chemical potential. Via quantum Monte Carlo simulations, we find a multicritical line separating the weak-disorder regime, where a random potential is irrelevant, from the strong-disorder regime. In the weak-disorder regime, the Mott-insulator-to-superfluid transition occurs, while, in the strong-disorder regime, the Bose-glass-to-superfluid transition occurs. On the multicritical line, the insulator-to-superfluid transition has the dynamical critical exponent $z=1.35 \pm 0.05$ and the correlation length critical exponent $ν=0.67 \pm 0.03$, that are different from the values for the transitions off the line. We suggest that the proliferation of the particle-hole pairs screens out the weak disorder effects.

cond-mat.dis-nn↗

arXiv2001

Anomalous Roughness, Localization, and Globally Constrained Random Walks

The scaling properties of a random walker subject to the global constraint that it needs to visit each site an even number of times are determined. Such walks are realized in the equilibrium state of one dimensional surfaces that are subject to dissociative dimer-type surface dynamics. Moreover, they can be mapped onto unconstrained random walks on a random surface, and the latter corresponds to a non-Hermitian random free fermion model which describes electron localization near a band edge. We show analytically that the dynamic exponent of this random walk is $z=d+2$ in spatial dimension $d$. This explains the anomalous roughness, with exponent $α=1/3$, in one dimensional equilibrium surfaces with dissociative dimer-type dynamics.

cond-mat.stat-mech↗

arXiv2001

Bethe Ansatz Solutions and Excitation Gap of the Attractive Bose-Hubbard Model

The energy gap between the ground state and the first excited state of the one-dimensional attractive Bose-Hubbard Hamiltonian is investigated in connection with directed polymers in random media. The excitation gap Δis obtained by exact diagonalization of the Hamiltonian in the two- and three-particle sectors and also by an exact Bethe Ansatz solution in the two-particle sector. The dynamic exponent z is found to be 2. However, in the intermediate range of the size L where UL~O(1), U being the attractive interaction, the effective dynamic exponent shows an anomalous peak reaching high values of 2.4 and 2.7 for the two- and the three-particle sectors, respectively. The anomalous behavior is related to a change in the sign of the first excited-state energy. In the two-particle sector, we use the Bethe Ansatz solution to obtain the effective dynamic exponent as a function of the scaling variable UL/π. The continuum version, the attractive delta-function Bose-gas Hamiltonian, is integrable by the Bethe Ansatz with suitable quantum numbers, the distributions of which are not known in general. Quantum numbers are proposed for the first excited state and are confirmed numerically for an arbitrary number of particles.

cond-mat.stat-mech↗

arXiv2001

Two-point correlation functions of the diffusion-limited annihilation in one dimension

Two-point density-density correlation functions for the diffusive binary reaction system $A+A\to\emptyset$ are obtained in one dimension via Monte Carlo simulation. The long-time behavior of these correlation functions clearly deviates from that of a recent analytical prediction of Bares and Mobilia [Phys. Rev. Lett. {\bf 83}, 5214 (1999)]. An alternative expression for the asymptotic behavior is conjectured from numerical data.

cond-mat.stat-mech↗

arXiv2000

Path-Integral Formulation of Stochastic Processes for the Exclusive Particle Systems

We present the systematic formalism to derive the path-integral formulation for the hard-core particle systems far from equilibrium. Writing the master equation for a stochastic process of the system in terms of the annihilation and creation operators with the mixed commutation relations, we find the Kramers-Moyal coefficients for the corresponding Fokker-Planck equation (FPE) and the stochastic differential equation (SDE) is derived by connecting these coefficients in the FPE to those in the SDE. Finally, the SDE is mapped onto the field-theory using the path-integral, giving the field-theoretic action which may be analyzed by the renormalization group method. We apply this formalism to the two-species reaction-diffusion system with the drift, finding a universal decay expoent for the long-time behavior of the average concentration of particles in arbitrary dimensions.

cond-mat.stat-mech↗

arXiv2000

Origin of the singular Bethe ansatz solutions for the Heisenberg XXZ spin chain

We investigate symmetry properties of the Bethe ansatz wave functions for the Heisenberg $XXZ$ spin chain. The $XXZ$ Hamiltonian commutes simultaneously with the shift operator $T$ and the lattice inversion operator $V$ in the space of $Ω=\pm 1$ with $Ω$ the eigenvalue of $T$. We show that the Bethe ansatz solutions with normalizable wave functions cannot be the eigenstates of $T$ and $V$ with quantum number $(Ω,Υ)=(\pm 1,\mp 1)$ where $Υ$ is the eigenvalue of $V$. Therefore the Bethe ansatz wave functions should be singular for nondegenerate eigenstates of the Hamiltonian with quantum number $(Ω,Υ)=(\pm 1,\mp 1)$. It is also shown that such states exist in any nontrivial down-spin number sector and that the number of them diverges exponentially with the chain length.

cond-mat.stat-mech↗

arXiv2000

Comment on ``Solution of Classical Stochastic One-Dimensional Many-Body Systems''

In a recent Letter, Bares and Mobilia proposed the method to find solutions of the stochastic evolution operator $H=H_0 + {γ\over L} H_1$ with a non-trivial quartic term $H_1$. They claim, ``Because of the conservation of probability, an analog of the Wick theorem applies and all multipoint correlation functions can be computed.'' Using the Wick theorem, they expressed the density correlation functions as solutions of a closed set of integro-differential equations. In this Comment, however, we show that applicability of Wick theorem is restricted to the case $γ= 0$ only.

cond-mat.stat-mech↗

arXiv1999

Large Deviation Function of the Partially Asymmetric Exclusion Process

The large deviation function obtained recently by Derrida and Lebowitz for the totally asymmetric exclusion process is generalized to the partially asymmetric case in the scaling limit. The asymmetry parameter rescales the scaling variable in a simple way. The finite-size corrections to the universal scaling function and the universal cumulant ratio are also obtained to the leading order.

cond-mat.stat-mech↗

arXiv1999

Possibility of direct Mott insulator-to-superfluid transitions in weakly disordered boson systems

We study the zero-temperature phase transitions of a two-dimensional disordered boson Hubbard model at incommensurate boson densities. Via matrix diagonalization and quantum Monte Carlo simulations, we construct the phase diagram and evaluate the correlation length exponent nu. In the presence of weak disorder, we obtain nu=0.5 +- 0.1, the same value as that in the pure model, near the tip of a Mott insulator lobe, using the dynamical critical exponent z=2. As the strength of disorder is increased beyond a certain value, however, the value of nu is found to change to 0.9 +- 0.1. This result strongly suggests that there exist direct Mott insulator-to-superfluid transitions around the tip of a Mott insulator lobe in the weak disorder regime.

cond-mat↗

arXiv1998

Universal macroscopic background formation in surface super-roughening

We study a class of super-rough growth models whose structure factor satisfies the Family-Vicsek scaling. We demonstrate that a macroscopic background spontaneously develops in the local surface profile, which dominates the scaling of the local surface width and the height-difference. The shape of the macroscopic background takes a form of a finite-order polynomial whose order is decided from the value of the global roughness exponent. Once the macroscopic background is subtracted, the width of the resulting local surface profile satisfies the Family-Vicsek scaling. We show that this feature is universal to all super-rough growth models, and we also discuss the difference between the macroscopic background formation and the pattern formation in other models.

cond-mat.stat-mech↗

arXiv1997

Localization of Two Interacting Particles in One-Dimensional Random Potential

We investigate the localization of two interacting particles in one-dimensional random potential. Our definition of the two-particle localization length, $ξ$, is the same as that of v. Oppen et al. [Phys. Rev. Lett. 76, 491 (1996)] and $ξ$'s for chains of finite lengths are calculated numerically using the recursive Green's function method for several values of the strength of the disorder, $W$, and the strength of interaction, $U$. When U=0, $ξ$ approaches a value larger than half the single-particle localization length as the system size tends to infinity and behaves as $ξ\sim W^{-ν_0}$ for small $W$ with $ν_0 = 2.1 \pm 0.1$. When $U\neq 0$, we use the finite size scaling ansatz and find the relation $ξ\sim W^{-ν}$ with $ν= 2.9 \pm 0.2$. Moreover, data show the scaling behavior $ξ\sim W^{-ν_0} g(|U|/W^Δ)$ with $Δ= 4.0 \pm 0.5$.

cond-mat.mes-hall↗

arXiv1997

Extended Universality of the Surface Curvature in Equilibrium Crystal Shapes

We investigate the universal property of curvatures in surface models which display a flat phase and a rough phase whose criticality is described by the Gaussian model. Earlier we derived a relation between the Hessian of the free energy and the Gaussian coupling constant in the six-vertex model. Here we show its validity in a general setting using renormalization group arguments. The general validity of the relation is confirmed numerically in the RSOS model by comparing the Hessian of the free energy and the Gaussian coupling constant in a transfer matrix finite-size-scaling study. The Hessian relation gives clear understanding of the universal curvature jump at roughening transitions and facet edges and also provides an efficient way of locating the phase boundaries.

cond-mat.stat-mech↗