arXiv subjects

Joonhyun Yeo

Publications and source records attributed to Joonhyun Yeo.

At least 19 recordsLinked to original sources

arXiv2026

Role of System-Bath Interaction in Non-Markovian Quantum Brownian Otto Cycles

We study finite-time quantum Otto cycles whose working medium is a harmonic oscillator undergoing a quantum Brownian motion described by the Caldeira-Leggett model when the oscillator is in contact with heat baths in isochoric processes. The time evolution of the Otto cycle is studied by analytically solving the exact Heisenberg-Langevin equations for the system variables and the interaction energy between the system and the bath. This enables us to investigate non-Markovian strong-coupling effects on the quantum Otto cycle. We obtain cyclic steady states and study the thermodynamic properties of the Otto cycle for various values of the parameters describing the heat baths and the coupling between the system and the bath. We compare our results with those obtained in the Markovian limit, where the time evolution is described by the Lindblad equation. We find that the change in the interaction energy during the isochoric process contributes to both work and heat, and plays a crucial role in determining thermodynamic behavior of the cycle. In particular, we find that when the Otto cycle operates as an engine, the effect of the interaction energy is to reduce the work output. We also compare our results with the power-efficiency trade-off relation recently proposed for the Markovian quantum Otto engine. We find that the power of our non-Markovian engine for a given efficiency value falls below the Markovian power-efficiency bound.

cond-mat.stat-mech↗

arXiv2025

Structure of Quantum Mean Force Gibbs States for Coupled Harmonic Systems

An open quantum system interacting with a heat bath at given temperature is expected to reach the mean force Gibbs (MFG) state as a steady state. The MFG state is given by tracing out the bath degrees of freedom from the equilibrium Gibbs state of the total system plus bath. When the interaction between the system and the bath is not negligible, it is different from the usual system Gibbs state obtained from the system Hamiltonian only. Using the path integral method, we present the exact MFG state for a coupled system of quantum harmonic oscillators in contact with multiple thermal baths at the same temperature. We develop a nonperturbative method to calculate the covariances with respect to the MFG state. By comparing them with those obtained from the system Gibbs state, we find that the effect of coupling to the bath decays exponentially as a function of the distance from the system-bath boundary. This is similar to the skin effect found recently for a quantum spin chain interacting with an environment. Using the exact results, we also investigate the ultrastrong coupling limit where the coupling between the system and the bath gets arbitrarily large and make a connection with the recent result found for a general quantum system.

cond-mat.stat-mech↗

arXiv2023

Improved Numerical Scheme for the Generalized Kuramoto Model

We present an improved and more accurate numerical scheme for a generalization of the Kuramoto model of coupled phase oscillators to the three-dimensional space. The present numerical scheme relies crucially on our observation that the generalized Kuramoto model corresponds to particles on the unit sphere undergoing rigid body rotations with position-dependent angular velocities. We demonstrate that our improved scheme is able to reproduce known analytic results and capture the expected behavior of the three-dimensional oscillators in various cases. On the other hand, we find that the conventional numerical method, which amounts to a direct numerical integration with the constraint that forces the particles to be on the unit sphere at each time step, may result in inaccurate and misleading behavior especially in the long time limit. We analyze in detail the origin of the discrepancy between the two methods and present the effectiveness of our method in studying the limit cycle of the Kuramoto oscillators.

cond-mat.soft↗

arXiv2022

Perturbative Steady States of Completely Positive Quantum Master Equations

The Lindblad form guarantees complete positivity of a Markovian quantum master equation (QME). However, its microscopic derivation for a quantum system weakly interacting with a thermal bath requires several approximations, which may result in inaccuracies in the QME. Recently, various Lindbladian QMEs were derived without resorting to the secular approximation from the Redfield equation which does not guarantee the complete positivity. Here we explicitly calculate, in a perturbative manner, the equilibrium steady states of these Lindbladian QMEs. We compare the results with the steady state of the Redfield equation obtained from an analytic continuation method, which coincides with the so-called mean force Gibbs (MFG) state. The MFG state is obtained by integrating out the bath degrees of freedom for the Gibbs state of the total Hamiltonian. We explicitly show that the steady states of the Lindbladian QMEs are different from the MFG state. Our results indicate that manipulations of the Redfield equation needed to enforce complete positivity of a QME drives its steady state away from the MFG state. We also find that, in the high-temperature regime, both the steady states of the Lindbladian QMEs and MFG state reduce to the same Gibbs state of a system Hamiltonian under certain conditions.

quant-ph↗

arXiv2020

Comment on "Universal Lindblad equation for open quantum systems"

In this Comment, we show that the thermal Gibbs state given in terms of a time-independent system Hamiltonian is not a steady state solution of the quantum master equation introduced by Nathan and Rudner [Phys. Rev. B 102, 115109 (2020)], in contrast to their claim.

quant-ph↗

arXiv2020

Numerical Verification of Fluctuation Dissipation Theorem for Isolated Quantum Systems

The fluctuation dissipation theorem~(FDT) is a hallmark of thermal equilibrium systems in the Gibbs state. We address the question whether the FDT is obeyed by isolated quantum systems in an energy eigenstate. In the framework of the eigenstate thermalization hypothesis, we derive the formal expression for two-time correlation functions in the energy eigenstates or in the diagonal ensemble. They satisfy the Kubo-Martin-Schwinger condition, which is the sufficient and necessary condition for the FDT, in the infinite system size limit. We also obtain the finite size correction to the FDT for finite-sized systems. With extensive numerical works for the XXZ spin chain model, we confirm our theory for the FDT and the finite size correction. Our results can serve as a guide line for an experimental study of the FDT on a finite-sized system.

cond-mat.stat-mech↗

arXiv2020

Improved field theoretical approach to noninteracting Brownian particles in a quenched random potential

We construct a dynamical field theory for noninteracting Brownian particles in the presence of a quenched Gaussian random potential. The main variable for the field theory is the density fluctuation which measures the difference between the local density and its average value. The average density is spatially inhomogeneous for given realization of the random potential. It becomes uniform only after averaged over the disorder configurations. We develop the diagrammatic perturbation theory for the density correlation function and calculate the zero-frequency component of the response function exactly by summing all the diagrams contributing to it. From this exact result and the fluctuation dissipation relation, which holds in an equilibrium dynamics, we find that the connected density correlation function always decays to zero in the long-time limit for all values of disorder strength implying that the system always remains ergodic. This nonperturbative calculation relies on the simple diagrammatic structure of the present field theoretical scheme. We compare in detail our diagrammatic perturbation theory with the one used in a recent paper [B.\ Kim, M.\ Fuchs and V.\ Krakoviack, J.\ Stat.\ Mech.\ (2020) 023301], which uses the density fluctuation around the uniform average, and discuss the difference in the diagrammatic structures of the two formulations.

cond-mat.dis-nn↗

arXiv2019

Symmetry and its breaking in path integral approach to quantum Brownian motion

We study the Caldeira-Leggett model where a quantum Brownian particle interacts with an environment or a bath consisting of a collection of harmonic oscillators in the path integral formalism. Compared to the contours that the paths take in the conventional Schwinger-Keldysh formalism, the paths in our study are deformed in the complex time plane as suggested by the recent study [C. Aron, G. Biroli and L. F. Cugliandolo, SciPost Phys.\ {\bf 4}, 008 (2018)]. This is done to investigate the connection between the symmetry properties in the Schwinger-Keldysh action and the equilibrium or non-equilibrium nature of the dynamics in an open quantum system. We derive the influence functional explicitly in this setting, which captures the effect of the coupling to the bath. We show that in equilibrium the action and the influence functional are invariant under a set of transformations of path integral variables. The fluctuation-dissipation relation is obtained as a consequence of this symmetry. When the system is driven by an external time-dependent protocol, the symmetry is broken. From the terms that break the symmetry, we derive a quantum Jarzynski-like equality for quantum mechanical work given as a function of fluctuating quantum trajectory. In the classical limit, the transformations becomes those used in the functional integral formalism of the classical stochastic thermodynamics to derive the classical fluctuation theorem.

cond-mat.stat-mech↗

arXiv2018

Three heats in strongly coupled system and bath

We investigate three kinds of heat produced in a system and a bath strongly coupled via an interaction Hamiltonian. By studying the energy flows between the system, the bath, and their interaction, we provide rigorous definitions of two types of heat, $Q_{\rm S}$ and $Q_{\rm B}$ from the energy loss of the system and the energy gain of the bath, respectively. This is in contrast to the equivalence of $Q_{\rm S}$ and $Q_{\rm B}$, which is commonly assumed to hold in the weak coupling regime. The bath we consider is equipped with a thermostat which enables it to reach an equilibrium. We identify another kind of heat $Q_{\rm SB}$ from the energy dissipation of the bath into the super bath that provides the thermostat. We derive the fluctuation theorems (FT's) with the system variables and various heats, which are discussed in comparison with the FT for the total entropy production. We take an example of a sliding harmonic potential of a single Brownian particle in a fluid and calculate the three heats in a simplified model. These heats are found to equal on average in the steady state of energy, but show different fluctuations at all times.

cond-mat.stat-mech↗

arXiv2018

Self-organized critical behavior and marginality in Ising spin glasses

We have studied numerically the states reached in a quench from various temperatures in the one-dimensional fully-connected Kotliar, Anderson and Stein Ising spin glass model. This is a model where there are long-range interactions between the spins which falls off a\ s a power $σ$ of their separation. We have made a detailed study in particular of the energies of the states reached in a quench from infinite temperature and their overlaps, including the spin glass susceptibility. In the regime where $σ\le 1/2$, where th\ e model is similar to the Sherrington-Kirkpatrick model, we find that the spin glass susceptibility diverges logarithmically with increasing $N$, the number of spins in the system, whereas for $σ> 1/2$ it remains finite. We attribute the behavior for $σ\le 1/\ 2$ to \emph {self-organized critical behavior}, where the system after the quench is close to the transition between states which have trivial overlaps and those with the non-trivial overlaps associated with replica symmetry breaking. We have also found by studying the d\ istribution of local fields that the states reached in the quench have marginal stability but only when $σ\le 1/2$.

cond-mat.stat-mech↗

arXiv2016

The metastable minima of the Heisenberg spin glass in a random magnetic field

We have studied zero temperature metastable states in classical $m$-vector component spin glasses in the presence of $m$-component random fields (of strength $h_{r}$) for a variety of models, including the Sherrington Kirkpatrick (SK) model, the Viana Bray (VB) model and the randomly diluted one-dimensional models with long-range power law interactions. For the SK model we have calculated analytically its complexity (the log of the number of minima) for both the annealed case and the quenched case, both for fields above and below the de Almeida Thouless (AT) field ($h_{AT} > 0$ for $m>2$). We have done quenches starting from a random initial state by putting spins parallel to their local fields until convergence and found that in zero field it always produces minima which have zero overlap with each other. For the $m=2$ and $m=3$ cases in the SK model the final energy reached in the quench is very close to the energy $E_c$ at which the overlap of the states would acquire replica symmetry breaking features. These minima have marginal stability and will have long-range correlations between them. In the SK limit we have analytically studied the density of states $ρ(λ)$ of the Hessian matrix in the annealed approximation. Despite the absence of continuous symmetries, the spectrum extends down to zero with the usual $\sqrtλ$ form for the density of states for $h_{r} h_{AT}$, there is a gap in the spectrum which closes up as $h_{AT}$ is approached. For the VB model and the other models our numerical work shows that there always exist some low-lying eigenvalues and there never seems to be a gap. There is no sign of the AT transition in the quenched states reached from infinite temperature for any model but the SK model, which is the only model which has zero complexity above $h_{AT}$.

cond-mat.dis-nn↗

arXiv2016

Reply to "Comment on "Critical Point Scaling of Ising Spin Glasses in a Magnetic Field" "

In his Comment, Temesvári objects to a remark in our paper [Phys.\ Rev.\ B {\bf 91}, 104432 (2015)] that his result for the form of the Almeida-Thouless (AT) line obtained in an earlier paper with Parisi [Nucl.\ Phys.\ B {\bf 858}, 293 (2012)] in six dimensions can be obtained by taking the limit of $d \to 6$ in the equations valid for $d>6$, but that this violated one of the inequalities needed for their validity. He is just pointing out that they gave a derivation of the form of the AT line in six dimensions in [Nucl.\ Phys.\ B {\bf 858}, 293 (2012)] which avoided this difficulty. However, it is still a perturbative approach, and does not deal with the lack of a perturbative fixed point found by Bray and Roberts [J. Phys. C {\bf 13}, 5405 (1980)] long ago.

cond-mat.dis-nn↗

arXiv2016

Housekeeping Entropy in Continuous Stochastic Dynamics with Odd-Parity Variables

We investigate the decomposition of the total entropy production in continuous stochastic dynamics when there are odd-parity variables that change their signs under time reversal. The first component of the entropy production, which satisfies the fluctuation theorem, is associated with the usual excess heat that appears during transitions between stationary states. The remaining housekeeping part of the entropy production can be further split into two parts. We show that this decomposition can be achieved in infinitely many ways characterized by a single parameter σ. For an arbitrary value of σ, one of the two parts contributing to the housekeeping entropy production satisfies the fluctuation theorem. We show that for a range of σ values this part can be associated with the breakage of the detailed balance in the steady state, and can be regarded as a continuous version of the corresponding entropy production that has been obtained previously for discrete state variables. The other part of the housekeeping entropy does not satisfy the fluctuation theorem and is related to the parity asymmetry of the stationary state distribution. We discuss our results in connection with the difference between continuous and discrete variable cases especially in the conditions for the detailed balance and the parity symmetry of the stationary state distribution.

cond-mat.stat-mech↗

arXiv2016

Finite-size critical scaling in Ising spin glasses in the mean-field regime

We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida-Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida-Thouless transition even though it is absent.

cond-mat.dis-nn↗

arXiv2015

Unconventional entropy production in the presence of momentum-dependent forces

We investigate an unconventional nature of the entropy production (EP) in nonequilibrium systems with odd-parity variables that change signs under time reversal. We consider the Brownian motion of a particle in contact with a heat reservoir, where particle momentum is an odd-parity variable. In the presence of an {\it external} momentum-dependent force, the EP transferred to environment is found {\em not} equivalent to usual reservoir entropy change due to heat transfer. There appears an additional unconventional contribution to the EP, which is crucial for maintaining the non-negativity of the (average) total EP enforced by the thermodynamic second law. A few examples are considered to elucidate the novel nature of the EP. We also discuss detailed balance conditions with a momentum-dependent force.

cond-mat.stat-mech↗

arXiv2015

Critical Point Scaling of Ising Spin Glasses in a Magnetic Field

Critical point scaling in a field $H$ applies for the limits $t\to 0$, (where $t=T/T_c-1$) and $H\to 0$ but with the ratio $R=t/H^{2/Δ}$ finite. $Δ$ is a critical exponent of the zero-field transition. We study the replicon correlation length $ξ$ and from it the crossover scaling function $f(R)$ defined via $1/(ξH^{4/(d+2-η)}) \sim f(R)$. We have calculated analytically $f(R)$ for the mean-field limit of the Sherrington-Kirkpatrick model. In dimension d=3 we have determined the exponents and the critical scaling function $f(R)$ within two versions of the Migdal-Kadanoff (MK) renormalization group procedure. One of the MK versions gives results for $f(R)$ in d=3 in reasonable agreement with those of the Monte Carlo simulations at the values of R for which they can be compared. If there were a de Almeida-Thouless (AT) line for $d \le 6$ it would appear as a zero of the function $f(R)$ at some negative value of R, but there is no evidence for such behavior. This is consistent with the arguments that there should be no AT line for $d \le 6$, which we review.

cond-mat.dis-nn↗

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↗

arXiv2012

Origin of the Growing Length Scale in M-p-Spin Glass Models

Two versions of the M-p-spin glass model have been studied with the Migdal-Kadanoff renormalization group approximation. The model with p=3 and M=3 has at mean-field level the ideal glass transition at the Kauzmann temperature and at lower temperatures still the Gardner transition to a state like that of an Ising spin glass in a field. The model with p=3 and M=2 has only the Gardner transition. In the dimensions studied, d=2,3 and 4, both models behave almost identically, indicating that the growing correlation length as the temperature is reduced in these models -- the analogue of the point-to-set length scale -- is not due to the mechanism postulated in the random first order transition theory of glasses, but is more like that expected on the analogy of glasses to the Ising spin glass in a field.

cond-mat.dis-nn↗