Yong Woon Kim

Work fluctuations for Bose particles in grand canonical initial states.

We consider bosons in a harmonic trap and investigate the fluctuations of the work performed by an adiabatic change of the trap curvature. Depending on the reservoir conditions such as temperature and chemical potential that provide the initial equilibrium state, the exponentiated work average (EWA) defined in the context of the Crooks relation and the Jarzynski equality may diverge if the trap becomes wider. We investigate how the probability distribution function (PDF) of the work signals this divergence. It is shown that at low temperatures the PDF is highly asymmetric with a steep fall-off at one side and an exponential tail at the other side. For high temperatures it is closer to a symmetric distribution approaching a Gaussian form. These properties of the work PDF are discussed in relation to the convergence of the EWA and to the existence of the hypothetical equilibrium state to which those thermodynamic potential changes refer that enter both the Crooks relation and the Jarzynski equality.

Nonequilibrium work and entropy production by quantum projective measurements.

We study the thermodynamic notion of quantum projective measurements, using a framework for the fluctuation theorem of nonequilibrium work. The energy change induced by measurements satisfies the Jarzynski equality, leading us to the interpretation that the quantum projective measurements perform nonequilibrium work on the measured system. The work average exhibits intriguing limiting behaviors due to the heat-up effect caused by repeated measurements and the quantum Zeno effect caused by measurements of an infinite frequency. If the measured system relaxes back to its initial equilibrium state, the work is completely dissipated in the form of heat into a reservoir. The corresponding entropy increase in the reservoir is shown to be not less than the von Neumann entropy change generated during the course of the measurements, proving Landauers principle.

Single-temperature quantum engine without feedback control

A cyclically working quantum-mechanical engine that operates at a single temperature is proposed. Its energy input is delivered by a quantum measurement. The functioning of the engine does not require any feedback control. We analyze work, heat, and the efficiency of the engine for the case of a working substance that is governed by the laws of quantum mechanics and that can be adiabatically compressed and expanded. The obtained general expressions are exemplified for a spin in an adiabatically changing magnetic field and a particle moving in a potential with slowly changing shape.

Scaling and criticality of the Manning transition

Abstract.We consider a system consisting of a charged cylinder in the presence of neutralizing counterions. This system is well known to exhibit the Manning transition of counterion condensation onto the charged cylinder. We study the criticality and the scaling properties of the Manning transition, analyzing involved thermodynamic quantities such as condensed fraction, its fluctuation, and heat capacity. Through the Monte Carlo simulations and finite-size scaling analysis, we find that near the transition point the examined quantities exhibit scale-invariant behaviors with specific exponents, which provides an evidence that the Manning transition is a critical phenomenon having a scale-invariant property, analogous to bulk phase transitions. Furthermore, we numerically confirm that such scaling properties are not affected by the coupling strength.Graphical abstract

Hidden Criticality of Counterion Condensation Near a Charged Cylinder

Counterion condensation onto a charged cylinder, known as the Manning transition, has received a great deal of attention since it is essential to understand the properties of polyelectrolytes in ionic solutions. However, the current understanding is still far from complete and poses a puzzling question: While the strong-coupling theory valid at large ionic correlations suggests a discontinuous nature of the counterion condensation, the mean-field theory always predicts a continuous transition at the same critical point. This naturally leads to a question how one can reconcile the mean-field theory with the strong-coupling prediction. Here, we study the counterion condensation transition on a charged cylinder via Monte Carlo simulations. Varying the cylinder radius systematically in relation to the system size, we find that in addition to the Manning transition, there exists a novel transition where all counterions are bound to the cylinder and the heat capacity shows a drop at a finite Manning parameter. A finite-size scaling analysis is carried out to confirm the criticality of the complete condensation transition, yielding the same critical exponents with the Manning transition. We show that the existence of the complete condensation is essential to explain how the condensation nature alters from continuous to discontinuous transition.

Parallel random target searches in a confined space

We study a random target searching performed by N independent searchers in a d-dimensional domain of a large but finite volume. Considering the two initial distributions of searchers where searchers are either uniformly or point distributed, we estimate the mean time for the first of the searchers to reach the target and refer to it as searching time. The searching time for the uniformly distributed searchers exhibits a universal power-law dependence on N, irrespective of dimensionality and the target-to-domain size ratio. For point-distributed searching, the searching time has a logarithmic dependence on N in the large N limit, while in the small N limit, it shows qualitatively different behaviors depending upon r_{0}, the initial distance of the searchers from a target. We obtain a diagram by comparing the searching times of the two initial distributions in the parameter space (r_{0},N) and therein present the asymptotic lines separating three characteristic regions to explain numerical simulation results.

Fluctuations of red blood cell membranes: The role of the cytoskeleton.

We theoretically investigate the membrane fluctuations of red blood cells with focus laid on the role of the cytoskeleton, viewing the system as a membrane coupled to a sparse spring network. This model is exactly solvable and enables us to examine the coupling strength dependence of the membrane undulation. We find that the coupling modifies the fluctuation spectrum at wavelengths longer than the mesh size of the network, while leaving the fluid-like behavior of the membrane intact at shorter wavelengths. The fluctuation spectra can be markedly different, depending on not only the relative amplitude of the bilayer bending energy with respect to the cytoskeleton deformation energy but also the bilayer-cytoskelton coupling strength.

Analysis of diffusion trajectories of anisotropic objects

We theoretically analyze diffusion trajectories of an anisotropic object moving on a two dimensional space in the absence of an external field. In determining diffusion parameters associated with the shape anisotropy, we devise a measure based on the gyration tensor and obtain its analytic expression exactly. Its efficiency and statistical convergence are examined in comparison with the fourth cumulant of particle displacement. We find that the estimation of diffusion constants based on the gyration measure is more efficient than the analysis adopting the fourth cumulant.

Role of work in matter exchange between finite quantum systems

Close to equilibrium, the exchange of particles and heat between macroscopic systems at different temperatures and different chemical potentials is known to be governed by a matrix of transport coefficients which are positive and symmetric. We investigate the amounts of heat and particles that are exchanged between two small quantum systems within a given time, and find them characterized by a transport matrix which neither needs to be symmetric nor positive. At larger times even spontaneous transport can be observed in the total absence of temperature and chemical potential differences provided that the two systems are different in size. All these deviations from standard transport behavior can be attributed to the fact that work is done on the system in the processes contacting and separating those parts of the system that initially possess different temperatures and chemical potentials. The standard transport properties are recovered for vanishing work and also in the limit of large systems and sufficiently large contact times. The general results are illustrated by an example.

Chiral Separation by Flows: The Role of Flow Symmetry and Dimensionality

Separation of enantiomers by flows is a promising chiral resolution method using cost-effective microfluidics. Notwithstanding a number of experimental and numerical studies, a fundamental understanding still remains elusive, and an important question as to whether it is possible to specify common physical properties of flows that induce separation has not been addressed. Here, we study the separation of rigid chiral objects of an arbitrary shape induced by a linear flow field at low Reynolds numbers. Based on a symmetry property under parity inversion, we show that the rate-of-strain field is essential to drift the objects in opposite directions according to chirality. From eigenmode analysis, we also derive an analytic expression for the separation conditions which shows that the flow field should be quasi-two-dimensional for the precise and efficient resolutions of microscopic enantiomers. We demonstrate this prediction by Langevin dynamics simulations with hydrodynamic interactions fully implemented. Finally, we discuss the practical feasibility of the linear flow analysis, considering separations by a vortex flow or an extensional flow under a confining potential.