arXiv subjects

Kazuhiko Seki

Publications and source records attributed to Kazuhiko Seki.

At least 19 recordsLinked to original sources

arXiv2026

Generalized Mpemba effect in diffusion-controlled spin-dependent delayed fluorescence

The Mpemba effect is commonly associated with anomalous thermal relaxation, in which a system prepared at a higher temperature reaches equilibrium faster than one prepared at a lower temperature. In modern formulations, however, its defining feature is broader: a state initially farther from equilibrium can relax faster than a closer one, or, equivalently, relaxation trajectories can cross. Here, we show that magnetic-field-dependent delayed fluorescence in triplet-fusion systems realizes a generalized Mpemba effect driven by external control of spin-selective kinetics. Using a diffusion-controlled geminate-recombination extension of the Johnson--Merrifield model, we demonstrate that delayed-fluorescence trajectories obtained at different magnetic fields cross when geminate fusion is effective. We further derive a compact kinetic criterion for such crossing in terms of the competition between intermediate-time decay rates and long-time power-law amplitudes. This criterion captures the interplay between effective fast and slow relaxation contributions. Within this kinetic framework, the final state is independent of the external control parameter and is defined as the fully relaxed state in which no separated triplet population remains. The generalized Mpemba effect therefore arises from the redistribution of transient relaxation pathways associated with geminate recombination, whereas bulk diffusion-controlled processes contribute only to the final relaxation. These results link anomalous relaxation in spin-dependent photokinetics to modern formulations of the generalized Mpemba effect and show how trajectory crossing can emerge in systems governed by diffusion-controlled geminate recombination and non-Markovian kinetics.

physics.chem-ph↗

arXiv2026

Integral-equation analysis of transient diffusion-limited currents at disk electrodes: Asymptotic expansion and compact approximation

The transient diffusion-limited current at a disk electrode following a change in interfacial ion concentration induced by a potential step is analyzed with direct relevance to chronoamperometric measurements. The mixed-boundary diffusion problem is formulated in the Laplace domain and reduced to a Fredholm integral equation that directly determines the Faradaic current. The steady-state limit recovers Saito's equation, while a systematic long-time asymptotic expansion quantifies the approach to steady state. A Padé approximant yields a compact analytical expression in the time domain that accurately describes the current over experimentally relevant time ranges. In contrast to existing high-accuracy numerical procedures based on hybrid asymptotic and polynomial approximations, the present formulation provides an explicit and compact analytical representation that facilitates interpretation and practical implementation. The short-time response exhibits Cottrell's equation with edge effects characteristic of disk electrodes. Overall, the framework provides practical tools for analyzing transient currents, extracting diffusion parameters, and assessing the accuracy of widely used analytical approximations in disk-electrode chronoamperometry.

physics.chem-ph↗

arXiv2026

Temperature-Gradient Effects on Electric Double Layer Screening in Electrolytes

Temperature gradients drive asymmetric ion distributions via thermodiffusion (the Soret effect), leading to deviations from the classical Debye--Hückel potential.We introduce the Eastman entropy of transfer, $\hat{S}_\pm = α_\pm k_{\rm B}$ for cations and anions, respectively, where $k_{\rm B}$ is the Boltzmann constant, and analyze non-isothermal electric double layers in terms of the dimensionless Soret coefficients $α_\pm$. Analytical solutions of the generalized Debye--Hückel equation show that, for $α_+ = α_-$, the potential is exactly described by a modified Bessel function, while the marginal case $α_\pm = 1$ exhibits algebraic decay. An effective screening length, $λ_{\rm eff}$, characterizes the near-electrode potential and increases with temperature, resulting in weaker screening on the hot side and stronger screening on the cold side for $α_\pm > -1$. The differential capacitance is controlled by $α_\pm$ via $λ_{\rm eff}$, with its minimum coinciding with the potential of zero charge (PZC) even in the presence of a temperature gradient. These findings highlight the fundamental coupling between electrostatics and thermodiffusion in non-isothermal electrolytes.

cond-mat.soft↗

arXiv2025

Method of images for one-dimensional discrete random walk under a reflecting barrier

The transition probability for a one-dimensional discrete symmetric random walk under a reflecting barrier was once given by the method of images. [S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).] However, several inconsistencies have been reported when the method of images is applied in cases where a reflecting barrier is considered, even after the exact solution has been obtained. Here, we explicitly show that the method of images becomes applicable if the image position is shifted.

cond-mat.stat-mech↗

arXiv2024

Photoluminescence decay of mobile carriers influenced by imperfect quenching at particle surfaces with subdiffusive spread

We recently presented a quantitative model to explain the particle-size dependence of photoluminescence (PL) quantum yields and revealed that exciton quenching is not diffusion controlled, but limited by surface reactions. However, the exciton decay kinetics has not yet been analyzed using our theoretical model. Here, we study kinetic aspects of the model and show that it should be extended to take into account subdiffusion rather than normal diffusion to maintain consistency with the observed complex decay kinetics; we also show that the PL decay kinetics is nonexponential even when the PL quenching is limited by surface reactions under subdiffusion. Our theoretical analysis of the PL quantum yield and the PL decay kinetics provides a comprehensive picture of mobile charge carriers, immobile polarons, and self-trapped excitons.

physics.chem-ph↗

arXiv2023

Fluctuation relation in continuous-time random walks driven by an external field

We study a fluctuation relation representing a nonequilibrium equality indicating that the ratio between the distribution of trajectories obtained by exchanging the initial and final positions is characterized by free energy differences for the duration of the trajectories. We examine the fluctuation relation for noninteracting charge carriers driven by an external electric field by using a continuous-time lattice random walk model with a general waiting-time distribution of transitions. The fluctuation relation is obtained regardless of the lattice structure factor or the form of the waiting-time distribution. However, the fluctuation relation is satisfied only after taking the continuum limit in the presence of a reflecting boundary. Moreover, in free space without boundary conditions, exchanging the initial and final positions is equivalent to exchanging the field (or drift) directions. However, we show that the exchanging field (or drift) directions is not relevant for studying the fluctuation relation under the reflecting boundary condition.

cond-mat.stat-mech↗

arXiv2023

Persistent effects of inertia on diffusion-influenced reactions: Theoretical methods and applications

The Cattaneo-Vernotte model has been widely studied to take momentum relaxation into account in transport equations. Yet, the effect of reactions on the Cattaneo-Vernotte model has not been fully elucidated. At present, it is unclear how the current density associated with reactions can be expressed in the Cattaneo-Vernotte model. Herein, we derive a modified Cattaneo-Vernotte model by applying the projection operator method to the Fokker-Planck-Kramers equation with a reaction sink. The same modified Cattaneo-Vernotte model can be derived by a Grad procedure. We show that the inertial effect influences the reaction rate coefficient differently depending on whether the intrinsic reaction rate constant in the reaction sink term depends on the solute relative velocity or not. The momentum relaxation effect can be expressed by a modified Smoluchowski equation including a memory kernel using the Cattaneo-Vernotte model. When the intrinsic reaction rate constant is independent of the reactant velocity and is localized, the modified Smoluchowski equation should be generalized to include a reaction term without a memory kernel. When the intrinsic reaction rate constant depends on the relative velocity of reactants, an additional reaction term with a memory kernel is required because of competition between the current density associated with the reaction and the diffusive flux during momentum relaxation. The competition effect influences even the long-time reaction rate coefficient.

physics.chem-ph↗

arXiv2023

Transient photocurrent and optical absorption of disordered thin-film semiconductors: in-depth injection and nonlinear response

The time-of-flight method is a fundamental approach for characterizing the transport properties of semiconductors. Recently, the transient photocurrent and optical absorption kinetics have been simultaneously measured for thin films; pulsed-light excitation of thin films should give rise to non-negligible in-depth carrier injection. Yet, the effects of in-depth carrier injection on the transient currents and optical absorption have not yet been elucidated theoretically. Here, by considering the in-depth carrier injection in simulations, we found a 1/t^{1-alpha/2} initial time (t) dependence rather than the conventional $1/t^{1-alpha}$ dependence under a weak external electric field, where alpha<1 is the index of dispersive diffusion.The asymptotic transient currents are not influenced by the initial in-depth carrier injection and follow the conventional 1/t^{1+alpha} time dependence. We also present the relation between the field-dependent mobility coefficient and the diffusion coefficient when the transport is dispersive. The field dependence of the transport coefficients influences the transit time in the photocurrent kinetics dividing two power-law decay regimes. The classical Scher--Montroll theory predicts a_1+a_2=2 when the initial photocurrent decay is given by 1/t^{a_1} and the asymptotic photocurrent decay is given by 1/t^{a_2}. The results shed light on the interpretation of the power-law exponent of 1/t^{a_1} when a_1+a_2neq 2.

physics.chem-ph↗

arXiv2022

Thickness optimization of the output power and effective thermoelectric figure of merit of thin thermoelectric generator

The conventional thermoelectric figure of merit and the power factor are not sufficient as a measure of thin film quality of thermoelectric materials, where the power conversion efficiency depends on the film dimensions. By considering the film size, the effective thermoelectric figure of merit and effective Seebeck coefficient are introduced to guarantee that the maximum energy conversion efficiency increases as the effective thermoelectric figure of merit increases. Similarly, the effective power factor is defined. By introducing typical material properties for Bi$_2$Te$_3$ and PEDOT, we study the thickness dependence of the effective figure of merit and the effective power factor.

physics.app-ph↗

arXiv2021

On the definition of the domain growth rate constant on a two dimensional substrate

In chemical vapor deposition (CVD) methods, the domain grows by attachment of diffusing surface bound species on the substrate to an island of solid domain. We formulate the process of single domain growth under two-dimensional diffusion by taking into account the movement of the domain boundary. We first discuss two types of definition of the domain area growth rate constant; the one defined through the domain size divided by the time duration of CVD growth and the other defined through the area divided by time. Then, we show that the domain size is proportional to time for the reaction limited growth and the domain area is proportional to time for the diffusion limited growth. We also show that the domain area growth rate changes from the reaction limited growth to the diffusion limited growth as the domain size increases beyond a characteristic size.

cond-mat.stat-mech↗

arXiv2021

Effect of vibronic relaxation in fluorescence resonance energy transfer: An exact analytical solution

Fluorescence resonance energy transfer (FRET) is widely used as a 'spectroscopic ruler' to measure fluctuations in macromolecules because of the strong dependence of the rate on the separation (R) between the donor (D) and acceptor (A). However, the well-known Forster rate expression that predicts an $R^{-6}$ dependence, is limited by several approximations. Notable among them is the neglect of the vibronic relaxation in the reactant (donor) and product (acceptor) manifolds. Vibronic relaxation can play an important role when the energy transfer rate is faster than the vibronic relaxation rate. Under such conditions, donor to acceptor energy transfer can occur from the excited vibronic states. This phenomenon is not captured by the usual formulation based on the overlap of donor emission and acceptor absorption spectra. Here, we attempt to eliminate this lacuna, by allowing relaxation in the vibronic energy levels and adopting a relaxation model to account for vibronic cascading down in the donor manifold. We develop a Green's function based generalized formalism and provide an exact solution for the excited state population relaxation and the rate of energy transfer in the presence of vibronic relaxation. We find and verify that the neglect of vibronic relaxations can significantly alter the energy transfer rate and overestimates the distance between D and A.

physics.chem-ph↗

arXiv2019

Scaling theory for two-dimensional single domain growth driven by attachment of diffusing adsorbates

Epitaxial growth methods are a key technology used in producing large-area thin films on substrates but as a result of various factors controlling growth processes the rational optimization of growth conditions is rather difficult. Mathematical modeling is one approach used in studying the effects of controlling factors on domain growth. The present study is motivated by a recently found scaling relation between the domain radius and time for chemical vapor deposition of graphene. Mathematically, we need to solve the Stefan problem; when the boundary moves, its position should be determined separately from the boundary conditions needed to obtain the spatial profile of diffusing adsorbates. We derive a closed equation for the growth rate constant defined as the domain area divided by the time duration. We obtain approximate analytical expressions for the growth rate; the growth rate constant is expressed as a function of the two-dimensional diffusion constant and the rate constant for the attachment of adsorbates to the solid domain. In experiments, the area is decreased by stopping the source gas flow. The rate of decrease of the area is obtained from theory. The theoretical results presented provide a foundation to study controlling factors for domain growth.

cond-mat.stat-mech↗

arXiv2019

Motional Narrowing under Markovian and Non-Markovian Hopping Transitions in Inhomogeneous Broadened Absorption Line Shape

Inspired by recent experiments showing a minimum of electron paramagnetic resonance (ESR/EPR) line width as a function of inverse temperature, we studied the motional narrowing effect by considering a combined model of carrier transitions and static dispersion of the angular frequency giving rise to an inhomogeneous broadening in the spectrum. The dispersion of the angular frequency results from the distribution of the local field. The transition between the sites under inhomogeneous static local field induces adiabatic relaxation of the spin. We also considered the on-site inherent (nonadiabatic) relaxation of the spin. We obtained the exact solution of the spin correlation function by explicitly considering transitions between two sites for both Markovian and non-Markovian transition processes. The absorption line shape is expressed in terms of the Voigt function, which is a convolution of a Gaussian function and a Lorentzian function. Using the known properties of the Voigt function, we discuss the correlation between the change in the full-width at half-maximum and the change in line shape, both of which are induced by motional narrowing. By assuming thermal activation processes for both the hopping transition and the on-site inherent relaxation, we show that the minimum of the width appears as a function of inverse temperature as observed experimentally in organic materials.Contrary to the general belief, we also show that the narrowing of the Gaussian line shape under a local random field did not necessarily lead to a Lorentzian line shape in particular under the presence of heavy tail property in the waiting time distribution of hopping transitions.

cond-mat.stat-mech↗

arXiv2018

The Jellium Edge and the Size Effect of the Chemical Potential and Surface Energy in Metal Slabs

Although free electron models have been established in order to capture the essential physics of interfacial and bulk properties in metals, some issues still remain regarding the application of free electron models to thin metal films. One of the issues relates to whether the geometric edge coincides with the potential edge in order to satisfy the charge neutrality condition when the potential profile is modeled as a rectangular potential well. We show that they coincide by rigorously taking into account the quantization effect arising from electron confinement in a thin metal slab. As a result, the overall behaviors of the chemical potential and surface energy show an increasing trend by decreasing the thickness of the slab. The chemical potential and surface energy show an oscillatory thickness dependence by further taking into account the discreteness of the total number of free electrons.

cond-mat.mtrl-sci↗

arXiv2018

Possible influence of the Kuramoto length in a photo-catalytic water splitting reaction revealed by Poisson--Nernst--Planck equations involving ionization in a weak electrolyte

We studied ion concentration profiles and the charge density gradient caused by electrode reactions in weak electrolytes by using the Poisson--Nernst--Planck equations without assuming charge neutrality. In weak electrolytes, only a small fraction of molecules is ionized in bulk. Ion concentration profiles depend on not only ion transport but also the ionization of molecules. We considered the ionization of molecules and ion association in weak electrolytes and obtained analytical expressions for ion densities, electrostatic potential profiles, and ion currents. We found the case that the total ion density gradient was given by the Kuramoto length which characterized the distance over which an ion diffuses before association. The charge density gradient is characterized by the Debye length for 1:1 weak electrolytes. We discuss the role of these length scales for efficient water splitting reactions using photo-electrocatalytic electrodes.

cond-mat.soft↗

arXiv2016

Equivalent circuit representation of hysteresis in solar cells that considers interface charge accumulation: Potential cause of hysteresis in perovskite solar cells

If charge carriers accumulate in the charge transport layer of a solar cell, then the transient response of the electric field that originates from these accumulated charges results in hysteresis in the current-voltage ($J$-$V$) characteristics. While this mechanism was previously known, a theoretical model to explain these $J$-$V$ characteristics has not been considered to date. We derived an equivalent circuit from the proposed hysteresis mechanism. By solving the equivalent circuit model, we were able to reproduce some of the features of hysteresis in perovskite solar cells.

cond-mat.mtrl-sci↗

arXiv2016

Temperature scaling of effective polaron mobility in energetically disordered media

We study effective mobility in 2 dimensional (2D) and 3 dimensional (3D) systems, where hopping transitions of carriers are described by the Marcus equation under a Gaussian density of states in the dilute limit. Using an effective medium approximation (EMA), we determined the coefficient $C_d$ for the effective mobility expressed by $μ_{\rm eff}\propto\exp\left[-λ/\left(4 k_{\rm B} T\right)- C_dσ^2/\left(k_{\rm B} T\right)^2 \right]/\left[\sqrtλ (k_{\rm B} T)^{3/2}\right]$, where $λ$ is the reorganization energy, $σ$ is the standard deviation of the Gaussian density of states, and $k_{\rm B} T$ takes its usual meaning. We found $C_d=1/2$ for both 2D and 3D. While various estimates of the coefficient $C_d$ for 3D systems are available in the literature, we provide for the first time the expected $C_d$ value for a 2D system. By means of kinetic Monte-Carlo simulations, we show that the effective mobility is well described by the equation shown above under certain conditions on $λ$. We also give examples of analysis of experimental data for 2D and 3D systems based on our theoretical results.

cond-mat.dis-nn↗

arXiv2016

Anomalous dimensionality dependence of diffusion in a rugged energy landscape : How pathological is one dimension ?

Rugged (or, rough) energy landscape (REL) with spatially distributed maxima and minima are often employed in applications of physics, chemistry and biology (enzyme kinetics, protein folding, diffusion in disordered solids, transport in organic semiconductors, relaxation in random spin systems, in supercooled liquids and glasses). Sometimes the system needs to be modeled as a random walker in high dimensions (like in protein folding/unfolding) where dimensions could be the distances between different amino acid residues (as in unfolding of HP-36). Nevertheless, most of the theoretical studies of these phenomena still employ a one dimensional description. This is despite the prediction that in a rough (or, rugged) energy landscape (REL), diffusion in one dimension (1d) is predicted to be pathologically different from any higher dimension with the increased chance of encountering broken ergodicity (Stein and Newman, 2012). We explore the dimensionality dependent diffusion on REL by carrying out an effective medium approximation based analytical calculations and compare them with the available computer simulation results. We find that at intermediate level of ruggedness (assumed to have a Gaussian distribution), where diffusion is well-defined, the value of the effective diffusion coefficient depends on dimensionality and changes (increases) by several factors (~5-10) in going from 1d to 2d. In contrast, the changes in subsequent transitions (like 2d to 3d and 3d to 4d and so on) are far more modest, of the order of 10-20% only. When ruggedness is given by random traps with an exponential distribution of barrier heights, the mean square displacement is sub-diffusive (a well-known result), but the growth of MSD is described by different exponents in one and higher dimensions. The exponent of growth is larger in higher dimensions than in 1d.

cond-mat.soft↗