arXiv subjects

Hisao Hayakawa

Publications and source records attributed to Hisao Hayakawa.

At least 19 recordsLinked to original sources

arXiv2026

Quantum non-Markovian Hatano-Nelson model

While considering non-Hermitian Hamiltonians arising in the presence of dissipation, in most cases, the dissipation is taken to be frequency independent. However, this idealization may not always be applicable in experimental settings, where dissipation can be frequency-dependent. Such frequency-dependent dissipation leads to non-Markovian behavior. In this work, we demonstrate how a quantum non-Markovian Hatano-Nelson model arises microscopically in a quasi-one-dimensional dissipative lattice. This is achieved using non-equilibrium Green's functions without requiring any approximation like weak system-bath coupling or a time-scale separation, which would have been necessary for a Markovian treatment. The resulting effective system exhibits nonreciprocal hopping, the defining characteristic of the Hatano-Nelson model, as well as uniform dissipation, both of which are frequency-dependent. This holds for both bosonic and fermionic settings. We find solely non-Markovian nonreciprocal features like unidirectional frequency blocking in bosonic settings, and a particular type of non-equilibrium dissipative quantum phase transition in fermionic settings, that cannot be captured in a Markovian theory, nor have any analog in reciprocal systems. Our results lay the groundwork for describing and engineering non-Markovian nonreciprocal quantum lattices.

quant-ph↗

arXiv2026

Quantum tunneling Mpemba effect

We investigate a quantum tunneling Mpemba effect for a particle in a continuous one-dimensional symmetric double-well potential subject to irreversible boundary loss. The dissipation is described by a complex absorbing potential (CAP) and the corresponding conditional no-jump evolution. Using a biorthogonal spectral representation, we derive the exact non-Hermitian decomposition of the subnormalized density matrix and analyze the corresponding relaxation dynamics. We show that the off-diagonal coefficients exhibit a parity selection rule, leaving same-parity interference terms in general. To isolate the interplay between thermal spectral preparation and mode-dependent decay rates, we introduce a diagonal spectral relaxation measure $S(t,T_i)$. For a quartic double well, numerical calculations reveal finite-time crossings of $S(t,T_i)$ prepared at different initial temperatures, as well as a non-monotonic temperature dependence of selected diagonal spectral weights. These features are explained by the enhanced thermal population of spatially extended, rapidly leaking excited states. In contrast, the trace distance of the normalized conditional state to the asymptotic quasi-stationary state exhibits no crossing, demonstrating that the anomalous ordering is specifically a spectral Mpemba effect rather than a universal acceleration of the complete conditional state. Our continuous-space formulation provides a real-space perspective on anomalous quantum relaxation without invoking universal nodal or topological theorems.

cond-mat.stat-mech↗

arXiv2026

Geometric Thermodynamics of Scallop Motion with Two Control Parameters

According to Purcell's scallop theorem, reciprocal single-degree-of-freedom shape deformations cannot achieve net propulsion in a viscous fluid. We show that this limitation is bypassed by thermal fluctuations in a two-parameter driven potential landscape. Formulating the stochastic shape dynamics via a Smoluchowski equation with position-dependent mobility $M_\mathrm{eff}(x)$, we utilize a generalized inverse operator to evaluate the slow-driving response. Cyclic modulation of the control parameters induces a non-zero Berry-Sinitsyn-Nemenman curvature $F_{12}(\bmθ)$, resulting in directed geometric propulsion. Simultaneously, the non-adiabatic excess dissipation is dictated by a Riemannian thermodynamic metric $g_{ij}(\bmθ)$. Our results provide a unified geometric foundation that bridges hydrodynamic friction, stochastic mechanics, and thermodynamic trade-offs in micro-swimmers.

cond-mat.stat-mech↗

arXiv2026

Mpemba effect in a two-dimensional bistable potential

We present an exactly solvable model of the Mpemba effect in an overdamped Langevin system confined to a two-dimensional, radially symmetric bistable potential. The potential is constructed as a piecewise quadratic-logarithmic function that is continuous and differentiable at the matching radii, enabling an exact mapping of the corresponding Fokker-Planck operator to a Schrödinger-type eigenvalue problem. The relaxation spectrum and eigenmodes are obtained analytically in each region in terms of confluent hypergeometric functions, with eigenvalues determined from matching conditions. % Focusing on isotropic equilibrium initial states at inverse temperature $β_{\rm ini}$ quenched to a bath at inverse temperature $β$, we derive explicit expressions for the mode amplitudes governing long-time relaxation. We demonstrate that the coefficient of the slowest mode exhibits a non-monotonic dependence on $β_{\rm ini}$ and identify a sufficient crossing condition for the Kullback-Leibler divergence in terms of the two slowest modes, if the global minimum of the potential is located far away from the origin and the second minimum exists near the origin. For corresponding parameters, we demonstrate that the Mpemba effect can be realized. % Our results provide a rare example of an analytically tractable two-dimensional model exhibiting anomalous relaxation without any confining walls, extending previous one-dimensional constructions with a hard wall and clarifying the role of radial geometry in nonequilibrium relaxation phenomena.

cond-mat.stat-mech↗

arXiv2026

Geometric Quantum Thermodynamic Engine under an Isothermal Operation: An Application of a Thouless Pumping

Geometric pumping in open quantum systems is commonly described in terms of the Berry--Sinitsyn--Nemenman (BSN) curvature, which determines the geometric contribution to transported quantities under cyclic parameter modulation. In this work, we show that a cyclically driven open quantum system can operate as an isothermal engine through a mechanism that is fundamentally distinct from curvature-driven pumping. In the adiabatic limit, the instantaneous pumping current vanishes, yet a finite work per cycle survives. We demonstrate that this work originates from the parametric dependence of the instantaneous steady state rather than from the BSN curvature. Using a general superoperator formulation, we derive the non-adiabatic expansion of the density matrix and separate reversible and irreversible contributions to work, heat, and entropy production. The entropy production per cycle scales linearly with the operation speed, ensuring reversibility in the strict adiabatic limit. Finite-speed corrections are expressed in terms of a thermodynamic metric defined on the steady-state manifold, leading to a geometric bound on efficiency degradation. As a concrete example, we apply the theory to the Anderson impurity model under cyclic modulation of electrochemical potentials and the strength of Coulomb interaction. In the sequential-tunneling regime, we obtain finite work in the non-adiabatic regime and confirm that finite work persists in the adiabatic limit. These results clarify the geometric structure underlying isothermal cyclic thermodynamics and reveal a class of reversible steady-state engines whose operation is controlled by the geometry of the steady-state manifold rather than by the BSN curvature.

cond-mat.stat-mech↗

arXiv2026

Non-Hermitian Random Matrix Theory of Jamming in Active Disordered Media

We develop a theoretical framework for the mechanics of active jammed systems based on non-Hermitian random matrix theory. Starting from a microscopic model of active particles with non-reciprocal interactions, we formulate the linearized dynamical matrix as a non-Hermitian perturbation of a Wishart ensemble describing the passive contact network. Using Girko's Hermitization together with the self-consistent Born approximation, we derive a self-consistent equation for the low-frequency resolvent based on the full Marchenko--Pastur distribution. We show that active non-reciprocity regularizes the soft-mode divergence at the jamming transition, leading to a scaling law for the mechanical compliance. We further establish a crossover between perturbative and activity-dominated regimes and propose a corresponding scaling form near the active jamming point.

cond-mat.stat-mech↗

arXiv2026

Weakly Nonlinear Dynamics of Unstable Modes in Jammed Amorphous Solids

We investigate the structural evolution in jammed amorphous solids by analyzing the eigenmodes of a generalized Hessian matrix that incorporates spatial modulation via wave numbers. Unlike the conventional Hessian, this generalized formulation captures linearly unstable modes through a Fourier-based extension of the Hessian matrix, enabling us to study responses beyond the mechanically stable regime. We demonstrate that the excitation of unstable eigenmodes leads to structural rearrangements independent of the initial perturbation by the simulation. Furthermore, we derive a weakly nonlinear amplitude equation to describe the growth and saturation of these unstable modes, analogous to the Landau equation. Our framework provides a pathway to understand instability-driven configuration changes in disordered solids.

cond-mat.stat-mech↗

arXiv2026

The Mpemba effect likes to hit a wall

The original Mpemba effect refers to the idea that a macroscopic hot system cools faster than an initially colder one. In its microscopic and classical versions, the system is modeled as an overdamped particle in an external potential, and the corresponding Mpemba effect has been observed experimentally and explored theoretically. We establish that the existence of the one-dimensional Mpemba effect for a particle in an asymmetric polynomial double-well potential is driven solely by the presence of a hard wall, irrespective of the potential's double-well shape and metastability. The Mpemba effect disappears if we consider an infinitely large system. We then show that the underlying mechanism of the Mpemba effect is governed by the fine structure of the initial statistical population as it probes the tails of the potential, which also explains the Mpemba effect in single-well and symmetric double-well potentials.

cond-mat.stat-mech↗

arXiv2026

Predicting the conditions for observing the Mpemba effect

The Mpemba effect, a counterintuitive phenomenon where a hotter system relaxes faster than a colder one, has been widely observed in various nonequilibrium systems. Despite this progress, the fundamental structural features of the energy landscape required for its emergence remain a subject of debate. In this study, we investigate the conditions for the Mpemba effect within one-dimensional overdamped Langevin dynamics. We classify the potential landscapes based on the presence of single or double wells, their symmetry properties, and the existence of walls. We establish that the existence of the effect is primarily driven by the presence of boundaries, either hard or soft, rather than the specific internal structure of the potential landscape, such as metastability or the number of minima. By employing a spectral decomposition of the Fokker-Planck operator, we analyze the behavior of the first nontrivial eigenmode and demonstrate that its derivative acts as a Dirac delta peak in the low-temperature regime. This helps us elucidate the mechanism underlying the Mpemba effect: it appears as the interplay between this behavior and the initial population dynamics in a non-trivial way induced by the presence of the wall. Our analysis provides a unified classification across single- and double-well potentials, highlighting the crucial role of boundary conditions and asymmetry. Furthermore, we demonstrate that this framework allows for the engineering of potential landscapes capable of producing multistage Mpemba transitions.

cond-mat.stat-mech↗

arXiv2025

Early-stage impact dynamics in dense suspensions of millimeter-sized particles

This study investigates the phenomenon of the early-stage dynamics of impact-induced hardening in dense suspensions, where materials undergo solidification upon impact. While Stokes flow theory traditionally applies to suspensions with micrometer-sized particles due to their low Reynolds numbers, suspensions containing larger particles defy such idealizations. Our work focuses on the early-stage impact-induced hardening of suspensions containing millimeter-sized particles through dynamic impact experiments. We are particularly interested in the maximum drag force $F_\mathrm{max}$ acting on the projectile as a function of the impact speed $u_0$. We successfully conducted experiments using these suspensions and confirmed the relation $F_\mathrm{max}\sim u_0^{3/2}$ for relatively large $u_0$ as observed in the previous studies suspensions of micrometer-sized particles. Our findings reveal that the early-stage behaviors of millimeter-sized particle suspensions align well with predictions from the floating model, typically applicable under Stokes flow conditions. This research sheds light on the complex dynamics of impact-induced hardening in dense suspensions, particularly with larger particles, advancing our understanding beyond conventional micrometer-sized systems.

cond-mat.soft↗

arXiv2025

Discontinuous shear thickening of a moderately dense inertial suspension of hydrodynamically interacting frictionless soft particles

We demonstrate that discontinuous shear thickening (DST) can occur even in moderately dense, inertial suspensions of hydrodynamically interacting, frictionless soft particles. Using the Lubrication-Friction Discrete Element Method, our simulations reveal that DST can emerge at lower particle densities, provided that both the inertia of the suspended particles and their softness are sufficiently pronounced. Furthermore, we show that, under these conditions, the DST behavior obtained from the simulation qualitatively agrees with that predicted by kinetic theory, even without accounting for hydrodynamic interactions. These findings expand the understanding of DST in soft particle systems and highlight the importance of particle inertia and softness in controlling rheological behavior.

cond-mat.soft↗

arXiv2025

Entanglement Spectrum Dynamics as a Probe for Non-Hermitian Bulk-Boundary Correspondence in Systems with Periodic Boundaries

It has recently been established that open quantum systems may exhibit a strong spectral sensitivity to boundary conditions, known as the non-Hermitian/Liouvillian skin effect (NHSE/LSE), making the topological properties of the system boundary-condition sensitive. In this Letter, we ask the query: Can topological phase transitions of open quantum systems, captured by open boundary conditioned invariants, be observed in the dynamics of a system in a periodic boundary condition, even in the presence of NHSE/LSE? We affirmatively respond to this question, by considering the quench dynamics of entanglement spectrum in a periodic open quantum fermionic system. We demonstrate that the entanglement spectrum exhibits zero-crossings only when this periodic system is quenched from a topologically trivial to non-trivial phase, defined from the spectrum in open boundary conditions, even in systems featuring LSE. Our results reveal that non-Hermitian topological phases leave a distinctive imprint on the unconditional dynamics within a subsystem of fermionic systems.

cond-mat.stat-mech↗

arXiv2025

Kinetic theory of discontinuous shear thickening of a moderately dense inertial suspension of frictionless soft particles

We demonstrate that a discontinuous shear thickening (DST) can take place even in a moderately dense inertial suspension consisting of frictionless soft particles. This DST can be regarded as an ignited-quenched transition in the inertial suspension. An approximate kinetic theory well recovers the results of the Langevin simulation in the wide range of the volume fraction without any fitting parameters.

cond-mat.soft↗

arXiv2025

Thermomajorization Mpemba Effect

The Mpemba effect is a counterintuitive physical phenomenon where a hot system cools faster than a warm one. In recent years, theoretical analyses of the Mpemba effect have been developed for microscopic systems and experimentally verified. However, the conventional theory relies on a specific choice of distance measure to quantify relaxation speed, leading to several theoretical ambiguities. In this Letter, we derive a rigorous quantification of the Mpemba effect based on thermomajorization theory, referred to as the thermomajorization Mpemba effect. This approach resolves all existing ambiguities and provides a unification of the conventional Mpemba effect across all monotone measures. Furthermore, we demonstrate the generality of the thermomajorization Mpemba effect for Markovian dynamics, rigorously proving that it can occur in any temperature regime with fixed energy levels.

cond-mat.stat-mech↗

arXiv2024

Microscopic theory of Mpemba effects and a no-Mpemba theorem for monotone many-body systems

Mpemba effects (MPEs), where a hotter system cools faster than a colder one, present intriguing anomalies in relaxation processes. Despite their universal observation and significant fundamental and practical implications, a comprehensive theoretical understanding based on microscopic properties remains elusive. In this Letter, we introduce two universal frameworks for classical systems to address this gap. Firstly, we reveal that MPEs, traditionally defined by macroscopic temperature comparisons, can be understood through microstate comparisons. This insight offers a straightforward and universal microscopic perspective on MPEs, relevant for experiments and numerical simulations to identify their microscopic origins. Secondly, we establish a "no-Mpemba theorem," a rigorous sufficient condition for the absence of MPEs, thereby identifying specific classes of systems devoid of these effects. Our findings are exemplified using ferromagnetic Ising models and one-dimensional multiparticle systems, demonstrating the practical applicability of our theoretical advancements.

cond-mat.stat-mech↗

arXiv2024

Multiple quantum Mpemba effect: exceptional points and oscillations

We explore the role of exceptional points and complex eigenvalues on the occurrence of the quantum Mpemba effect. To this end, we study a two-level driven dissipative system subjected to an oscillatory electric field and dissipative coupling with the environment. We find that both exceptional points and complex eigenvalues can lead to $multiple$ quantum Mpemba effect. It occurs in an observable when time evolved copies corresponding to two different initial conditions, one initially having higher observable value compared to the other and both relaxing towards the same steady state, intersect each other more than once during their relaxation process. Each of the intersections denotes a quantum Mpemba effect and marks the reversal of identities between the two copies i.e. the copy with higher observable value before the intersection becomes the lower valued copy (and vice versa) after the intersection. Such multiple intersections originate from additional algebraic time dependence at the exceptional points and due to oscillatory relaxation in the case of complex eigenvalues. We provide analytical results for quantum Mpemba effect in the density matrix in presence of coherence. Depending on the control parameters (drive and dissipation), observables such as energy, von Neumann entropy, temperature etc. exhibit either single or multiple quantum Mpemba effect. However, the distance from steady state measured in terms of the Kullback-Leibler divergence shows only single quantum Mpemba effect although the corresponding speed gives rise to either single or multiple quantum Mpemba effect.

quant-ph↗

arXiv2023

Rheology of a dilute binary mixture of inertial suspension under simple shear flow

The rheology of a dilute binary mixture of inertial suspension under simple shear flow is analyzed in the context of the Boltzmann kinetic equation. The effect of the surrounding viscous gas on the solid particles is accounted for by means of a deterministic viscous drag force plus a stochastic Langevin-like term defined in terms of the environmental temperature $T_\text{env}$. Grad's moment method is employed to determine the temperature ratio and the pressure tensor in terms of the coefficients of restitution, concentration, the masses and diameters of the components of the mixture, and the environmental temperature. Analytical results are compared against event-driven Langevin simulations for mixtures of hard spheres with the same mass density $m_1/m_2=(σ^{(1)}/σ^{(2)})^3$, $m_i$ and $σ^{(1)}$ being the mass and diameter, respectively, of the species $i$. It is confirmed that the theoretical predictions agree with simulations of various size ratios $σ^{(1)}/σ^{(2)}$ and for elastic and inelastic collisions in the wide range of parameters' space. It is remarkable that the temperature ratio $T_1/T_2$ and the viscosity ratio $η_1/η_2$ ($η_i$ being the partial contribution of the species $i$ to the total shear viscosity $η=η_1+η_2$) discontinuously change at a certain shear rate as the size ratio increases; this feature (which is expected to occur in the thermodynamic limit) cannot be completely captured by simulations due to small system size. In addition, a Bhatnagar--Gross--Krook (BGK)-type kinetic model adapted to mixtures of inelastic hard spheres is exactly solved when $T_\text{env}$ is much smaller than the kinetic temperature $T$. A comparison between the velocity distribution functions obtained from Grad's method, BGK model, and simulations is carried out.

cond-mat.soft↗

arXiv2023

Quantum Mpemba effect in a quantum dot with reservoirs

We demonstrate the quantum Mpemba effect in a quantum dot coupled to two reservoirs, described by the Anderson model. We show that the system temperatures starting from two different initial values (hot and cold), cross each other at finite time (and thereby reverse their identities i.e. hot becomes cold and vice versa) to generate thermal quantam Mpemba effect. The slowest relaxation mode believed to play the dominating role in Mpemba effect in Markovian systems, does not contribute to such anomalous relaxation in the present model. In this connection, our analytical result provides necessary condition for producing quantum Mpemba effect in the density matrix elements of the quantum dot, as a combined effect of the remaining relaxation modes.

cond-mat.stat-mech↗