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Hidetsugu Sakaguchi

Publications and source records attributed to Hidetsugu Sakaguchi.

At least 19 recordsLinked to original sources
arXiv2026

Quantum-mechanical wave functions in singular potentials: linear and nonlinear states

It is known that the attractive singular inverse-square potential gives rise to the critical quantum collapse in the framework of the three-dimensional (3D) linear Schroedinger equation. This article summarizes theoretical results which demonstrate suppression of the collapse, caused by this singular potential, and the creation of the otherwise missing ground state (GS) in a 3D gas of bosonic particles, carrying an electric dipole moment, which are pulled to the central electric charge, with repulsive contact interactions between the particles. In the mean-field approximation, the repulsive interactions are represented by the cubic term in the respective Gross-Pitaevskii (GP) equation. In addition to the GS, excited states with angular momentum are briefly considered too. Another topic considered in the article is 1D and 2D bound states in the linear Schroedinger and GP equations with the repulsive potential, which demonstrates a singularity at r --> infinity. A very recent result is that such a potential, growing faster than the negative harmonic-oscillator potential, produces a full spectrum of counter-intuitive normalizable (localized) bound states. The article puts forward perspectives for further studies of linear and nonlinear bound states existing under the action of the potentials with the singularity at r --> 0 or r --> infinity.

quant-ph↗
arXiv2026

Spatially-Periodic Cluster Pattern of Coupled Forced Oscillators

We propose a simple model for periodic clustering of particles under forced oscillation. Effective viscosity is assumed to increase owing to neighboring particles by analogy with the Einstein viscosity law. The linear stability analysis and numerical simulations show that the uniform distribution is unstable, and spatially-periodic and stripe patterns appear respectively in one and two dimensions.

nlin.PS↗
arXiv2025

An amended Ehrenfest theorem for the Gross-Pitaevskii equation in one- and two-dimensional potential boxes

It is known that the usual form of the Ehrenfest theorem (ET), which couples the motion of the center of mass (COM) of the one-dimensional (1D) wave function to the respective classical equation of motion, is not valid in the case of the potential box, confined by the zero boundary conditions. A modified form of the ET was proposed for this case, which includes an effective force originating from the interaction of the 1D quantum particle with the box edges. In this work, we derive an amended ET for the Gross-Pitaevskii equation (GPE), which includes the cubic nonlinear term, as well as for the 2D square-shaped potential box. In the latter case, we derive an amended COM equation of motion with an effective force exerted by the edges of the rectangular box, while the nonlinear term makes no direct contribution to the 1D and 2D versions of the ET. Nonetheless, the nonlinearity affects the amended ET through the edge-generated force. As a result, the nonlinearity of the underlying GPE can make the COM motion in the potential box irregular. The validity of the amended ET for the 1D and 2D GPEs with the respective potential boxes is confirmed by the comparison of numerical simulations of the underlying GPE and the corresponding amended COM equation of motion. The reported findings are relevant to the ongoing experiments carried out for atomic Bose-Einstein condensates trapped in the box potentials.

cond-mat.quant-gas↗
arXiv2025

Spontaneous symmetry breaking in continuous waves, dark solitons, and vortices in linearly coupled bimodal systems

We introduce a model governing the copropagation of two components which represent circular polarizations of light in the optical fiber with relative strength g = 2 of the nonlinear repulsion between the components, and linear coupling between them. A more general system of coupled Gross-Pitaevskii (GP) equations, with g =/= 2 and the linear mixing between the components, is considered too. The latter system is introduced in its one- and two-dimensional (1D and 2D) forms. A new finding is the spontaneous symmetry breaking (SSB) of bimodal CW (continuous-wave) states in the case of g > 1 (in the absence of the linear coupling, it corresponds to the immiscibility of the nonlinearly interacting components). The SSB is represented by an exact asymmetric CW solution. An exact solution is also found, in the case of g = 3, for stable dark solitons (DSs) supported by the asymmetric CW background. For g =/= 3, numerical solutions are produced for stable DSs supported by the same background. Moreover, we identify a parameter domain where the fully miscible (symmetric) CW background maintains stable DSs with the inner SSB (separation between the components) in its core. In 2D, the GP system produces stable vortex states with a shift between the components and broken isotropy. The vortices include ones with the inter-component shift imposed by the asymmetric CW background, and states supported by the symmetric background, in which the intrinsic shift (splitting) is exhibited by vortical cores of the two components.

nlin.PS↗
arXiv2025

Spontaneous symmetry and antisymmetry breaking in a ring with two potential barriers

We propose a fundamental setup for the realization of spontaneous symmetry breaking (SSB) and spontaneous antisymmetry breaking (SASB) in the framework of the nonlinear Schroedinger equation with the self-attractive and repulsive cubic term, respectively, on a one-dimensional ring split in two mutually symmetric boxes by delta-functional potential barriers, placed at opposite points. The system is relevant to optics and BEC. The spectrum of the linearized system is found in analytical and numerical forms. SSB and SASB are predicted by dint of the variational approximation, and studied in the numerical form. A particular stable solution, which demonstrates strong asymmetry, is found in an exact form. In the system with the attractive nonlinearity, the SSB of the symmetric ground state is initiated by the modulational instability. It creates stationary asymmetric states through a supercritical bifurcation. In the self-repulsive system, SASB makes the lowest antisymmetric excited state unstable, transforming it into an antisymmetry-breaking oscillatory mode.

nlin.PS↗
arXiv2024

Rotating nonlinear states in trapped binary Bose-Einstein condensates under the action of the spin-orbit coupling

We report results of systematic analysis of confined steadily rotating patterns in the two-component BEC including the spin-orbit coupling (SOC) of the Rashba type, which acts in the interplay with the attractive or repulsive intra-component and inter-component nonlinear interactions and confining potential. The analysis is based on the system of the Gross-Pitaevskii equations (GPEs) written in the rotating coordinates. The resulting GPE system includes effective Zeeman splitting. In the case of the attractive nonlinearity, the analysis, performed by means of the imaginary-time simulations, produces deformation of the known two-dimensional SOC solitons (semi-vortices and mixed-modes). Essentially novel findings are reported in the case of the repulsive nonlinearity. They demonstrate patterns arranged as chains of unitary vortices which, at smaller values of the rotation velocity Omega, assume the straight (single-string) form. At larger Omega, the straight chains become unstable, being spontaneously replaced by a trilete star-shaped array of vortices. At still large values of Omega, the trilete pattern rebuilds itself into a star-shaped one formed of five and, then, seven strings. The transitions between the different patterns are accounted for by comparison of their energy. It is shown that the straight chains of vortices, which form the star-shaped structures, are aligned with boundaries between domains populated by plane waves with different wave vectors. A transition from an axisymmetric higher-order (multiple) vortex state to the trilete pattern is investigated too.

cond-mat.quant-gas↗
arXiv2024

Nonequilibrium dynamics of coupled oscillators under the shear-velocity boundary condition

Deterministic and stochastic coupled oscillators with inertia are studied on the rectangular lattice under the shear-velocity boundary condition. Our coupled oscillator model exhibits various nontrivial phenomena and there are various relationships with wide research areas such as the coupled limit-cycle oscillators, the dislocation theory, a block-spring model of earthquakes, and the nonequilibrium molecular dynamics. We show numerically several unique nonequilibrium properties of the coupled oscillators. We find that the spatial profiles of the average value and variance of the velocity become non-uniform when the dissipation rate is large. The probability distribution of the velocity sometimes deviates from the Gaussian distribution. The time evolution of kinetic energy becomes intermittent when the shear rate is small and the temperature is small but not zero. The intermittent jumps of the kinetic energy cause a long tail in the velocity distribution.

cond-mat.stat-mech↗
arXiv2024

Two-dimensional solitons in second-harmonic-generating media with fractional diffraction

We introduce a system of propagation equations for the fundamental-frequency (FF) and second-harmonic (SH) waves in the bulk waveguide with the effective fractional diffraction and quadratic (chi ^(2)) nonlinearity. The numerical solution produces families of ground-state (zero-vorticity) two-dimensional solitons in the free space, which are stable in exact agreement with the Vakhitov-Kolokolov criterion, while vortex solitons are completely unstable in that case. Mobility of the stable solitons and inelastic collisions between them are briefly considered too. In the presence of a harmonic-oscillator (HO) trapping potential, families of partially stable single- and two-color solitons (SH-only or FF-SH ones, respectively) are obtained, with zero and nonzero vorticities. The single-and two-color solitons are linked by a bifurcation which takes place withthe increase of the soliton's power.

nlin.PS↗
arXiv2024

Repetitive Infection Spreading and Directed Evolution in the Susceptible-Infected-Recovered-Susceptible Model

We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the SIRS model including the recruitment and death terms and the SIR model in which the recovered population is assumed to be never infected again. When the decay rate δof the immune is sufficiently small, the multiple infection spreading occurs in spikes. The model equation can be reduced to be a map when the decay rate δis sufficiently small, and the spike-like multiple infection spreading is reproduced in the mapping. The period-doubling bifurcation and chaos are found in the simplified SIRS model with seasonal variation. The nonlinear phenomena are reproduced by the map. Next, we study coupled SIRS equations for the directed evolution where the mutation is expressed with a diffusion-type term. A kind of reaction-diffusion equation is derived by the continuum approximation for the infected population I. The reaction-diffusion equation with the linear dependence of infection rate on the type space has an exact Gaussian solution with a time-dependent average and variance. The propagation of the Gaussian pulse corresponds to the successive transitions of the dominant variant.

q-bio.PE↗
arXiv2023

Angular-momentum modes in a bosonic condensate trapped in the inverse-square potential

In the mean-field approximation, the well-known effect of the critical quantum collapse in a 3D gas of particles pulled to the center by potential U(r) = -U_0/r^2 is suppressed by repulsive interparticle interactions, which create the otherwise non-existing s-wave ground state. Here, we address excited bound states carrying angular momentum, with the orbital and magnetic quantum numbers, l and m. They exist above a threshold value of the potential's strength, U_0 > l(l+1). The sectoral, tesseral, and zonal modes, which correspond to m = l, 0 < m < l, and m = 0, respectively, are found in an approximate analytical form for relatively small values of U_0 - l(l+1). Explicit results are produced for the p- and d-wave states, with l = 1 and 2, respectively. In the general form, the bound states are obtained numerically, confirming the accuracy of the analytical approximation.

cond-mat.quant-gas↗
arXiv2023

Second-harmonic generation in the system with fractional diffraction

We construct a family of bright optical solitons composed of fundamental frequency (FF) and second-harmonic (SH) components in the one-dimensional (planar) waveguide with the quadratic (second-harmonic-generating) nonlinearity and effective fractional diffraction, characterized by the Levy index α, taking values between 2 and 0.5, which correspond to the non-fractional diffraction and critical collapse, respectively. The existence domain and stability boundary for the solitons are delineated in the space of α, FF-SH mismatch parameter, and propagation constant. The stability boundary is tantamount to that predicted by the Vakhitov-Kolokolov criterion, while unstable solitons spontaneously evolve into localized breathers. A sufficiently weak transverse kick applied to the stable solitons excite small internal vibrations in the stable solitons, without setting them in motion. A stronger kick makes the solitons' trajectories tilted, simultaneously destabilizing the solitons.

nlin.PS↗
arXiv2022

One- and two-dimensional solitons in spin-orbit-coupled Bose-Einstein condensates with fractional kinetic energy

We address effects of spin-orbit coupling (SOC), phenomenologically added to a two-component Bose-Einstein condensate composed of particles moving by Levy flights, in one- and two-dimensional (1D and 2D) settings. The corresponding system of coupled Gross-Pitaevskii equations includes fractional kinetic-energy operators, characterized by the Levy index, α< 2 (the normal kinetic energy corresponds to α= 2). The SOC terms, with strength λ, produce strong effects in the 2D case: they create families of stable solitons of the semi-vortex (SV) and mixed-mode (MM) types in the interval of 1 < α< 2, where the supercritical collapse does not admit the existence of stable solitons in the absence of the SOC. At λ--> 0, amplitudes of these solitons vanish as (λ)^{1/(α- 1)}.

cond-mat.quant-gas↗
arXiv2021

Dragging spin-orbit-coupled solitons by a moving optical lattice

It is known that the interplay of the spin-orbit-coupling (SOC) and mean-field self-attraction creates stable two-dimensional (2D) solitons (ground states) in spinor Bose-Einstein condensates. However, SOC destroys the system's Galilean invariance, therefore moving solitons exist only in a narrow interval of velocities, outside of which the solitons suffer delocalization. We demonstrate that the application of a relatively weak moving optical lattice (OL), with the 2D or quasi-1D structure, makes it possible to greatly expand the velocity interval for stable motion of the solitons. The stability domain in the system's parameter space is identified by means of numerical methods. In particular, the quasi-1D OL produces a stronger stabilizing effect than its full 2D counterpart. Some features of the domain are explained analytically.

cond-mat.quant-gas↗
arXiv2021

Damping of macroscopic oscillation and interference pattern in coupled Gross-Pitaevskii equations without self-interaction

Quantum phenomena appear in a macroscopic scale in Bose-Einstein condensates. The Gross-Pitaevskii (GP) equation describes the dynamics of the weakly interacting Bose-Einstein condensates. The GP equation has a form of the Schroedinger equation with self-interaction. The coupled Gross-Pitaevskii equations are used to describe some mixtures of Bose-Einstein condensates. In this paper, we will show some numerical results of coupled Gross-Pitaevskii equations without self-interaction, which has a form of nonlinearly-coupled Schroedinger equations. We demonstrate that the macroscopic oscillation and the interference of two quantum wave packets decay in time owing to mutual interaction, which is analogous to the decoherence in quantum mechanics of many particles.

cond-mat.quant-gas↗
arXiv2020

Slow decay of infection in the inhomogeneous SIR model

The SIR model with spatially inhomogeneous infection rate is studied with numerical simulations in one, two, and three dimensions, considering the case that the infection spreads inhomogeneously in densely populated regions or hot spots. We find that the total population of infection decays very slowly in the inhomogeneous systems in some cases, in contrast to the exponential decay of the infected population I(t) in the SIR model of the ordinary differential equation. The slow decay of the infected population suggests that the infection is locally maintained for long and it is difficult for the disease to disappear completely.

physics.med-ph↗
arXiv2020

Star shaped patterns caused by colloidal aggregation during the spreading process of a droplet

This research found that when an acidic solution with a low surface tension spread on the surface of a glycerol solution mixed with milk, a star shaped pattern was spontaneously formed on the surface in the horizontal plane during the spreading process. We investigated the emergence of the star shaped pattern owing to an interfacial instability in experiments using glycerol solutions with several viscosities and 2-methoxyethanol aqueous solutions, which are acidic solutions, with several concentrations. This result demonstrated that the star shaped pattern emerged in the high concentration of 2-methoxyethanol. We proposed a phenomenological model, based on our experimental results, which explains three points as follows; the spreading of the 2-methoxyethanol aqueous solution on the surface of the glycerol solution, the colloidal aggregation of the milk protein colloids caused by the denaturation that occurs when mixed with 2-methoxyethanol, and the accumulation of the aggregates toward the dent regions of the moving interface by a sweeping effect. The model reproduces the formation of the star shaped pattern which was similar to the experimental one. Furthermore, the model provided a phase diagram against the concentration of the 2-methoxyethanol solution and the viscosity of the glycerol solution as control parameters in our experiments. The phase diagram was close to that obtained from our experiments. The results suggest that the above three points are important for the formation of the star shaped pattern.

cond-mat.soft↗