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Hiroki Saito

Publications and source records attributed to Hiroki Saito.

At least 19 recordsLinked to original sources
arXiv2026

The Kerman-Sawyer trace theorem for product Morrey spaces

By using parallel corona decomposition, the Kerman-Sawyer trace theorem is extended from Lebesgue spaces to \textit{product Morrey spaces}. By discretizing the multilinear fractional integral operator based on dyadic analysis, the framework of \textit{product Morrey spaces} naturally arises in the course of estimating the operator. Within this natural setting, by establishing Sawyer-type testing estimates (to the setting of measures), we obtain an extension of the Kerman-Sawyer trace theorem. The classical approach to the Kerman-Sawyer trace theorem typically relies on a reduction to Carleson's embedding theorem. In contrast, in this paper we employ a parallel corona decomposition, which allows us to overcome the difficulties inherent in the multilinear setting and to provide a transparent and streamlined proof. By incorporating recent developments in the theory of weights, this work clarifies the relationship between trace inequalities and Morrey spaces and contributes to a deeper understanding of these topics.

math.FA↗
arXiv2026

Self-Organized Stabilization of Straight Dark Solitons in Stripe Supersolids

Straight dark solitons in two-dimensional (2D) quantum fluids usually decay by transverse modulational instability, with no intrinsic suppression in contact-interacting Bose--Einstein condensates (BECs). We theoretically show that anisotropic long-range interactions in a quasi-2D dipolar BEC stabilize an embedded straight soliton, with spontaneous stripe order providing stronger pinning. The excitation spectra show that the lowest transverse solitonic branch remains gapped, while stripe-supersolid density modulation further hardens this branch and increases the soliton bending stiffness, penalizing transverse deformation. Accessible in current $^{166}$Er and $^{164}$Dy platforms, these results establish interaction-driven protection for straight dark solitons in structured quantum fluids.

cond-mat.quant-gas↗
arXiv2026

Barnett effect in rotating spinor dipolar quantum droplets

We propose releasing the spin degree of freedom to stabilize the vortex state in self-bound droplets of dipolar Bose-Einstein condensates. When a vortex is embedded into the droplet, spontaneous magnetization arises in the axial direction via a mechanism similar to the Barnett effect; that is, the orbital angular momentum is transferred to the spin angular momentum. When an external magnetic field is applied to the spontaneously magnetized droplet, the entire atomic cloud starts to rotate without changing its shape, which can be regarded as mechanical Larmor precession of a macroscopic object. A chirally different pair of droplets can form a stable bound state because of the attractive interaction between the spontaneously magnetized droplets.

cond-mat.quant-gas↗
arXiv2026

Multilinear embedding theorem for fractional sparse operators

We show some simple sufficient conditions for which the multilinear embedding theorem holds for fractional sparse operators. By verifying these conditions, we establish the theorem for power weights. We also provide Morrey-type sufficient conditions for which the $L^p \to L^q$, $1<p,q<\infty$, infinitesimal relative bounds hold for Schrödinger operators of the form $(-Δ)^{α/2}+v$.

math.FA↗
arXiv2026

Neural-network quantum states for solving few-body problems: application to Efimov physics

Neural-network quantum states have recently emerged as a powerful method for solving quantum many-body problems, with notable successes in lattice systems. Here, we extend this approach to strongly interacting few-body problems in continuous space, and demonstrate its capability by computing the Efimov states and associated few-body bound states. Using a fully connected feedforward neural network with Jacobi coordinates as inputs, combined with a projection method, we compute the ground and first excited states for three- to six-body systems of identical bosons at unitarity, as well as a mass-imbalanced fermionic system consisting of two identical fermions and a third particle. The obtained energies of the ground and first excited states agree well with previously reported results. Furthermore, the proposed approach also reproduces key features of Efimov states, including the discrete scale invariance, the characteristic geometric structure of the wave function, and the critical-mass behavior in mass-imbalanced fermionic systems. Our method can be readily applied to a broad class of strongly correlated few-body problems in continuous space.

cond-mat.quant-gas↗
arXiv2026

Quantum many-body analysis of spin-2 bosons with two-body inelastic decay

Bose-Einstein condensates of $^{87}\mathrm{Rb}$ atoms with a hyperfine spin of 2 are open quantum systems, where the atoms are lost through two-body inelastic collisions. In this dissipation process, a collision channel with total spin of 4 is forbidden by angular momentum conservation, which results in magnetization of the atoms remaining in the condensate. Here, we investigate the quantum many-body properties of spin-2 bosons that undergo two-body atomic loss. We show that the system finally reaches a steady state, which is a mixture of the states with maximum total spins. In addition, we find that a nonclassical steady state can be obtained by applying and quenching the quadratic Zeeman field.

cond-mat.quant-gas↗
arXiv2026

Emergent aperiodicity in Bose-Bose mixtures induced by spin-dependent periodic potentials

We study the ground-state and low-lying metastable phases of repulsive binary Bose-Einstein condensates confined in twisted, spin-dependent periodic optical lattices. For balanced mixtures, weak intercomponent interactions yield a fourfold momentum-space symmetry dictated by the lattice geometry. Increasing the coupling strength leads to the emergence of additional momentum peaks that combine with the lattice-induced structure to produce an eightfold rotationally symmetric pattern, signaling quasicrystalline order. At intermediate interactions, global phase separation suppresses this quasicrystalline state; however, at stronger coupling, local phase separation gives rise to a long-lived metastable phase in which the eightfold symmetry is restored. In this regime, a secondary ring of dominant momentum peaks appears at smaller wave vectors, indicating longer-wavelength density modulations and a crossover from lattice-dominated to interaction-driven quasicrystalline order. In contrast, imbalanced mixtures form partially miscible density clusters with eightfold-symmetric aperiodic patterns only at intermediate coupling, while stronger interactions drive global phase separation and permanently destroy quasicrystalline order. Real-time simulations demonstrate that these aperiodic structures are dynamically stable and experimentally accessible. Our results show that quasicrystalline order can emerge in binary condensates without explicitly aperiodic lattices and reveal population balance as a key ingredient for stabilizing quantum quasicrystals.

cond-mat.quant-gas↗
arXiv2024

Spontaneous creation of skyrmions in a two-component Bose-Einstein condensate

We investigate the stability of a vortex ring in a miscible two-component Bose-Einstein condensate confined in a harmonic potential, where the vortex cores in the two components are initially overlapped. Solving the Gross-Pitaevskii equation numerically, we find that the overlapped vortex rings in the two components are dynamically unstable against separation and that they can form linked vortex rings, resulting in a three-dimensional skyrmion. The parameter range for spontaneous skyrmion generation is determined by the Bogoliubov analysis

cond-mat.quant-gas↗
arXiv2024

Phase separation and metastability in a mixture of spin-1 and spin-2 Bose-Einstein condensates

We investigate the ground state and dynamics of a mixture of spin-1 and spin-2 Bose-Einstein condensates of ${}^{87}{\rm{Rb}}$ atoms. For the experimentally measured interaction coefficients, the ground state exhibits phase separation between the spin-1 ferromagnetic state and the spin-2 nematic state. At the interface between them, a partially polarized spin state emerges. The uniformly mixed state of the spin-1 polar state and spin-2 biaxial nematic state is metastable, and the phase separation via nucleation can be triggered by a local perturbation.

cond-mat.quant-gas↗
arXiv2024

Quantum droplets with magnetic vortices in spinor dipolar Bose-Einstein condensates

Motivated by the recent experimental realization of a Bose-Einstein condensate (BEC) of europium atoms, we investigate the self-bound droplet state of a europium BEC with spin degrees of freedom. Under a sufficiently weak magnetic field, the droplet has a torus shape with circulating spin vectors, which is referred to as a magnetic vortex. The ground state transforms from the torus to cigar shape through bistability with an increase in the magnetic field. Dynamical change of the magnetic field causes the torus to rotate due to the Einstein-de Haas effect. The magnetic vortices form a supersolid in a confined system.

cond-mat.quant-gas↗
arXiv2023

Choquet integrals, Hausdorff content and sparse operators

Let $H^d$, $0 0$. In this paper we verify that the sparse operator ${\mathcal A}_{\mathcal S}$ maps ${\mathcal L}^p(H^d)$, $1\le p<\infty$, into an associate space of Orlicz-Morrey space ${{\mathcal M}^{p'}_{Φ_0}(H^d)}'$, $Φ_0(t)=t\log(e+t)$. We also give another characterizations of those associate spaces using the tiling ${\mathcal T}$ of ${\mathbb R}^n$.

math.FA↗
arXiv2023

Engineering mixing properties of fluids by spatial modulations

We propose a method to change the effective interaction between two fluids by modulation of their local density distributions with external periodic potentials, whereby the mixing properties can be controlled. This method is applied to a mixture of dilute bosonic gases, and binodal and spinodal curves emerge in the phase diagram. Spinodal decomposition into a mixed-bubble state becomes possible, in which one of the coexisting phases has a finite mixing ratio. A metastable mixture is also realized, which undergoes phase separation via nucleation.

cond-mat.quant-gas↗
arXiv2023

Kolmogorov-Hinze scales in turbulent superfluids

When a two-component mixture of immiscible fluids is stirred, the fluids are split into smaller domains with more vigorous stirring. We numerically investigate the sizes of such domains in a fully-developed turbulent state of a two-component superfluid stirred with energy input rate $ε$. For the strongly immiscible condition, the typical domain size is shown to be proportional to $ε^{-2/5}$, as predicted by the Kolmogorov-Hinze theory in classical fluids. For the weakly immiscible condition, quantum effects become pronounced and the power changes from $-2 / 5$ to $-1 / 4$.

cond-mat.quant-gas↗
arXiv2023

Choquet integrals, Hausdorff content and fractional operators

It is shown that the fractional integral operator $I_α$, $0<α<n$, and the fractional maximal operator $M_α$, $0\leα<n$, are bounded on weak Choquet spaces with respect to Hausdorff content. We also investigate these operators on Choquet-Morrey spaces. These results are extensions of the previous works due to Adams, Orobitg and Verdera, and Tang. The results for the fractional integral operator $I_α$ are essentially new.

math.FA↗
arXiv2022

Rossby-Haurwitz wave in a rotating bubble-shaped Bose-Einstein condensate

A Rossby-Haurwitz (RH) wave is an excitation mode of a fluid on a rotating spherical surface, which propagates westward in the rotating frame of reference. Motivated by the recent realization of the shell-shaped Bose-Einstein condensate in microgravity, we investigate the RH wave in a superfluid rotating on a spherical-surface geometry. We employ the point-vortex model and the three-dimensional Gross-Pitaevskii equation, and numerically demonstrate that RH waves can be observed in the system of a superfluid with quantized vortices.

cond-mat.quant-gas↗
arXiv2022

Long lifetime supersolid in a two-component dipolar Bose-Einstein condensate

Recent studies on supersolidity in a single-component Bose-Einstein condensate (BEC) have relied on the Lee-Huang-Yang (LHY) correction for stabilization of self-bound droplets, which however involves a high density inside the droplets, limiting the lifetime of the supersolid. Here we propose a two-component mixture of dipolar and nondipolar BECs, such as an $^{166}$Er-$^{87}$Rb mixture, to create and stabilize a supersolid without the LHY correction, which can suppress the atomic loss and may allow observation of the long-time dynamics of the supersolid. In such a system, supersolidity can be controlled by the difference in the trap centers between the two components.

cond-mat.quant-gas↗
arXiv2022

Phase separation and multistability of two-component Bose-Einstein condensate in an optical cavity

We examine the multistability associated with miscibility-immiscibility conditions for a two-component Bose-Einstein condensate coupled to the light field in an optical cavity. For a strongly immiscible condition, the system exhibits a variety of density structures, including separated state, stripe state, and their coexistence. The multistability arises from these spatial structures of the two-component condensate, which significantly alter the hysteresis curve with respect to the intensity of cavity pumping. We present a variational approach to confirm our numerical results.

cond-mat.quant-gas↗