arXiv subjects

Kazuya Fujimoto

Publications and source records attributed to Kazuya Fujimoto.

At least 19 recordsLinked to original sources

arXiv2026

Criteria for Feasible Monte Carlo Stochastic Simulations of Bosonic Markovian Open Quantum Dynamics

The Monte Carlo sampling of the stochastic differential equations (SDEs) based on the quasiprobability distribution function, such as the Glauber--Sudarshan P, Wigner, and Husimi Q functions provides a powerful framework for investigating bosonic open quantum many-body dynamics described by the Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) equation, while considering the effects of quantum fluctuations beyond the mean-field approximation. However, the stochastic Monte Carlo simulation is possible only when the corresponding Fokker--Planck equation has a positive-semidefinite diffusion matrix, and the general conditions for the diffusion matrix to be positive semidefinite have remained unclear. In this work, starting from the path integral formulation, we first derive the sufficient conditions under which the diffusion matrix is positive semidefinite for an arbitrary Hamiltonian, jump operators, and choice of quasiprobability distribution functions. We also analytically derive the corresponding SDEs to be solved. We then investigate the dynamics of the GKSL equation in the thermodynamic limit and show that, depending on the form of the jump operators, the mean-field approximation may fail to describe the dynamics accurately, making stochastic Monte Carlo simulations indispensable. Furthermore, we derive the sufficient conditions under which the higher-order quantum fluctuation terms beyond the Fokker--Planck description vanish identically, even when the jump operators contain quadratic terms. Under these conditions, whenever the corresponding SDEs can be derived, the stochastic Monte Carlo simulation reproduces the exact dynamics. These results clarify the conditions under which the stochastic Monte Carlo simulations are both feasible and necessary for accurately describing the dynamics governed by the GKSL equation in phase space.

cond-mat.quant-gas↗

arXiv2026

Integral formula for the propagator of the one-dimensional Hubbard model

We present an exact integral formula for the multi-particle propagator of the one-dimensional Fermi--Hubbard model on an infinite lattice. The proof is based on the nested Bethe ansatz without relying on the string hypothesis. Our formula enables an explicit integral representation of the time evolution of arbitrary finite-particle wave functions and thereby provides a foundation for the exact analysis of nonequilibrium dynamics in the Hubbard model. It can further be applied to related open quantum models.

cond-mat.stat-mech↗

arXiv2026

Exact Current Fluctuations in a Tight-Binding Chain with Dephasing Noise

The full counting statistics (FCS) of current has long provided fundamental insights into nonequilibrium systems. Recently, the FCS in quantum many-body systems has attracted growing attention, driven by rapid experimental progress in measuring current fluctuations. Nevertheless, for diffusive quantum many-body dynamics, the FCS of current has yet to be obtained exactly. In this Letter, we present the first exact solution for the FCS of current in a diffusive quantum many-body system, specifically a tight-binding chain with dephasing noise. By leveraging the system's SU(2) symmetry and a mapping to the one-dimensional Hubbard model, we derive an exact Fredholm determinant representation for the moment generating function of the time-integrated current. Our long-time asymptotic analysis shows that the cumulant generating function, and hence the corresponding large-deviation function, exhibit diffusive scaling for any nonzero dephasing. We compare our theoretical predictions with experimentally measured current variance and find consistent diffusive scaling.

cond-mat.stat-mech↗

arXiv2026

An Equation of State for Turbulence in the Gross-Pitaevskii model

We report the numerical observation of a far-from-equilibrium equation of state (EOS) in the Gross-Pitaevskii model. We first show that the momentum distribution of the turbulent cascade is well described by wave-turbulent kinetic theory in the appropriate limits. Calculating the energy and particle fluxes $Π_\varepsilon(k)$ and $Π_N(k)$, we show that the turbulent state possesses the hallmarks of a direct energy cascade. Building on this, we show that the GP model encodes a universal EOS in the form of a relationship between the turbulent cascade's momentum distribution amplitude $n_0$ and the energy flux $ε$ in the steady state. We find that in our regime of `mixed' turbulence - where both vortices and waves play a significant role - $n_0\propto ε^{0.67(2)}$, a result that is not captured by any existing theory of turbulence but that agrees with a recent experimental measurement for large energy fluxes. Finally, we find that the concept of quasi-static thermodynamic processes between equilibrium states extends to far-from-equilibrium steady states.

cond-mat.quant-gas↗

arXiv2026

Exact Anomalous Current Fluctuations in Quantum Many-Body Dynamics

Fluctuations of integrated currents have attracted considerable interest over the past decades in the context of statistical mechanics. Recently, anomalous current fluctuations, characterized by the M-Wright function, were obtained exactly in a classical automaton [$Ž$. Krajnik et al., Phys. Rev. Lett. 128, 160601 (2022)], and previous studies have shown that the anomalous behavior can arise in a variety of classical systems. Despite the rapidly growing interest in such anomalous behaviors, which capture a universal aspect of one-dimensional many-body transport, the exact derivation of the M-Wright function in quantum many-body systems has remained elusive. In this Letter, we present the first exact microscopic derivation of the M-Wright function in quantum many-body dynamics by analyzing the integrated spin current in a one-dimensional Fermi-Hubbard model with infinitely strong repulsive interactions. Our results lay the groundwork for exploring anomalous integrated currents in a broad class of quantum many-body systems.

cond-mat.stat-mech↗

arXiv2026

Universal Family-Vicsek scaling in quantum gases far from equilibrium

Fluctuations in the growing surfaces of classical systems can exhibit universal scaling behavior, known as Family-Vicsek (FV) scaling. Although this phenomenon was originally discovered in classical stochastic models, recent theoretical studies have demonstrated the presence of FV scaling in quantum many-body systems as well. Here, we observe the universal FV scaling in a one-dimensional Bose gas in an optical lattice. By monitoring the fluctuations of particle number in half of the system, which corresponds to the surface roughness, we extract all scaling exponents and demonstrate that the entire relaxation-from the growth of quantum fluctuations to their saturation-is captured by a single universal scaling function. Our results demonstrate that universal scaling laws of classical surface growth extend to quantum many-body systems, establishing a unified framework for nonequilibrium universality across classical and quantum systems.

cond-mat.quant-gas↗

arXiv2025

Path-Integral Formulation of Bosonic Markovian Open Quantum Dynamics with Monte Carlo stochastic trajectories using the Glauber-Sudarshan P, Wigner, and Husimi Q Functions and Hybrids

The Monte Carlo (MC) trajectory sampling of stochastic differential equations (SDEs) based on the quasiprobabilities, such as the Glauber-Sudarshan P, Wigner, and Husimi Q functions, enables us to investigate bosonic open quantum many-body dynamics described by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. In this method, the MC samplings for the initial distribution and stochastic noises incorporate quantum fluctuations, and thus, we can go beyond the mean-field approximation. However, description using SDEs is possible only when the corresponding Fokker-Planck equation has a positive-semidefinite diffusion matrix. In this work, we analytically derive the SDEs for arbitrary Hamiltonian and jump operators based on the path-integral formula, independently of the derivation of the Fokker-Planck equation (FPE). In the course of the derivation, we formulate the path-integral representation of the GKSL equation by using the $s$-ordered quasiprobability, which systematically describes the aforementioned quasiprobabilities by changing the real parameter $s$. The essential point of this derivation is that we employ the Hubbard-Stratonovich (HS) transformation in the path integral, and its application is not always feasible. We find that the feasible condition of the HS transformation is identical to the positive-semidefiniteness condition of the diffusion matrix in the FPE. In the benchmark calculations, we confirm that the MC simulations of the obtained SDEs well reproduce the exact dynamics of physical quantities and non-equal time correlation functions of numerically solvable models, including the Bose-Hubbard model. This work clarifies the applicability of the approximation and gives systematic and simplified procedures to obtain the SDEs to be numerically solved.

cond-mat.quant-gas↗

arXiv2025

Path-Integral Formulation of Truncated Wigner Approximation for Bosonic Markovian Open Quantum Systems

The truncated Wigner approximation (TWA) enables us to investigate bosonic quantum many-body dynamics, including open quantum systems described by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. In the TWA, the Weyl-Wigner transformation, a way of mapping from quantum-mechanical operators to $c$-numbers, of the GKSL equation leads to the Fokker-Planck equation, which we calculate by reducing it to the corresponding stochastic differential equations. However, the Fokker-Planck equation is not always reduced to the stochastic differential equations depending on details of jump operators. In this work, we clarify the condition for obtaining the stochastic differential equations from the Fokker-Planck equation and derive analytical expressions of these equations for a system with an arbitrary Hamiltonian with jump operators that do not couple different states. This result enables us to shortcut the conventional complicated calculations in applying the TWA. In the course of the derivation, we formulate the GKSL equation by using the path-integral representation based on the Weyl-Wigner transformation, which gives us a clear interpretation of the relation between the TWA and quantum fluctuations and allows us to calculate the non-equal time correlation functions in the TWA. In the benchmark calculations, we numerically confirm that the relaxation dynamics of physical quantities including the non-equal time correlation functions obtained in our formulation agrees well with the exact ones in the numerically solvable models.

cond-mat.stat-mech↗

arXiv2025

Exact density profile in a tight-binding chain with dephasing noise

We theoretically investigate the many-body dynamics of a tight-binding chain with dephasing noise on the infinite interval. We obtain the exact solution of an average particle-density profile for the domain wall and the alternating initial conditions via the Bethe ansatz, analytically deriving the asymptotic expressions for the long time dynamics. For the domain wall initial condition, we obtain the scaling form of the average density, elucidating that the diffusive transport always emerges in the long time dynamics if the strength of the dephasing, no matter how small, is positive. For the alternating initial condition, our exact solution leads to the fact that the average density displays oscillatory decay or over-damped decay depending on the strength of the dissipation. Furthermore, we demonstrate that the asymptotic forms approach those of the symmetric simple exclusion process, identifying corrections from it.

cond-mat.stat-mech↗

arXiv2024

Quantum Transport in Interacting Spin Chains: Exact Derivation of the GUE Tracy-Widom Distribution

We theoretically study quantum spin transport in a one-dimensional folded XXZ model with an alternating domain-wall initial state via the Bethe ansatz technique, exactly demonstrating that a probability distribution of finding a left-most up-spin with an appropriate scaling variable converges to the Tracy-Widom distribution for the Gaussian unitary ensemble (GUE), which is a universal distribution for the largest eigenvalue of GUE under a soft-edge scaling limit. Our finding presented here offers a first exact derivation of the GUE Tracy-Widom distribution in the dynamics of the interacting quantum model not being mapped to a noninteracting fermion Hamiltonian via the Jordan-Wigner transformation. On the basis of the exact solution of the folded XXZ model and our numerical analysis of the XXZ model, we discuss a universal behavior for the probability of finding the left-most up-spin in the XXZ model.

cond-mat.stat-mech↗

arXiv2024

Exact Solution of Bipartite Fluctuations in One-Dimensional Fermions

Emergence of hydrodynamics in quantum many-body systems has recently garnered growing interest. The recent experiment of ultracold atoms [J. F. Wienand {\it et al.}, Nat. Phys. (2024), doi:10.1038/s41567-024-02611-z] studied emergent hydrodynamics in hard-core bosons using a bipartite fluctuation, which quantifies how the particle number fluctuates in a subsystem. In this Letter, we theoretically study the variance of a bipartite fluctuation in one-dimensional noninteracting fermionic dynamics starting from an alternating state, deriving the exact solution of the variance and its asymptotic linear growth law for the long-time dynamics. To compare the theoretical prediction with the experiment, we generalize our exact solution by incorporating the incompleteness of the initial alternating state, deriving the general linear growth law analytically. We find that it shows good agreement with the experimentally observed variance growth without any fitting parameters. Furthermore, we estimate a time scale for the local equilibration using our exact solution, finding that the time scale is independent of the initial incompleteness. To investigate the interaction effect, we implement numerical studies for the variance growth in interacting fermions, which has yet to be explored experimentally. As a result, we find that the presence of interactions breaks the linear variance growth derived in the noninteracting fermions. Our exact solutions and numerical findings here lay a foundation for growing bipartite fluctuations in quantum many-body dynamics.

cond-mat.quant-gas↗

arXiv2023

Designing nontrivial one-dimensional Floquet topological phases using a spin-1/2 double-kicked rotor

A quantum kicked rotor model is one of the promising systems to realize various Floquet topological phases. We consider a double-kicked rotor model for a one-dimensional quasi-spin-1/2 Bose-Einstein condensate with spin-dependent and spin-independent kicks which are implementable for cold atomic experiments. We theoretically show that the model can realize all the Altland-Zirnbauer classes with nontrivial topology in one dimension. In the case of class CII, we show that a pair of winding numbers $(w_0,w_π)\in 2\mathbb{Z}\times 2\mathbb{Z}$ featuring the edge states at zero and $π$ quasienergy, respectively, takes various values depending on the strengths of the kicks. We also find that the winding numbers change to $\mathbb{Z}$ when we break the time-reversal and particle-hole symmetries by changing the phase of a kicking lattice. We numerically confirm that the winding numbers can be obtained by measuring the mean chiral displacement in the long-time limit in the present case with four internal degrees of freedom. We further propose two feasible methods to experimentally realize the spin-dependent and spin-independent kicks required for various topological phases.

cond-mat.quant-gas↗

arXiv2023

Random Matrix Statistics in Propagating Correlation Fronts of Fermions

We theoretically study propagating correlation fronts in non-interacting fermions on a one-dimensional lattice starting from an alternating state, where the fermions occupy every other site. We find that, in the long-time asymptotic regime, all the moments of dynamical fluctuations around the correlation fronts are described by the universal correlation functions of Gaussian orthogonal and symplectic random matrices at the soft edge. Our finding here sheds light on a hitherto unknown connection between random matrix theory and correlation propagation in quantum dynamics.

quant-ph↗

arXiv2023

Controlling particle current in a many-body quantum system by external driving

We propose a method to control the particle current of a one-dimensional quantum system by resonating two many-body states through an external driving field. We consider the Bose-Hubbard and spinless Fermi-Hubbard models with the Peierls phase which induces net particle currents in the many-body eigenstates. A driving field couples the ground state with one of the excited states having large net currents, enabling us to control the system's current via Rabi oscillation. Employing the Floquet analysis, we find that the resonate excited states are determined by the symmetry of the driving field, which allows us to selectively excite only certain states among the dense spectrum of a many-body quantum system.

cond-mat.quant-gas↗

arXiv2022

Impact of Dissipation on Universal Fluctuation Dynamics in Open Quantum Systems

Recent experimental and theoretical works have uncovered nontrivial quantum dynamics due to external dissipation. Using an exact numerical method and a renormalization-group-based analytical technique, we theoretically elucidate that dissipation drastically alters universal particle-number-fluctuation dynamics related to surface-roughness growth in non-interacting fermions and bosons. In a system under dephasing that causes loss of spatial coherence, we find that a universality class of surface-roughness dynamics changes from the ballistic class to a class with the Edwards-Wilkinson scaling exponents and an unconventional scaling function. On the other hand, in a system under dissipation with in- and out-flow of particles that breaks particle-number conservation, the universal dynamics is lost.

quant-ph↗

arXiv2021

Dynamical Scaling of Surface Roughness and Entanglement Entropy in Disordered Fermion Models

Localization is one of the most fundamental interference phenomena caused by randomness, and its universal aspects have been extensively explored from the perspective of one-parameter scaling mainly for static properties. We numerically study dynamics of fermions on disordered onedimensional potentials exhibiting localization and find dynamical one-parameter scaling for surface roughness, which represents particle-number fluctuations at a given lengthscale, and for entanglement entropy when the system is in delocalized phases. This dynamical scaling corresponds to the Family-Vicsek scaling originally developed in classical surface growth, and the associated scaling exponents depend on the type of disorder. Notably, we find that partially localized states in the delocalized phase of the random-dimer model lead to anomalous scaling, where destructive interference unique to quantum systems leads to exponents unknown for classical systems and clean systems.

cond-mat.quant-gas↗

arXiv2021

Spin-wave growth via Shapiro resonances in a spinor Bose-Einstein condensate

We theoretically study the resonant phenomenon in a spin-1 Bose-Einstein condensate periodically driven by a quadratic Zeeman coupling. This phenomenon is closely related to the Shapiro steps in superconducting Josephson junctions, and the previous experimental work [Evrard $et al.,$ Phys. Rev. A 100, 023604 (2019)] for a spin-1 bosonic system observed the resonant dynamics and then called it Shapiro resonance. In this work, using the spin-1 Gross-Pitaevskii equation, we study the Shapiro resonance beyond the single-mode approximation used in the previous work, which assumes that all components of the spinor wavefunction have the same spatial configuration. Considering resonant dynamics starting from a polar state, we analytically calculate the Floquet-Lyapunov exponents featuring an onset of the resonance under a linear analysis and find that spin waves with finite wavenumbers can be excited. This kind of non-uniform excitation cannot be described by the single-mode approximation. Furthermore, to study the long-time resonant dynamics beyond the linear analysis, we numerically solve the one-dimensional spin-1 Gross-Pitaevskii equation, finding that the nonresonant hydrodynamic variables also grow at wavelengths of even multiples of the resonant one due to the nonlinear effect.

cond-mat.quant-gas↗

arXiv2020

Magnetic soliton: from two to three components with SO(3) symmetry

Recent theoretical and experimental research has explored magnetic solitons in binary Bose-Einstein condensates (BECs). Here we demonstrate that such solitons are part of an SO(3) soliton family when embedded within a full three-component spin-1 manifold with spin-rotational symmetry. To showcase this, we have experimentally created a new type of domain wall magnetic soliton (DWMS) obtained by 90 degree rotations, which consist of a boundary between easy-axis and easy-plane polar phases. Collisions between SO(3) solitons are investigated by numerically solving the Gross-Pitaevskii equations, which exhibit novel properties including rotation and dissipation of soliton spin polarization.

cond-mat.quant-gas↗