arXiv subjects

Toma Yoneya

Publications and source records attributed to Toma Yoneya.

3 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↗

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↗