Syo Kamata

• Ph.D.
• Project assistant prof. at The University of Tokyo

We explore the application of the exact Wentzel-Kramers-Brillouin (WKB) analysis to two-level Floquet systems and establish a systematic procedure to calculate the quasi-energy and Floquet effective Hamiltonian. We show that, in the exact-WKB analysis, the quasi-energy and Floquet effective Hamiltonian can be expressed in terms of cycle integrals (...

We consider resurgence for the nonconformal Bjorken flow with Fermi-Dirac and Bose-Einstein statistics in the extended relaxation-time approximation. First, we examine the full formal transseries expanded around the equilibrium and then construct the resurgent relation by looking at the structure of Borel-transformed ordinary differential equations...

This is a pedagogical review of the possible connection between the stochastic quantization in physics and the diffusion models in machine learning. For machine-learning applications, the denoising diffusion model has been established as a successful technique, which is formulated in terms of the stochastic differential equation (SDE). In this revi...

We discuss the machine-learning inference and uncertainty quantification for the equation of state (EOS) of the neutron star matter directly using the NS probability distribution from the observations. We previously proposed a prescription for uncertainty quantification based on ensemble learning by evaluating output variance from independently tra...

We study exact Wentzel–Kramers–Brillouin analysis (EWKB) for a P T symmetric quantum mechanics (QM) defined by the potential V P T ( x ) = ω 2 x 2 + g x 2 K ( i x ) ϵ with ω ∈ R ≥ 0 , g ∈ R > 0 and K , ϵ ∈ N to clarify its perturbative/nonperturbative structure. In our analysis, we mainly consider the massless cases, i.e., ω = 0 , and derive the ex...

We study exact Wentzel-Kramers-Brillouin analysis (EWKB) for a ${\cal PT}$ symmetric quantum mechanics (QM) defined by the potential that $V_{\cal PT}(x) = \omega^2 x^2 + g x^{2 K} (i x)^{\varepsilon}$ with $\omega \in {\mathbb R}_{\ge 0}$, $g \in {\mathbb R}_{>0}$ and $K, \varepsilon \in {\mathbb N}$ to clarify its perturbative/non-perturbative st...

We consider exact Wentzel-Kramers-Brillouin analysis to a P T symmetric quantum mechanics defined by the potential, V ( x ) = ω 2 x 2 + g x 2 ( i x ) ϵ = 2 with ω ∈ R ≥ 0 , g ∈ R > 0 . We in particular aim to verify a conjecture proposed by Ai-Bender-Sarkar (ABS), that pertains to a relation between D -dimensional P T -symmetric theories and analyt...

In this work we investigate the impact of conformal symmetry breaking on hydrodynamization of a far-from-equilibrium fluid. We find a new kind of transseries solutions for the nonconformal hydrodynamic equations of a longitudinal boost invariant expanding plasma. The new transseries solutions unveil a rich physical structure which arises due to the...

We discuss all-order transseries in one of the simplest quantum mechanical systems: a U(1) symmetric single-degree-of-freedom system with a first-order time derivative term. Following the procedure of the Lefschetz thimble method, we explicitly evaluate the path integral for the generating function of the Noether charge and derive its exact transse...

Quantum deformed potentials arise naturally in quantum mechanical systems of one bosonic coordinate coupled to Nf Grassmann valued fermionic coordinates, or to a topological Wess-Zumino term. These systems decompose into sectors with a classical potential plus a quantum deformation. Using exact Wentzel-Kramers-Brillouin, we derive exact quantizatio...

We consider resurgence for the nonconformal Bjorken flow with Fermi-Dirac and Bose-Einstein statistics on the extended relaxation-time approximation. We firstly consider full formal transseries expanded around the equilibrium and then construct the resurgent relation by looking to the structure of Borel transformed ODEs. We form a conjecture of the...

In this work we investigate the impact of conformal symmetry breaking on hydrodynamization of a far-from-equilibrium fluid. We find a new kind of transseries solutions for the non-conformal hydrodynamic equations of a longitudinal boost invariant expanding plasma. The new transseries solutions unveil a rich physical structure which arises due to th...

We discuss all-order transseries in one of the simplest quantum mechanical systems: a U(1) symmetric single-degree-of-freedom system with a first-order time derivative term. Following the procedure of the Lefschetz thimble method, we explicitly evaluate the path integral for the generating function of the Noether charge and derive its exact transse...

Quantum deformed potentials arise naturally in quantum mechanical systems of one bosonic coordinate coupled to $N_f$ Grassmann valued fermionic coordinates, or to a topological Wess-Zumino term. These systems decompose into sectors with a classical potential plus a quantum deformation. Using exact WKB, we derive exact quantization condition and its...

It is frequently supposed that quark-gluon plasma created in heavy-ion collisions undergoes free streaming at early times. We examine this issue based on the assumption that a universal attractor dominates the dynamics already at the earliest stages, which offers a way to connect the initial state with the start of the hydrodynamic expansion in an...

We study a resurgence structure of a quantum field theory with a phase transition to uncover relations between resurgence and phase transitions. In particular, we focus on three-dimensional N = 4 supersymmetric quantum electrodynamics (SQED) with multiple hypermultiplets, where a second-order quantum phase transition has been recently proposed in t...

A bstract We investigate the exact-WKB analysis for quantum mechanics in a periodic potential, with N minima on S ¹ . We describe the Stokes graphs of a general potential problem as a network of Airy-type or degenerate Weber-type building blocks, and provide a dictionary between the two. The two formulations are equivalent, but with their own pros...

We study a resurgence structure of a quantum field theory with a phase transition to uncover relations between resurgence and phase transitions. In particular, we focus on three-dimensional $\mathcal{N}=4$ supersymmetric quantum electrodynamics (SQED) with multiple hypermultiplets, where a second-order quantum phase transition has been recently pro...

We investigate the nonlinear transport processes and hydrodynamization of a system of gluons undergoing longitudinal boost-invariant expansion. The dynamics is described within the framework of the Boltzmann equation in the small-angle approximation. The kinetic equations for a suitable set of moments of the one-particle distribution function are d...

We investigate the exact-WKB analysis for quantum mechanics in a periodic potential, with $N $ minima on $S^{1}$. We describe the Stokes graphs of a general potential problem as a network of Airy-type or degenerate Weber-type building blocks, and provide a dictionary between the two. The two formulations are equivalent, but with their own pros and...

It is frequently supposed that quark-gluon plasma created in heavy-ion collisions undergoes free streaming at early times. We examine this issue based on the assumption that a universal attractor dominates the dynamics already at the earliest stages. Adopting fairly standard theoretical assumptions, we find that certain observables are discernibly...

A bstract There are two well-known approaches to studying nonperturbative aspects of quantum mechanical systems: saddle point analysis of the partition functions in Euclidean path integral formulation and the exact-WKB analysis based on the wave functions in the Schrödinger equation. In this work, based on the quantization conditions obtained from...

We investigate the non-linear transport processes and hydrodynamization of a system of gluons undergoing longitudinal boost-invariant expansion. The dynamics is described within the framework of the Boltzmann equation in the small-angle approximation. The kinetic equations for a suitable set of moments of the one-particle distribution function are...

Nonequilibrium Green’s functions provide an efficient way to describe the evolution of the energy-momentum tensor during the early-time preequilibrium stage of high-energy heavy-ion collisions. Besides their practical relevance they also provide a meaningful way to address the question when and to what extent a hydrodynamic description of the syste...

There are two well-known approaches to studying nonperturbative aspects of quantum mechanical systems: Saddle point analysis of the partition functions in Euclidean path integral formulation and the exact-WKB analysis based on the wave functions in the Schr\"{o}dinger equation. In this work, based on the quantization conditions obtained from the ex...

A bstract In this work we introduce the generic conditions for the existence of a non-equilibrium attractor that is an invariant manifold determined by the long-wavelength modes of the physical system. We investigate the topological properties of the global flow structure of the Gubser flow for the Israel-Stewart theory and a kinetic model for the...

Non-equilibrium Green's functions provide an efficient way to describe the evolution of the energy-momentum tensor during the early time pre-equilibrium stage of high-energy heavy ion collisions. Besides their practical relevance they also provide a meaningful way to address the question when and to what extent a hydrodynamic description of the sys...

We investigate the singularity structure of the (−1)F graded partition function in QCD with nf≥1 massive adjoint fermions in the large-N limit. Here, F is fermion number and N is the number of colors. The large N partition function is made reliably calculable by taking space to be a small three-sphere S3. Singularities in the graded partition funct...

The topological properties of the global flow structure of the Gubser flow for the Israel-Stewart theory and a kinetic model for the Boltzmann equation are investigated by employing Morse-Smale theory. We present a complete classification of the invariant submanifolds of the flow based on the skew product flow formalism of nonautonomous dynamical s...

We investigate the singularity structure of the $(-1)^F$ graded partition function in QCD with $n_f \geq 1$ massive adjoint fermions in the large-$N$ limit. Here, $F$ is fermion number and $N$ is the number of colors. The large $N$ partition function is made reliably calculable by taking space to be a small three-sphere $S^3$. Singularites in the g...

For the Bjorken flow we investigate the hydrodynamization of different modes of the one-particle distribution function by analyzing its relativistic kinetic equations. We calculate the constitutive relations of each mode written as a multi-parameter trans-series encoding the non-perturbative dissipative contributions quantified by the Knudsen Kn an...

In relativistic kinetic theory, the one-particle distribution function is approximated by an asymptotic perturbative power series in the Knudsen number which is divergent. For the Bjorken flow, we expand the distribution function in terms of its moments and study their nonlinear evolution equations. The resulting coupled dynamical system can be sol...

A bstract We derive the semiclassical contributions from the real and complex bions in the two-dimensional ℂ P N − 1 sigma model on ℝ× S ¹ with a twisted boundary condition. The bion configurations are saddle points of the complexified Euclidean action, which can be viewed as bound states of a pair of fractional instantons with opposite topological...

In relativistic kinetic theory, the one-particle distribution function is approximated by an asymptotic perturbative power series in Knudsen number which is divergent. For the Bjorken flow, we expand the distribution function in terms of its moments and study their nonlinear evolution equations. The resulting coupled dynamical system can be solved...

We study a certain class of supersymmetric (SUSY) observables in three-dimensional |$\mathcal{N}=2$| SUSY Chern–Simons (CS) matter theories and investigate how their exact results are related to the perturbative series with respect to coupling constants given by inverse CS levels. We show that the observables have non-trivial resurgent structures b...

We derive the semiclassical contributions from the real and complex bions in the two-dimensional $\mathbb C P^{N-1}$ sigma model on ${\mathbb R} \times S^{1}$ with a twisted boundary condition. The bion configurations are saddle points of the complexified Euclidean action, which can be viewed as bound states of a pair of fractional instantons with...

We study a certain class of supersymmetric (SUSY) observables in 3d $\mathcal{N}=2$ SUSY Chern-Simons (CS) matter theories and investigate how their exact results are related to the perturbative series with respect to coupling constants given by inverse CS levels. We show that the observables have nontrivial resurgent structures by expressing the e...

For the Bjorken flow we investigate the hydrodynamization of different modes of the one-particle distribution function by analyzing its relativistic kinetic equations. We calculate the constitutive relations of each mode written as a multi-parameter trans-series encoding the nonperturbative dissipative contributions quantified by the Knudsen $Kn$ a...

Statistical sampling with the complex Langevin (CL) equation is applied to (0+1)-dimensional Thirring model, and its uniform-field variant, at finite fermion chemical potential $\mu$. The CL simulation reproduces a crossover behavior which is similar to but actually deviating from the exact solution in the transition region, where we confirm that t...

We investigate the resurgence structure in quantum mechanical models originating in 2d non-linear sigma models with emphasis on nearly supersymmetric and quasi-exactly solvable parameter regimes. By expanding the ground state energy in powers of a supersymmetry-breaking deformation parameter $\delta \epsilon$, we derive exact results for the expans...

We investigate the resurgence structure in quantum mechanical models originating in 2d non-linear sigma models with emphasis on nearly supersymmetric and quasi-exactly solvable parameter regimes. By expanding the ground state energy in powers of a supersymmetry-breaking deformation parameter $\delta \epsilon$, we derive exact results for the expans...

The full resurgent trans-series is found exactly in near-supersymmetric CP1 quantum mechanics. By expanding in powers of the supersymmetry-breaking deformation parameter, we obtain the first and second expansion coefficients of the ground-state energy. They are an absolutely convergent series of nonperturbative exponentials corresponding to multibi...

The full resurgent trans-series is found exactly in near-supersymmetric $\mathbb C P^1$ quantum mechanics. By expanding in powers of the SUSY breaking deformation parameter, we obtain the first and second expansion coefficients of the ground state energy. They are absolutely convergent series of nonperturbative exponentials corresponding to multi-b...

We perform a numerical simulation of the two-dimensional ${\cal N}=(2,2)$ supersymmetric Yang-Mills (SYM) theory on the discretized curved space. The $U(1)_{A}$ anomaly of the continuum theory is maintained also in the discretized theory as an unbalance of the number of the fermions. In the process, we propose a new phase-quenched approximation, wh...

We discuss the nonperturbative contributions from real and complex saddle point solutions in the CP1 quantum mechanics with fermionic degrees of freedom, using the Lefschetz thimble formalism beyond the Gaussian approximation. We find bion solutions, which correspond to (complexified) instanton-anti-instanton configurations stabilized in the presen...

We discuss the non-perturbative contributions from real and complex saddle point solutions in the $\mathbb{C}P^1$ quantum mechanics with fermionic degrees of freedom, using the Lefschetz thimble formalism beyond the gaussian approximation. We find bion solutions, which correspond to (complexified) instanton-antiinstanton configurations stabilized i...

We investigate the two-dimensional $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills (SYM) theory on the discretized curved space (polyhedra). We first revisit that the number of supersymmetries of the continuum $\mathcal{N}=(2,2)$ SYM theory on any curved manifold can be enhanced at least to two by introducing an appropriate $U(1)$ gauge background as...

Based on the Lefschetz thimble formulation of path-integration, we analyze the (0+1) dimensional Thirring model at finite chemical potentials and perform hybrid Monte Carlo (HMC) simulations. We adopt the lattice action defined with the staggered fermion and a compact link field for the auxiliary vector field. We firstly locate the critical points...

We consider the one-dimensional massive Thirring model formulated on the lattice with staggered fermions and an auxiliary compact vector (link) field, which is exactly solvable and shows a phase transition with increasing the chemical potential of fermion number: the crossover at a finite temperature and the first order transition at zero temperatu...

We investigate Lefschetz thimble structure of the complexified path-integration in the one-dimensional lattice massive Thirring model with finite chemical potential. The lattice model is formulated with staggered fermions and a compact auxiliary vector boson (a link field), and the whole set of the critical points (the complex saddle points) are so...

We study the gauge/gravity duality for supersymmetric SU(N) Yang-Mills theory in 1+0 dimension with sixteen supercharges using lattice simulations. The conjectured duality states that the gravity side is described by N D0-branes in type IIA superstring at large N, and the thermal gauge theory reproduces the black hole thermodynamics at low temperat...

We construct two dimensional non-$\gamma_{5}$hermiticity fermions based on the minimal doubling fermion. We investigate basic properties: symmetries, eigenvalue distribution and number of poles for our fermions. As simple tests for application the fermion to concrete models, the Gross-Neveu model in two dimensions is studied using the non-$\gamma_{...

We construct two dimensional non-$\gamma_{5}$hermiticity fermions based on the minimal doubling fermion. We investigate symmetries, reflection positivity, eigenvalue distribution and the number of poles for our fermions. As simple tests for application to the fermion, the Gross-Neveu model in two dimensions is studied using the non-$\gamma_{5}$herm...

We analyze the lattice fermion kinetic term using PT symmetry, R-hermiticity, and γ5-hermiticity. R-hermiticity is a condition for Hermite action and it is related to γ5-hermiticity and PT symmetry. Assuming that a translation-invariant kinetic term with continuum and periodic function does not have PT symmetry, it can have R-hermiticity or γ5-herm...

We report on numerical simulations of one dimensional maximally supersymmetric SU(N) Yang-Mills theory, by using the lattice action with two exact supercharges. Based on the gauge/gravity duality, the gauge theory corresponds to N D0-branes system in type IIA superstring theory at finite temperature. We aim to verify the gauge/gravity duality numer...

The two-dimensional N=(2,2)N=(2,2) Wess–Zumino (WZ) model with a cubic superpotential is numerically studied with a momentum-cutoff regularization that preserves supersymmetry. A numerical algorithm based on the Nicolai map is employed and the resulting configurations have no autocorrelation. This system is believed to flow to an N=(2,2)N=(2,2) sup...