@article{kamata_jankowski_martinez_2023, title={Novel features of attractors and transseries in nonconformal Bjorken flows}, volume={107}, ISSN={["2470-0029"]}, DOI={10.1103/PhysRevD.107.116004}, abstractNote={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 the interplay of different physical scales. In the perfect fluid case the non-conformal speed of sound slows down the cooling of the temperature due to the emergence of logarithmic corrections that depends on the mass of the particle. These terms propagate into the perturbative and non-perturbative sectors of the transseries once viscous corrections are included. The logarithmic mass contributions increase the asymptotic value of the Knudsen number while decreasing the damping rate of the transient non-hydrodynamic modes and thus, yielding to an extremely slow hydrodynamization process where flow lines merge to their forward attractor at extremely late times. The early time free streaming expansion is modified and receives logarithmic mass corrections induced by the shear-bulk couplings. The global flow structure and numerical analyses carried out in our work demonstrate the existence of the early and late-time attractors for the shear viscous tensor and bulk viscous pressure.}, number={11}, journal={PHYSICAL REVIEW D}, author={Kamata, Syo and Jankowski, Jakub and Martinez, Mauricio}, year={2023}, month={Jun} }
 @article{jankowski_kamata_martinez_spalinski_2021, title={Constraining the initial stages of ultrarelativistic nuclear collisions}, volume={104}, ISSN={["2470-0029"]}, DOI={10.1103/PhysRevD.104.074012}, abstractNote={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 sensitive to early-time behaviour. We show that the predicted final particle multiplicities measured in experiments point to an initial state with a pressure anisotropy of about 1 rather than 3/2, which would be expected in the case of free streaming. This result also implies a positive longitudinal pressure at early times.}, number={7}, journal={PHYSICAL REVIEW D}, author={Jankowski, Jakub and Kamata, Syo and Martinez, Mauricio and Spalinski, Michal}, year={2021}, month={Oct} }
 @article{sueishi_kamata_misumi_unsal_2021, title={Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on S-1}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP07(2021)096}, abstractNote={Abstract
                     We investigate the exact-WKB analysis for quantum mechanics in a periodic potential, with N minima on S1. 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 cons. Exact-WKB produces the quantization condition consistent with the known conjectures and mixed anomaly. The quantization condition for the case of N-minima on the circle factorizes over the Hilbert sub-spaces labeled by discrete theta angle (or Bloch momenta), and is consistent with ’t Hooft anomaly for even N and global inconsistency for odd N. By using Delabaere-Dillinger-Pham formula, we prove that the resurgent structure is closed in these Hilbert subspaces, built on discrete theta vacua, and by a transformation, this implies that fixed topological sectors (columns of resurgence triangle) are also closed under resurgence.}, number={7}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Sueishi, Naohisa and Kamata, Syo and Misumi, Tatsuhiro and Unsal, Mithat}, year={2021}, month={Jul} }
 @article{behtash_kamata_martinez_schafer_skokov_2021, title={Transasymptotics and hydrodynamization of the Fokker-Planck equation for gluons}, volume={103}, ISSN={["2470-0029"]}, url={http://inspirehep.net/record/1830583}, DOI={10.1103/PhysRevD.103.056010}, abstractNote={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 derived. By investigating the stability and asymptotic resurgent properties of this dynamical system, we demonstrate, that its solutions exhibit a rather different behavior for large (UV) and small (IR) effective Knudsen numbers. Close to the forward attractor in the IR regime the constitutive relations of each moment can be written as a multiparameter transseries. This resummation scheme allows us to extend the definition of a transport coefficient to the non-equilibrium regime naturally. Each transport coefficient is renormalized by the non-perturbative contributions of the non-hydrodynamic modes. The Knudsen number dependence of the transport coefficient is governed by the corresponding renormalization group flow equation. An interesting feature of the Yang-Mills plasma in this regime is that it exhibits transient non-Newtonian behavior while hydrodynamizing. In the UV regime the solution for the moments can be written as a power-law asymptotic series with a finite radius of convergence. We show that radius of convergence of the UV perturbative expansion grows linearly as a function of the shear viscosity to entropy density ratio. Finally, we compare the universal properties in the pullback and forward attracting regions to other kinetic models including the relaxation time approximation and the effective kinetic Arnold-Moore-Yaffe (AMY) theory.}, number={5}, journal={PHYSICAL REVIEW D}, publisher={American Physical Society (APS)}, author={Behtash, A. and Kamata, S. and Martinez, M. and Schafer, T. and Skokov, V}, year={2021}, month={Mar} }
 @article{behtash_kamata_martinez_shi_2020, title={Global flow structure and exact formal transseries of the Gubser flow in kinetic theory}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP07(2020)226}, abstractNote={Abstract
                     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 Boltzmann equation by employing Morse-Smale theory. We present a complete classification of the invariant submanifolds of the flow and determine all the possible flow lines connecting any pair of UV/IR fixed points. The formal transseries solutions to the Gubser dynamical system around the early-time (UV) and late-time (IR) fixed points are constructed and analyzed. It is proven that these solutions are purely perturbative (or power-law asymptotic) series with a finite radius of convergence. Based on these analyses, we find that Gubser-like expanding kinetic systems do not hydrodynamize owing to the failure of the hydrodynamization process which heavily relies on the classification of (non)hydrodynamic modes in the IR regime. This is in contrast to longitudinal boost-invariant plasmas where the asymptotic dynamics is described by a few terms of the hydrodynamic gradient expansion. We finally compare our results for both Bjorken and Gubser conformal kinetic models.}, number={7}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Behtash, Alireza and Kamata, Syo and Martinez, Mauricio and Shi, Haosheng}, year={2020}, month={Jul} }
 @article{kamata_martinez_plaschke_ochsenfeld_schlichting_2020, title={Hydrodynamization and nonequilibrium Green's functions in kinetic theory}, volume={102}, ISSN={["2470-0029"]}, DOI={10.1103/PhysRevD.102.056003}, abstractNote={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 system becomes applicable. Within the kinetic theory framework we derive a new method to calculate time dependent non-equilibrium Green's functions describing the evolution of energy and momentum perturbations on top of an evolving far-from-equilibrium background. We discuss the approach towards viscous hydrodynamics along with the emergence of various scaling phenomena for conformal systems. By comparing our results obtained in the relaxation time approximation to previous calculations in Yang-Mills kinetic theory, we further address the question which macroscopic features of the energy momentum tensor are sensitive to the underlying microscopic dynamics.}, number={5}, journal={PHYSICAL REVIEW D}, author={Kamata, Syo and Martinez, Mauricio and Plaschke, Philip and Ochsenfeld, Stephan and Schlichting, Soren}, year={2020}, month={Sep} }
 @article{sueishi_kamata_misumi_unsal_2020, title={On exact-WKB analysis, resurgent structure, and quantization conditions}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP12(2020)114}, abstractNote={AbstractThere 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 the exact-WKB method, we determine the relations between the two formalism and in particular show how the two Stokes phenomena are connected to each other: the Stokes phenomenon leading to the ambiguous contribution of different sectors of the path integral formulation corresponds to the change of the “topology” of the Stoke curves in the exact-WKB analysis. We also clarify the equivalence of different quantization conditions including Bohr-Sommerfeld, path integral and Gutzwiller’s ones. In particular, by reorganizing the exact quantization condition, we improve Gutzwiller’s analysis in a crucial way by bion contributions (incorporating complex periodic paths) and turn it into an exact result. Furthermore, we argue the novel meaning of quasi-moduli integral and provide a relation between the Maslov index and the intersection number of Lefschetz thimbles.}, number={12}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Sueishi, Naohisa and Kamata, Syo and Misumi, Tatsuhiro and Unsal, Mithat}, year={2020}, month={Dec} }
 @article{fujimori_kamata_misumi_nitta_sakai_2019, title={Bion non-perturbative contributions versus infrared renormalons in two-dimensional CPN-1 models}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP02(2019)190}, abstractNote={Abstract
          
          We derive the semiclassical contributions from the real and complex bions in the two-dimensional ℂP
            
              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 charges. We first derive the bion solutions by solving the equation of motion in the model with a potential which simulates an interaction induced by fermions in the ℂP
            
              N − 1 quantum mechanics. The bion solutions have quasi-moduli parameters corresponding to the relative distance and phase between the constituent fractional instantons. By summing over the Kaluza-Klein modes of the quantum fluctuations around the bion backgrounds, we find that the effective action for the quasi-moduli parameters is renormalized and becomes a function of the dynamical scale (or the renormalized coupling constant). Based on the renormalized effective action, we obtain the semiclassical bion contribution in a weak coupling limit by making use of the Lefschetz thimble method. We find in the supersymmetric case that the bion contribution vanishes as expected from supersymmetry. In non-supersymmetric cases, the non-perturbative contribution has an imaginary ambiguity which is consistent with the expected infrared renormalon ambiguity. Our results explicitly demonstrate that the complex bion can explain the infrared renormalon.}, number={2}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Fujimori, Toshiaki and Kamata, Syo and Misumi, Tatsuhiro and Nitta, Muneto and Sakai, Norisuke}, year={2019}, month={Feb} }
 @article{behtash_kamata_martinez_shi_2019, title={Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow}, volume={99}, ISSN={["2470-0029"]}, DOI={10.1103/PhysRevD.99.116012}, abstractNote={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 solved for each moment consistently using a multiparameter transseries which makes the constitutive relations inherit the same structure. A new nonperturbative dynamical renormalization scheme is born out of this formalism that goes beyond the linear response theory. We show that there is a Lyapunov function, also known as dynamical potential, which is, in general, a function of the moments and time satisfying Lyapunov stability conditions along renormalization group flows connected to the asymptotic hydrodynamic fixed point. As a result, the transport coefficients get dynamically renormalized at every order in the time-dependent perturbative expansion by receiving nonperturbative corrections present in the transseries. The connection between the integration constants and the UV data is discussed using the language of dynamical systems. Furthermore, we show that the first dissipative correction in the Knudsen number to the distribution function is not only determined by the known effective shear viscous term but also a new high-energy nonhydrodynamic mode. It is demonstrated that the survival of this new mode is intrinsically related to the nonlinear mode-to-mode coupling with the shear viscous term. Finally, we comment on some possible phenomenological applications of the proposed nonhydrodynamic transport theory.}, number={11}, journal={PHYSICAL REVIEW D}, author={Behtash, Alireza and Kamata, Syo and Martinez, Mauricio and Shi, Haosheng}, year={2019}, month={Jun} }
 @article{behtash_cruz-camacho_kamata_martinez_2019, title={Non-perturbative rheological behavior of a far-from-equilibrium expanding plasma}, volume={797}, ISSN={["1873-2445"]}, DOI={10.1016/j.physletb.2019.134914}, abstractNote={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 and inverse Reynolds Re−1 numbers. At any given order in the asymptotic expansion of each mode, the transport coefficients get effectively renormalized by summing over all non-perturbative sectors appearing in the trans-series. This gives an effective description of the transport coefficients that provides a new renormalization scheme with an associated renormalization group equation, going beyond the realms of linear response theory. As a result, the renormalized transport coefficients feature a transition to their equilibrium fixed point, which is a neat diagnostics of transient non-Newtonian behavior. As a proof of principle, we verify the predictions of the effective theory with the numerical solutions of their corresponding evolution equations. Our studies strongly suggest that the phenomenological success of fluid dynamics far from local thermal equilibrium is due to the transient rheological behavior of the fluid.}, journal={PHYSICS LETTERS B}, author={Behtash, Alireza and Cruz-Camacho, C. N. and Kamata, Syo and Martinez, M.}, year={2019}, month={Oct} }
 @article{martinez_behtash_cruz-camacho_kamata_2019, title={Relating the Lyapunov exponents to transport coefficients in kinetic theory}, volume={982}, ISSN={["1873-1554"]}, DOI={10.1016/j.nuclphysa.2018.10.078}, abstractNote={In this contribution, we report our recent findings on the phenomenological applications of non-equilibrium attractors to transport phenomena in fluid dynamics. Within the kinetic theory description, we study the non-linear hydrodynamization processes of a relativistic fluid undergoing Bjorken flow. The mathematical problem of solving the Boltzmann equation with a time-dependent relaxation time is recast into an infinite set of nonlinear ordinary differential equations for the moments of the one-particle distribution function. The constitutive relations of each non-hydrodynamic mode can be written as a multi-parameter trans-series that encodes the non-perturbative dissipative contributions quantified by the Knudsen Kn and inverse Reynolds Re−1 numbers. At a given order in the gradient expansion, we show that summing over all the non-perturbative sectors leads to a renormalized transport coefficient. The universal behavior of the renormalized shear viscosity is determined by the Lyapunov exponent and the anomalous dimension of the first moment at the stable fixed point. We comment on the relation between our findings and the physics of non-Newtonian fluids.}, journal={NUCLEAR PHYSICS A}, author={Martinez, M. and Behtash, A. and Cruz-Camacho, C. N. and Kamata, S.}, year={2019}, month={Feb}, pages={227–230} }
 @article{fujimori_honda_kamata_misumi_sakai_2018, title={Resurgence and Lefschetz thimble in three-dimensional N=2 supersymmetric Chern-Simons matter theories}, volume={2018}, ISSN={["2050-3911"]}, DOI={10.1093/ptep/pty118}, abstractNote={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 exact results as a full transseries consisting of perturbative and non-perturbative parts. As real mass parameters are varied, we encounter Stokes phenomena at an infinite number of points, where the perturbative series becomes non-Borel-summable due to singularities on the positive real axis of the Borel plane. We also investigate the Stokes phenomena when the phase of the coupling constant is varied. For these cases, we find that the Borel ambiguities in the perturbative sector are canceled by those in nonperturbative sectors and end up with an unambiguous result which agrees with the exact result even on the Stokes lines. We also decompose the Coulomb branch localization formula, which is an integral representation for the exact results, into Lefschetz thimble contributions and study how they are related to the resurgent transseries. We interpret the non-perturbative effects appearing in the transseries as contributions of complexified SUSY solutions which formally satisfy the SUSY conditions but are not on the original path integral contour.}, number={12}, journal={PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS}, author={Fujimori, Toshiaki and Honda, Masazumi and Kamata, Syo and Misumi, Tatsuhiro and Sakai, Norisuke}, year={2018}, month={Dec} }