We fill some of existed gaps in the correspondence between Supersymmetric Quantum Mechanics and the Inverse Scattering Transform by extending the consideration to the case of paired stationary and non-stationary Hamiltonians. We formulate the corresponding to the case Goursat problem and explicitly construct the kernel of the non-local Inverse Scattering Transform, which solves it. As a result, we find the way of constructing non-hermitian Hamiltonians from the initially hermitian ones, that leads, in the case of real-valued spectra of both potentials, to pairing of ${cal CPT/PT}$-invariant Hamiltonians. The relevance of our proposal to Quantum Optics and optical waveguides technology, as well as to non-linear dynamics and Black Hole Physics is briefly discussed.
{"title":"Non-stationary SQM/IST correspondence and CPT/PT-invariant paired hamiltonians on the line","authors":"V P Berezovoj, A J Nurmagambetov","doi":"10.1093/ptep/ptae074","DOIUrl":"https://doi.org/10.1093/ptep/ptae074","url":null,"abstract":"We fill some of existed gaps in the correspondence between Supersymmetric Quantum Mechanics and the Inverse Scattering Transform by extending the consideration to the case of paired stationary and non-stationary Hamiltonians. We formulate the corresponding to the case Goursat problem and explicitly construct the kernel of the non-local Inverse Scattering Transform, which solves it. As a result, we find the way of constructing non-hermitian Hamiltonians from the initially hermitian ones, that leads, in the case of real-valued spectra of both potentials, to pairing of ${cal CPT/PT}$-invariant Hamiltonians. The relevance of our proposal to Quantum Optics and optical waveguides technology, as well as to non-linear dynamics and Black Hole Physics is briefly discussed.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"21 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Krylov complexity is considered to provide a measure of the growth of operators evolving under Hamiltonian dynamics. The main strategy is the analysis of the structure of Krylov subspace $mathcal {K}_M(mathcal {H},eta )$ spanned by the multiple applications of the Liouville operator $mathcal {L}$ defined by the commutator in terms of a Hamiltonian $mathcal {H}$, $mathcal {L}:=[mathcal {H},cdot ]$ acting on an operator η, $mathcal {K}_M(mathcal {H},eta )=text{span}lbrace eta ,mathcal {L}eta ,ldots ,mathcal {L}^{M-1}eta rbrace$. For a given inner product ( ·, ·) of the operators, the orthonormal basis $lbrace mathcal {O}_nrbrace$ is constructed from $mathcal {O}_0=eta /sqrt{(eta ,eta )}$ by Lanczos algorithm. The moments $mu _m=(mathcal {O}_0,mathcal {L}^mmathcal {O}_0)$ are closely related to the important data {bn} called Lanczos coefficients. I present the exact and explicit expressions of the moments {μm} for 16 quantum mechanical systems which are exactly solvable both in the Schrödinger and Heisenberg pictures. The operator η is the variable of the eigenpolynomials. Among them six systems show a clear sign of ‘non-complexity’ as vanishing higher Lanczos coefficients bm = 0, m ≥ 3.
{"title":"Towards verifications of Krylov complexity","authors":"Ryu Sasaki","doi":"10.1093/ptep/ptae073","DOIUrl":"https://doi.org/10.1093/ptep/ptae073","url":null,"abstract":"Krylov complexity is considered to provide a measure of the growth of operators evolving under Hamiltonian dynamics. The main strategy is the analysis of the structure of Krylov subspace $mathcal {K}_M(mathcal {H},eta )$ spanned by the multiple applications of the Liouville operator $mathcal {L}$ defined by the commutator in terms of a Hamiltonian $mathcal {H}$, $mathcal {L}:=[mathcal {H},cdot ]$ acting on an operator η, $mathcal {K}_M(mathcal {H},eta )=text{span}lbrace eta ,mathcal {L}eta ,ldots ,mathcal {L}^{M-1}eta rbrace$. For a given inner product ( ·, ·) of the operators, the orthonormal basis $lbrace mathcal {O}_nrbrace$ is constructed from $mathcal {O}_0=eta /sqrt{(eta ,eta )}$ by Lanczos algorithm. The moments $mu _m=(mathcal {O}_0,mathcal {L}^mmathcal {O}_0)$ are closely related to the important data {bn} called Lanczos coefficients. I present the exact and explicit expressions of the moments {μm} for 16 quantum mechanical systems which are exactly solvable both in the Schrödinger and Heisenberg pictures. The operator η is the variable of the eigenpolynomials. Among them six systems show a clear sign of ‘non-complexity’ as vanishing higher Lanczos coefficients bm = 0, m ≥ 3.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"137 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pulsar wind nebulae (PWNe) are clouds of the magnetized relativistic electron/positron plasma supplied from the central pulsar. However, the number of radio-emitting particles inside a PWN is larger than the expectation from the study of pulsar magnetospheres and then their origin is still unclear. A stochastic acceleration of externally injected particles by a turbulence inside the PWN is proposed by our previous studies. In this paper, the previous stochastic acceleration model of the PWN broadband spectra is improved by taking into account the time evolution of the turbulent energy and then the total energy balance inside a PWN is maintained. The turbulent energy supplied from the central pulsar is wasted by the backreaction from the stochastic particle acceleration and the adiabatic cooling according the PWN expansion. The model is applied to the Crab Nebula and reproduce the current broadband emission spectrum, especially the flat radio spectrum although time evolution of the turbulent energy (diffusion coefficient) is a bit complicated compared with our previous studies, where we assumed an exponential behavior of the diffusion coefficient.
{"title":"A self-regulated stochastic acceleration model of pulsar wind nebulae","authors":"Shuta J Tanaka, Wataru Ishizaki","doi":"10.1093/ptep/ptae069","DOIUrl":"https://doi.org/10.1093/ptep/ptae069","url":null,"abstract":"Pulsar wind nebulae (PWNe) are clouds of the magnetized relativistic electron/positron plasma supplied from the central pulsar. However, the number of radio-emitting particles inside a PWN is larger than the expectation from the study of pulsar magnetospheres and then their origin is still unclear. A stochastic acceleration of externally injected particles by a turbulence inside the PWN is proposed by our previous studies. In this paper, the previous stochastic acceleration model of the PWN broadband spectra is improved by taking into account the time evolution of the turbulent energy and then the total energy balance inside a PWN is maintained. The turbulent energy supplied from the central pulsar is wasted by the backreaction from the stochastic particle acceleration and the adiabatic cooling according the PWN expansion. The model is applied to the Crab Nebula and reproduce the current broadband emission spectrum, especially the flat radio spectrum although time evolution of the turbulent energy (diffusion coefficient) is a bit complicated compared with our previous studies, where we assumed an exponential behavior of the diffusion coefficient.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"45 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We use the anti-de Sitter/conformal field theory (AdS/CFT) correspondence to find the least bounce action in an AdS false vacuum state, i.e., the most probable decay process of the metastable AdS vacuum within the Euclidean formalism by Callan and Coleman. It was shown that the O(4) symmetric bounce solution leads to the action minimum in the absence of gravity, but it is non-trivial in the presence of gravity. The AdS/CFT duality is used to evade the difficulties particular to a metastable gravitational system. To this end, we show that the Fubini bounce solution in CFT, corresponding to the Coleman de Luccia (CdL) bounce in AdS, gives the least action among all finite bounce solutions in a conformal scalar field theory. Thus, we prove that the CdL action is the least action among all possible large and thin-wall configurations under certain conditions.
{"title":"Is the coleman de luccia action minimum?: AdS/CFT approach","authors":"Naritaka Oshita, Yutaro Shoji, Masahide Yamaguchi","doi":"10.1093/ptep/ptae068","DOIUrl":"https://doi.org/10.1093/ptep/ptae068","url":null,"abstract":"We use the anti-de Sitter/conformal field theory (AdS/CFT) correspondence to find the least bounce action in an AdS false vacuum state, i.e., the most probable decay process of the metastable AdS vacuum within the Euclidean formalism by Callan and Coleman. It was shown that the O(4) symmetric bounce solution leads to the action minimum in the absence of gravity, but it is non-trivial in the presence of gravity. The AdS/CFT duality is used to evade the difficulties particular to a metastable gravitational system. To this end, we show that the Fubini bounce solution in CFT, corresponding to the Coleman de Luccia (CdL) bounce in AdS, gives the least action among all finite bounce solutions in a conformal scalar field theory. Thus, we prove that the CdL action is the least action among all possible large and thin-wall configurations under certain conditions.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"19 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
K Ichimura, K Chiba, Y Gando, H Ikeda, Y Kishimoto, M Kurasawa, K Nemoto, A Sakaguchi, Y Takaku, Y Sakakieda
We have established a method to measure picograms-per-gram (pg g−1) levels of 238U and 232Th in scintillation films by combining the dry ashing method and inductively coupled plasma mass spectrometry. Trace amounts of 238U and 232Th were measured in up to 2 g of the scintillation film with almost 100% collection efficiency. This paper details the experimental procedure, including the pretreatment of the samples and labware, detection limit of the method, collection efficiencies of 238U and 232Th, and measurement of 238U and 232Th in a polyethylene naphthalate film. This method is also applicable to 238U and 232Th measurements in other low-background organic materials for rare event search experiments.
{"title":"Development of a method to measure trace level of uranium and thorium in scintillation films","authors":"K Ichimura, K Chiba, Y Gando, H Ikeda, Y Kishimoto, M Kurasawa, K Nemoto, A Sakaguchi, Y Takaku, Y Sakakieda","doi":"10.1093/ptep/ptae071","DOIUrl":"https://doi.org/10.1093/ptep/ptae071","url":null,"abstract":"We have established a method to measure picograms-per-gram (pg g−1) levels of 238U and 232Th in scintillation films by combining the dry ashing method and inductively coupled plasma mass spectrometry. Trace amounts of 238U and 232Th were measured in up to 2 g of the scintillation film with almost 100% collection efficiency. This paper details the experimental procedure, including the pretreatment of the samples and labware, detection limit of the method, collection efficiencies of 238U and 232Th, and measurement of 238U and 232Th in a polyethylene naphthalate film. This method is also applicable to 238U and 232Th measurements in other low-background organic materials for rare event search experiments.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"16 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a six dimensional gauge theory compactified on $T^2/mathbb {Z}_2$ with magnetic flux. The configurations of models are classified by winding numbers at the fixed points. Requiring the existence of generation numbers and Yukawa coupling, we see that allowed and forbidden configurations are described by geometry of winding numbers.
{"title":"Toward realistic models in T2/ℤ2 flux compactification","authors":"Hiroki Imai, Nobuhito Maru","doi":"10.1093/ptep/ptae070","DOIUrl":"https://doi.org/10.1093/ptep/ptae070","url":null,"abstract":"We consider a six dimensional gauge theory compactified on $T^2/mathbb {Z}_2$ with magnetic flux. The configurations of models are classified by winding numbers at the fixed points. Requiring the existence of generation numbers and Yukawa coupling, we see that allowed and forbidden configurations are described by geometry of winding numbers.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"38 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Majorana fermions are spin-1/2 neutral particles that are their own antiparticles and were initially predicted by Ettore Majorana in particle physics but their observation still remains elusive. The concept of Majorana fermions has been borrowed into condensed matter physics, where, unlike particle physics, Majorana fermions emerge as zero-energy quasiparticles that can be engineered by combining electrons and holes and have therefore been coined Majorana zero modes. In this review, we provide a pedagogical explanation of the basic properties of Majorana zero modes in unconventional superconductors and their consequences in experimental observables, putting a special emphasis on the initial theoretical discoveries. In particular, we first show that Majorana zero modes are self-conjugated and emerge as a special type of zero energy surface Andreev bound states at the boundary of unconventional superconductors. We then explore Majorana zero modes in one-dimensional spin-polarized p-wave superconductors, where we address the formation of topological superconductivity and the physical realization in superconductor-semiconductor hybrids. In this part we highlight that Majorana quasiparticles appear as zero-energy edge states, exhibiting charge neutrality, spin-polarized, and spatial nonlocality as unique properties that can be already seen from their energies and wavefunctions. Next, we discuss analytically obtained Green’s functions of p-wave superconductors and demonstrate that the emergence of Majorana zero modes is always accompanied by the formation of odd-frequency spin-triplet pairing as a unique result of the self-conjugate nature of Majorana zero modes. We finally address the signatures of Majorana zero modes in tunneling spectroscopy, including the anomalous proximity effect, and the phase-biased Josephson effect.
马约拉纳费米子是自旋-1/2 的中性粒子，是自身的反粒子，最初是由埃托雷-马约拉纳（Ettore Majorana）在粒子物理学中预言的，但对它们的观测仍然遥不可及。马约拉纳费米子的概念被借用到凝聚态物理学中，与粒子物理学不同的是，马约拉纳费米子是以零能量准粒子的形式出现的，可以通过结合电子和空穴来实现，因此被称为马约拉纳零模。在这篇综述中，我们将对非常规超导体中马约拉纳零模的基本特性及其在实验观测指标中的后果进行教学解释，并特别强调最初的理论发现。特别是，我们首先证明了马约拉纳零模是自共轭的，是非常规超导体边界上一种特殊的零能面安德烈耶夫束缚态。然后，我们探讨了一维自旋极化 p 波超导体中的马约拉纳零模，并在此基础上讨论了拓扑超导的形成以及在超导体-半导体混合体中的物理实现。在这一部分中，我们强调马约拉纳准粒子作为零能级边缘态出现，表现出电荷中性、自旋极化和空间非局域性等独特性质，这些性质从它们的能量和波函数中已经可以看出。接下来，我们讨论了通过分析获得的 p 波超导体的格林函数，并证明马约拉纳零模的出现总是伴随着奇频自旋-三胞胎配对的形成，这是马约拉纳零模自共轭性质的独特结果。最后，我们讨论了马约拉纳零模在隧道光谱学中的特征，包括反常接近效应和相位偏约瑟夫森效应。
{"title":"Theory of majorana zero modes in unconventional superconductors","authors":"Yukio Tanaka, Shun Tamura, Jorge Cayao","doi":"10.1093/ptep/ptae065","DOIUrl":"https://doi.org/10.1093/ptep/ptae065","url":null,"abstract":"Majorana fermions are spin-1/2 neutral particles that are their own antiparticles and were initially predicted by Ettore Majorana in particle physics but their observation still remains elusive. The concept of Majorana fermions has been borrowed into condensed matter physics, where, unlike particle physics, Majorana fermions emerge as zero-energy quasiparticles that can be engineered by combining electrons and holes and have therefore been coined Majorana zero modes. In this review, we provide a pedagogical explanation of the basic properties of Majorana zero modes in unconventional superconductors and their consequences in experimental observables, putting a special emphasis on the initial theoretical discoveries. In particular, we first show that Majorana zero modes are self-conjugated and emerge as a special type of zero energy surface Andreev bound states at the boundary of unconventional superconductors. We then explore Majorana zero modes in one-dimensional spin-polarized p-wave superconductors, where we address the formation of topological superconductivity and the physical realization in superconductor-semiconductor hybrids. In this part we highlight that Majorana quasiparticles appear as zero-energy edge states, exhibiting charge neutrality, spin-polarized, and spatial nonlocality as unique properties that can be already seen from their energies and wavefunctions. Next, we discuss analytically obtained Green’s functions of p-wave superconductors and demonstrate that the emergence of Majorana zero modes is always accompanied by the formation of odd-frequency spin-triplet pairing as a unique result of the self-conjugate nature of Majorana zero modes. We finally address the signatures of Majorana zero modes in tunneling spectroscopy, including the anomalous proximity effect, and the phase-biased Josephson effect.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"50 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140835541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the gauge coupling unification (GCU) and proton decay in a non-supersymmetric SU(5) grand unified theory (GUT) incorporating a 45 representation Higgs field. Our analysis is based on the assumption that Georgi-Jarlskog-type mass matrices for fermions are responsible for explaining the mass ratio of the strange quark and the muon. We examine the conditions of GCU, taking into account the possibility that certain components of the 45 Higgs field have masses much smaller than the GUT scale. We have found that to satisfy the GCU conditions, at least two components of the 45 Higgs field should have such small masses. We search the parameter space to identify regions where the GCU conditions are satisfied, in the scenarios where two or three components of the 45 Higgs boson are hierarchically light. If the colored Higgs component of the 45 Higgs boson has a mass much smaller than the GUT scale, proton decay via colored Higgs boson exchange can occur with an observably large rate. We estimate the mass bounds for the colored Higgs component from the proton decay search at Super-Kamiokande and thereby further restrict the parameter space.
{"title":"Gauge coupling unification and proton decay via 45 Higgs boson in SU(5) GUT","authors":"Naoyuki Haba, Keisuke Nagano, Yasuhiro Shimizu, Toshifumi Yamada","doi":"10.1093/ptep/ptae066","DOIUrl":"https://doi.org/10.1093/ptep/ptae066","url":null,"abstract":"We study the gauge coupling unification (GCU) and proton decay in a non-supersymmetric SU(5) grand unified theory (GUT) incorporating a 45 representation Higgs field. Our analysis is based on the assumption that Georgi-Jarlskog-type mass matrices for fermions are responsible for explaining the mass ratio of the strange quark and the muon. We examine the conditions of GCU, taking into account the possibility that certain components of the 45 Higgs field have masses much smaller than the GUT scale. We have found that to satisfy the GCU conditions, at least two components of the 45 Higgs field should have such small masses. We search the parameter space to identify regions where the GCU conditions are satisfied, in the scenarios where two or three components of the 45 Higgs boson are hierarchically light. If the colored Higgs component of the 45 Higgs boson has a mass much smaller than the GUT scale, proton decay via colored Higgs boson exchange can occur with an observably large rate. We estimate the mass bounds for the colored Higgs component from the proton decay search at Super-Kamiokande and thereby further restrict the parameter space.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"5 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140812155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The observation of supernova neutrinos from SN1987A by KAMIOKANDE was an epoch-making event both for the neutrino astronomy and for supernova physics. The standard picture of stellar evolution and core-collapse supernovae were verified in basic points and their research entered into new advanced stages. In this article we overview the supernova neutrinos emitted from core-collapse supernova explosions as well as the significance of their observations.
{"title":"Neutrinos from core-collapse supernova explosions","authors":"Hideyuki Suzuki","doi":"10.1093/ptep/ptae056","DOIUrl":"https://doi.org/10.1093/ptep/ptae056","url":null,"abstract":"The observation of supernova neutrinos from SN1987A by KAMIOKANDE was an epoch-making event both for the neutrino astronomy and for supernova physics. The standard picture of stellar evolution and core-collapse supernovae were verified in basic points and their research entered into new advanced stages. In this article we overview the supernova neutrinos emitted from core-collapse supernova explosions as well as the significance of their observations.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"240 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a new method to solve the relativistic hydrodynamic equations based on implicit Runge-Kutta methods with a locally optimized fixed-point iterative solver. For numerical demonstration, we implement our idea for ideal hydrodynamics using the one-stage Gauss-Legendre method as an implicit method. The accuracy and computational cost of our new method are compared with those of explicit ones for the (1+1)-dimensional Riemann problem, as well as the (2+1)-dimensional Gubser flow and event-by-event initial conditions for heavy-ion collisions generated by TRENTo. We demonstrate that the solver converges with only one iteration in most cases, and as a result, the implicit method requires a smaller computational cost than the explicit one at the same accuracy in these cases, while it may not converge with an unrealistically large Δt. By showing a relationship between the one-stage Gauss-Legendre method with the iterative solver and the two-step Adams-Bashforth method, we argue that our method benefits from both the stability of the former and the efficiency of the latter.
{"title":"Efficient solver of relativistic hydrodynamics with implicit Runge-Kutta method","authors":"Nathan Touroux, Masakiyo Kitazawa, Koichi Murase, Marlene Nahrgang","doi":"10.1093/ptep/ptae058","DOIUrl":"https://doi.org/10.1093/ptep/ptae058","url":null,"abstract":"We propose a new method to solve the relativistic hydrodynamic equations based on implicit Runge-Kutta methods with a locally optimized fixed-point iterative solver. For numerical demonstration, we implement our idea for ideal hydrodynamics using the one-stage Gauss-Legendre method as an implicit method. The accuracy and computational cost of our new method are compared with those of explicit ones for the (1+1)-dimensional Riemann problem, as well as the (2+1)-dimensional Gubser flow and event-by-event initial conditions for heavy-ion collisions generated by TRENTo. We demonstrate that the solver converges with only one iteration in most cases, and as a result, the implicit method requires a smaller computational cost than the explicit one at the same accuracy in these cases, while it may not converge with an unrealistically large Δt. By showing a relationship between the one-stage Gauss-Legendre method with the iterative solver and the two-step Adams-Bashforth method, we argue that our method benefits from both the stability of the former and the efficiency of the latter.","PeriodicalId":20710,"journal":{"name":"Progress of Theoretical and Experimental Physics","volume":"78 1","pages":""},"PeriodicalIF":3.5,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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