We study classical lattice simulations of theories of electrodynamics coupled to charged matter at finite temperature, interpreting them using the higher-form symmetry formulation of magnetohydrodynamics (MHD). We compute transport coefficients using classical Kubo formulas on the lattice and show that the properties of the simulated plasma are in complete agreement with the predictions from effective field theories. In particular, the higher-form formulation allows us to understand from hydrodynamic considerations the relaxation rate of axial charge in the chiral plasma observed in previous simulations. A key point is that the resistivity of the plasma – defined in terms of Kubo formulas for the electric field in the 1-form formulation of MHD – remains a well-defined and predictive quantity at strong electromagnetic coupling. However, the Kubo formulas used to define the conventional conductivity vanish at low frequencies due to electrodynamic fluctuations, and thus the concept of the conductivity of a gauged electric current must be interpreted with care.
{"title":"Higher-form symmetry and chiral transport in real-time Abelian lattice gauge theory","authors":"Arpit Das, Adrien Florio, Nabil Iqbal, Napat Poovuttikul","doi":"10.21468/scipostphys.17.3.085","DOIUrl":"https://doi.org/10.21468/scipostphys.17.3.085","url":null,"abstract":"We study classical lattice simulations of theories of electrodynamics coupled to charged matter at finite temperature, interpreting them using the higher-form symmetry formulation of magnetohydrodynamics (MHD). We compute transport coefficients using classical Kubo formulas on the lattice and show that the properties of the simulated plasma are in complete agreement with the predictions from effective field theories. In particular, the higher-form formulation allows us to understand from hydrodynamic considerations the relaxation rate of axial charge in the chiral plasma observed in previous simulations. A key point is that the resistivity of the plasma – defined in terms of Kubo formulas for the electric field in the 1-form formulation of MHD – remains a well-defined and predictive quantity at strong electromagnetic coupling. However, the Kubo formulas used to define the conventional conductivity vanish at low frequencies due to electrodynamic fluctuations, and thus the concept of the conductivity of a gauged electric current must be interpreted with care.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}
Pub Date : 2024-09-19DOI: 10.21468/scipostphys.17.3.084
Bartlomiej Czech, Yu Liu, Bo Yu
We verify that the recently proven infinite families of holographic entropy inequalities are maximally tight, i.e. they are facets of the holographic entropy cone. The proof is technical but it offers some heuristic insight. On star graphs, both families of inequalities quantify how concentrated/spread information is with respect to a dihedral symmetry acting on subsystems. In addition, toric inequalities viewed in the K-basis show an interesting interplay between four-party and six-party perfect tensors.
我们验证了最近证明的全息熵不等式无穷族是最大紧密的，即它们是全息熵锥的面。这个证明是技术性的，但它提供了一些启发式的见解。在星形图上，这两组不等式都量化了作用于子系统的二面对称信息的集中/扩散程度。此外，以 K 为基础的环不等式显示了四方和六方完美张量之间有趣的相互作用。
{"title":"Two infinite families of facets of the holographic entropy cone","authors":"Bartlomiej Czech, Yu Liu, Bo Yu","doi":"10.21468/scipostphys.17.3.084","DOIUrl":"https://doi.org/10.21468/scipostphys.17.3.084","url":null,"abstract":"We verify that the recently proven infinite families of holographic entropy inequalities are maximally tight, i.e. they are facets of the holographic entropy cone. The proof is technical but it offers some heuristic insight. On star graphs, both families of inequalities quantify how concentrated/spread information is with respect to a dihedral symmetry acting on subsystems. In addition, toric inequalities viewed in the K-basis show an interesting interplay between four-party and six-party perfect tensors.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}
Pub Date : 2024-09-18DOI: 10.21468/scipostphys.17.3.082
Yuan Yao, Filippo Miatto, Nicolás Quesada
We propose a framework to design and optimize generic photonic quantum circuits composed of Gaussian objects (pure and mixed Gaussian states, Gaussian unitaries, Gaussian channels, Gaussian measurements) as well as non-Gaussian effects such as photon-number-resolving measurements. In this framework, we parametrize a phase space representation of Gaussian objects using elements of the symplectic group (or the unitary or orthogonal group in special cases), and then we transform it into the Fock representation using a single linear recurrence relation that computes the Fock amplitudes of any Gaussian object recursively. We also compute the gradient of the Fock amplitudes with respect to phase space parameters by differentiating through the recurrence relation. We can then use Riemannian optimization on the symplectic group to optimize $M$-mode Gaussian objects, avoiding the need to commit to particular realizations in terms of fundamental gates. This allows us to "mod out" all the different gate-level implementations of the same circuit, which now can be chosen after the optimization has completed. This can be especially useful when looking to answer general questions, such as bounding the value of a property over a class of states or transformations, or when one would like to worry about hardware constraints separately from the circuit optimization step. Finally, we make our framework extendable to non-Gaussian objects that can be written as linear combinations of Gaussian ones, by explicitly computing the change in global phase when states undergo Gaussian transformations. We implemented all of these methods in the freely available open-source library MrMustard, which we use in three examples to optimize the 216-mode interferometer in Borealis, and 2- and 3-modes circuits (with Fock measurements) to produce cat states and cubic phase states.
{"title":"Riemannian optimization of photonic quantum circuits in phase and Fock space","authors":"Yuan Yao, Filippo Miatto, Nicolás Quesada","doi":"10.21468/scipostphys.17.3.082","DOIUrl":"https://doi.org/10.21468/scipostphys.17.3.082","url":null,"abstract":"We propose a framework to design and optimize generic photonic quantum circuits composed of Gaussian objects (pure and mixed Gaussian states, Gaussian unitaries, Gaussian channels, Gaussian measurements) as well as non-Gaussian effects such as photon-number-resolving measurements. In this framework, we parametrize a phase space representation of Gaussian objects using elements of the symplectic group (or the unitary or orthogonal group in special cases), and then we transform it into the Fock representation using a single linear recurrence relation that computes the Fock amplitudes of any Gaussian object recursively. We also compute the gradient of the Fock amplitudes with respect to phase space parameters by differentiating through the recurrence relation. We can then use Riemannian optimization on the symplectic group to optimize $M$-mode Gaussian objects, avoiding the need to commit to particular realizations in terms of fundamental gates. This allows us to \"mod out\" all the different gate-level implementations of the same circuit, which now can be chosen after the optimization has completed. This can be especially useful when looking to answer general questions, such as bounding the value of a property over a class of states or transformations, or when one would like to worry about hardware constraints separately from the circuit optimization step. Finally, we make our framework extendable to non-Gaussian objects that can be written as linear combinations of Gaussian ones, by explicitly computing the change in global phase when states undergo Gaussian transformations. We implemented all of these methods in the freely available open-source library MrMustard, which we use in three examples to optimize the 216-mode interferometer in Borealis, and 2- and 3-modes circuits (with Fock measurements) to produce cat states and cubic phase states.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}
Pub Date : 2024-09-18DOI: 10.21468/scipostphys.17.3.083
Antoine Tilloy
This note derives the stochastic differential equations and partial differential equation of general hybrid quantum--classical dynamics from the theory of continuous measurement and general (non-Markovian) feedback. The advantage of this approach is an explicit parameterization, without additional positivity constraints. The construction also neatly separates the different effects: how the quantum influences the classical and how the classical influences the quantum. This modular presentation gives a better intuition of what to expect from hybrid dynamics, especially when used to construct possibly fundamental theories.
{"title":"General quantum-classical dynamics as measurement based feedback","authors":"Antoine Tilloy","doi":"10.21468/scipostphys.17.3.083","DOIUrl":"https://doi.org/10.21468/scipostphys.17.3.083","url":null,"abstract":"This note derives the stochastic differential equations and partial differential equation of general hybrid quantum--classical dynamics from the theory of continuous measurement and general (non-Markovian) feedback. The advantage of this approach is an explicit parameterization, without additional positivity constraints. The construction also neatly separates the different effects: how the quantum influences the classical and how the classical influences the quantum. This modular presentation gives a better intuition of what to expect from hybrid dynamics, especially when used to construct possibly fundamental theories.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}
Pub Date : 2024-09-18DOI: 10.21468/scipostphyscore.7.3.065
Juan Daniel Torres Luna, A. Mert Bozkurt, Michael Wimmer, Chun-Xiao Liu
Connecting quantum dots through Andreev bound states in a semiconductor-superconductor hybrid provides a platform to create a Kitaev chain. Interestingly, in a double quantum dot, a pair of poor man's Majorana zero modes can emerge when the system is fine-tuned to a sweet spot, where superconducting and normal couplings are equal in magnitude. Control of the Andreev bound states is crucial for achieving this, usually implemented by varying its chemical potential. In this work, we propose using Andreev bound states in a short Josephson junction to mediate both types of couplings, with the ratio tunable by the phase difference across the junction. Now a minimal Kitaev chain can be easily tuned into the strong coupling regime by varying the phase and junction asymmetry, even without changing the dot-hybrid coupling strength. Furthermore, we identify an optimal sweet spot at $pi$ phase, enhancing the excitation gap and robustness against phase fluctuations. Our proposal introduces a new device platform and a new tuning method for realizing quantum-dot-based Kitaev chains.
{"title":"Flux-tunable Kitaev chain in a quantum dot array","authors":"Juan Daniel Torres Luna, A. Mert Bozkurt, Michael Wimmer, Chun-Xiao Liu","doi":"10.21468/scipostphyscore.7.3.065","DOIUrl":"https://doi.org/10.21468/scipostphyscore.7.3.065","url":null,"abstract":"Connecting quantum dots through Andreev bound states in a semiconductor-superconductor hybrid provides a platform to create a Kitaev chain. Interestingly, in a double quantum dot, a pair of poor man's Majorana zero modes can emerge when the system is fine-tuned to a sweet spot, where superconducting and normal couplings are equal in magnitude. Control of the Andreev bound states is crucial for achieving this, usually implemented by varying its chemical potential. In this work, we propose using Andreev bound states in a short Josephson junction to mediate both types of couplings, with the ratio tunable by the phase difference across the junction. Now a minimal Kitaev chain can be easily tuned into the strong coupling regime by varying the phase and junction asymmetry, even without changing the dot-hybrid coupling strength. Furthermore, we identify an optimal sweet spot at $pi$ phase, enhancing the excitation gap and robustness against phase fluctuations. Our proposal introduces a new device platform and a new tuning method for realizing quantum-dot-based Kitaev chains.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}
Pub Date : 2024-09-16DOI: 10.21468/scipostphyscore.7.3.064
Anja Butter, Tomas Jezo, Michael Klasen, Mathias Kuschick, Sofia Palacios Schweitzer, Tilman Plehn
Off-shell effects in large LHC backgrounds are crucial for precision predictions and, at the same time, challenging to simulate. We present a novel method to transform high-dimensional distributions based on a diffusion neural network and use it to generate a process with off-shell kinematics from the much simpler on-shell one. Applied to a toy example of top pair production at LO we show how our method generates off-shell configurations fast and precisely, while reproducing even challenging on-shell features.
大型强子对撞机背景中的壳外效应对精确预测至关重要，同时也是模拟的挑战。我们提出了一种基于扩散神经网络转换高维分布的新方法，并用它从简单得多的壳上运动学过程生成壳外运动学过程。我们将其应用于一个在 LO 产生顶对的玩具例子，展示了我们的方法如何快速而精确地生成壳外构型，同时再现甚至具有挑战性的壳内特征。
{"title":"Kicking it off(-shell) with direct diffusion","authors":"Anja Butter, Tomas Jezo, Michael Klasen, Mathias Kuschick, Sofia Palacios Schweitzer, Tilman Plehn","doi":"10.21468/scipostphyscore.7.3.064","DOIUrl":"https://doi.org/10.21468/scipostphyscore.7.3.064","url":null,"abstract":"Off-shell effects in large LHC backgrounds are crucial for precision predictions and, at the same time, challenging to simulate. We present a novel method to transform high-dimensional distributions based on a diffusion neural network and use it to generate a process with off-shell kinematics from the much simpler on-shell one. Applied to a toy example of top pair production at LO we show how our method generates off-shell configurations fast and precisely, while reproducing even challenging on-shell features.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}
Pub Date : 2024-09-16DOI: 10.21468/scipostphys.17.3.081
Enrico Bothmann, Taylor Childers, Walter Giele, Stefan Höche, Joshua Isaacson, Max Knobbe
The rapid deployment of computing hardware different from the traditional CPU+RAM model in data centers around the world mandates a change in the design of event generators for the Large Hadron Collider, in order to provide economically and ecologically sustainable simulations for the high-luminosity era of the LHC. Parton-level event generation is one of the most computationally demanding parts of the simulation and is therefore a prime target for improvements. We present a production-ready leading-order parton-level event generation framework capable of utilizing most modern hardware and discuss its performance in the standard candle processes of vector boson and top-quark pair production with up to five additional jets.
{"title":"A portable parton-level event generator for the high-luminosity LHC","authors":"Enrico Bothmann, Taylor Childers, Walter Giele, Stefan Höche, Joshua Isaacson, Max Knobbe","doi":"10.21468/scipostphys.17.3.081","DOIUrl":"https://doi.org/10.21468/scipostphys.17.3.081","url":null,"abstract":"The rapid deployment of computing hardware different from the traditional CPU+RAM model in data centers around the world mandates a change in the design of event generators for the Large Hadron Collider, in order to provide economically and ecologically sustainable simulations for the high-luminosity era of the LHC. Parton-level event generation is one of the most computationally demanding parts of the simulation and is therefore a prime target for improvements. We present a production-ready leading-order parton-level event generation framework capable of utilizing most modern hardware and discuss its performance in the standard candle processes of vector boson and top-quark pair production with up to five additional jets.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}
Pub Date : 2024-09-13DOI: 10.21468/scipostphys.17.3.080
Salvatore D. Pace
We explore the rich landscape of higher-form and non-invertible symmetries that emerge at low energies in generic ordered phases. Using that their charge is carried by homotopy defects (i.e., domain walls, vortices, hedgehogs, etc.), in the absence of domain walls we find that their symmetry defects in $D$-dimensional spacetime are described by $(D-1)$-representations of a $(D-1)$-group that depends only on the spontaneous symmetry-breaking (SSB) pattern of the ordered phase. These emergent symmetries are not spontaneously broken in the ordered phase. We show that spontaneously breaking them induces a phase transition into a nontrivial disordered phase that can have symmetry-enriched (non-)Abelian topological orders, photons, and even more emergent symmetries. This SSB transition is between two distinct SSB phases--an ordinary and a generalized one--making it a possible generalized deconfined quantum critical point. We also investigate the 't Hooft anomalies of these emergent symmetries and conjecture that there is always a mixed anomaly between them and the microscopic symmetry spontaneously broken in the ordered phase. One way this anomaly can manifest is through the fractionalization of the microscopic symmetry's quantum numbers. Our results demonstrate that even the most exotic generalized symmetries emerge in ordinary phases and provide a valuable framework for characterizing them and their transitions.
{"title":"Emergent generalized symmetries in ordered phases and applications to quantum disordering","authors":"Salvatore D. Pace","doi":"10.21468/scipostphys.17.3.080","DOIUrl":"https://doi.org/10.21468/scipostphys.17.3.080","url":null,"abstract":"We explore the rich landscape of higher-form and non-invertible symmetries that emerge at low energies in generic ordered phases. Using that their charge is carried by homotopy defects (i.e., domain walls, vortices, hedgehogs, etc.), in the absence of domain walls we find that their symmetry defects in $D$-dimensional spacetime are described by $(D-1)$-representations of a $(D-1)$-group that depends only on the spontaneous symmetry-breaking (SSB) pattern of the ordered phase. These emergent symmetries are not spontaneously broken in the ordered phase. We show that spontaneously breaking them induces a phase transition into a nontrivial disordered phase that can have symmetry-enriched (non-)Abelian topological orders, photons, and even more emergent symmetries. This SSB transition is between two distinct SSB phases--an ordinary and a generalized one--making it a possible generalized deconfined quantum critical point. We also investigate the 't Hooft anomalies of these emergent symmetries and conjecture that there is always a mixed anomaly between them and the microscopic symmetry spontaneously broken in the ordered phase. One way this anomaly can manifest is through the fractionalization of the microscopic symmetry's quantum numbers. Our results demonstrate that even the most exotic generalized symmetries emerge in ordinary phases and provide a valuable framework for characterizing them and their transitions.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}
Pub Date : 2024-09-13DOI: 10.21468/scipostphyscore.7.3.063
Chu Guo, Ruofan Chen
The time-evolving matrix product operator (TEMPO) method has become a very competitive numerical method for studying the real-time dynamics of quantum impurity problems. For small impurities, the most challenging calculation in TEMPO is to construct the matrix product state representation of the Feynman-Vernon influence functional. In this work we propose an efficient method for this task, which exploits the time-translationally invariant property of the influence functional. The required number of matrix product state multiplication in our method is almost independent of the total evolution time, as compared to the method originally used in TEMPO which requires a linearly scaling number of multiplications. The accuracy and efficiency of this method are demonstrated for the Toulouse model and the single impurity Anderson model.
时间演化矩阵积算子（TEMPO）方法已成为研究量子杂质问题实时动态的一种极具竞争力的数值方法。对于小杂质，TEMPO 最具挑战性的计算是构建费曼-弗农影响函数的矩阵积状态表示。在这项工作中，我们提出了利用影响函数的时变不变特性来完成这项任务的高效方法。在我们的方法中，所需的矩阵乘积状态乘法次数几乎与总演化时间无关，而 TEMPO 最初使用的方法则需要按线性比例增加乘法次数。图卢兹模型和单杂质安德森模型证明了这种方法的准确性和高效性。
{"title":"Efficient construction of the Feynman-Vernon influence functional as matrix product states","authors":"Chu Guo, Ruofan Chen","doi":"10.21468/scipostphyscore.7.3.063","DOIUrl":"https://doi.org/10.21468/scipostphyscore.7.3.063","url":null,"abstract":"The time-evolving matrix product operator (TEMPO) method has become a very competitive numerical method for studying the real-time dynamics of quantum impurity problems. For small impurities, the most challenging calculation in TEMPO is to construct the matrix product state representation of the Feynman-Vernon influence functional. In this work we propose an efficient method for this task, which exploits the time-translationally invariant property of the influence functional. The required number of matrix product state multiplication in our method is almost independent of the total evolution time, as compared to the method originally used in TEMPO which requires a linearly scaling number of multiplications. The accuracy and efficiency of this method are demonstrated for the Toulouse model and the single impurity Anderson model.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}
Pub Date : 2024-09-12DOI: 10.21468/scipostphyscore.7.3.062
Steven Glenn Jackson, Hélène Perrin, Grigori E. Astrakharchik, Maxim Olshanii
The recently proposed exact quantum solution for two $delta$-function-interacting particles with a mass-ratio $3!:!1$ in a hard-wall box [Y. Liu, F. Qi, Y. Zhang and S. Chen, iScience 22, 181 (2019)] violates the conventional necessary condition for a Bethe Ansatz integrability, the condition being that the system must be reducible to a superposition of semi-transparent mirrors that is invariant under all the reflections it generates. In this article, we found a way to relax this condition: some of the semi-transparent mirrors of a known self-invariant mirror superposition can be replaced by the perfectly reflecting ones, thus breaking the self-invariance. The proposed name for the method is asymmetric Bethe Ansatz (asymmetric BA). As a worked example, we study in detail the bound states of the nominally non-integrable system comprised of a bosonic dimer in a $delta$-well. Finally, we show that the exact solution of the Liu-Qi-Zhang-Chen problem is a particular instance of the the asymmetric BA.
最近提出的关于硬壁盒中两个质量比为3!:!1＄的$delta＄函数相互作用粒子的精确量子解[Y. Liu, F. Qi, Y. Zhang and S. Chen, iScience 22, 181 (2019)]违反了贝特安萨兹可积分性的传统必要条件，该条件是系统必须可还原为半透明镜子的叠加，并且在其产生的所有反射下都是不变的。在这篇文章中，我们找到了放宽这一条件的方法：已知自不变镜像叠加中的一些半透明镜像可以被完全反射的镜像取代，从而打破自不变性。这种方法被命名为非对称贝特安萨特兹（asymmetric Bethe Ansatz）。作为一个工作实例，我们详细研究了由$delta$阱中的玻色二聚体组成的名义上不可整的系统的束缚态。最后，我们证明了刘-齐-张-陈问题的精确解是非对称 BA 的一个特殊实例。
{"title":"Asymmetric Bethe Ansatz","authors":"Steven Glenn Jackson, Hélène Perrin, Grigori E. Astrakharchik, Maxim Olshanii","doi":"10.21468/scipostphyscore.7.3.062","DOIUrl":"https://doi.org/10.21468/scipostphyscore.7.3.062","url":null,"abstract":"The recently proposed exact quantum solution for two $delta$-function-interacting particles with a mass-ratio $3!:!1$ in a hard-wall box [Y. Liu, F. Qi, Y. Zhang and S. Chen, iScience 22, 181 (2019)] violates the conventional necessary condition for a Bethe Ansatz integrability, the condition being that the system must be reducible to a superposition of semi-transparent mirrors that is invariant under all the reflections it generates. In this article, we found a way to relax this condition: some of the semi-transparent mirrors of a known self-invariant mirror superposition can be replaced by the perfectly reflecting ones, thus breaking the self-invariance. The proposed name for the method is asymmetric Bethe Ansatz (asymmetric BA). As a worked example, we study in detail the bound states of the nominally non-integrable system comprised of a bosonic dimer in a $delta$-well. Finally, we show that the exact solution of the Liu-Qi-Zhang-Chen problem is a particular instance of the the asymmetric BA.","PeriodicalId":21682,"journal":{"name":"SciPost Physics","volume":null,"pages":null},"PeriodicalIF":5.5,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142187374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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