Pub Date : 2024-09-18DOI: 10.1088/1751-8121/ad79cc
Malik Mamode
The paper investigates the truncation error between the Green function and the lattice Green function (LGF) for the Laplacian operator defined on the 2-torus and its discretization on a regular square lattice. Extensions to the cylinder and the rectangular domain with free (or Neumann) boundary conditions are also proposed. In each of these instances, the Green function and its discrete analog are given in exact analytical closed-form allowing to infer accurate estimates as the lattice spacing tends to zero. As expected, it is shown that the continuum limit of the LGF coincides well with the Green function in every case. In particular, the issue of logarithmic singularity regularization of the Green function by the lattice discretization is addressed through two related application examples regarding the rectangular domain, and devoted to the computation of corner-to-corner resistance of an electrical conducting square and the mean first-passage time between the diagonally opposite vertices of a square for a standard Brownian motion, both derived considering the continuum limit.
{"title":"Laplacian operator and its square lattice discretization: Green function vs. Lattice Green function for the flat 2-torus and other related 2D manifolds","authors":"Malik Mamode","doi":"10.1088/1751-8121/ad79cc","DOIUrl":"https://doi.org/10.1088/1751-8121/ad79cc","url":null,"abstract":"The paper investigates the truncation error between the Green function and the lattice Green function (LGF) for the Laplacian operator defined on the 2-torus and its discretization on a regular square lattice. Extensions to the cylinder and the rectangular domain with free (or Neumann) boundary conditions are also proposed. In each of these instances, the Green function and its discrete analog are given in exact analytical closed-form allowing to infer accurate estimates as the lattice spacing tends to zero. As expected, it is shown that the continuum limit of the LGF coincides well with the Green function in every case. In particular, the issue of logarithmic singularity regularization of the Green function by the lattice discretization is addressed through two related application examples regarding the rectangular domain, and devoted to the computation of corner-to-corner resistance of an electrical conducting square and the mean first-passage time between the diagonally opposite vertices of a square for a standard Brownian motion, both derived considering the continuum limit.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"38 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-09-17DOI: 10.1088/1751-8121/ad6cb6
Beatrice Nettuno, Davide Toffenetti, Christoph Metzl, Linus Weigand, Florian Raßhofer, Richard Swiderski and Erwin Frey
The general epidemic process (GEP), also known as susceptible-infected-recovered model, provides a minimal model of how an epidemic spreads within a population of susceptible individuals who acquire permanent immunization upon recovery. This model exhibits a second-order absorbing state phase transition, commonly studied assuming immobile healthy individuals. We investigate the impact of mobility on the scaling properties of disease spreading near the extinction threshold by introducing two generalizations of GEP, where the mobility of susceptible and recovered individuals is examined independently. In both cases, including mobility violates GEP’s rapidity reversal symmetry and alters the number of absorbing states. The critical dynamics of the models are analyzed through a perturbative renormalization group (RG) approach and large-scale stochastic simulations using a Gillespie algorithm. The RG analysis predicts both models to belong to the same novel universality class describing the critical dynamics of epidemic spreading when the infected individuals interact with a diffusive species and gain immunization upon recovery. At the associated RG fixed point, the immobile species decouples from the dynamics of the infected species, dominated by the coupling with the diffusive species. Numerical simulations in two dimensions affirm our RG results by identifying the same set of critical exponents for both models. Violation of the rapidity reversal symmetry is confirmed by breaking the associated hyperscaling relation. Our study underscores the significance of mobility in shaping population spreading dynamics near the extinction threshold.
{"title":"The role of mobility in epidemics near criticality","authors":"Beatrice Nettuno, Davide Toffenetti, Christoph Metzl, Linus Weigand, Florian Raßhofer, Richard Swiderski and Erwin Frey","doi":"10.1088/1751-8121/ad6cb6","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6cb6","url":null,"abstract":"The general epidemic process (GEP), also known as susceptible-infected-recovered model, provides a minimal model of how an epidemic spreads within a population of susceptible individuals who acquire permanent immunization upon recovery. This model exhibits a second-order absorbing state phase transition, commonly studied assuming immobile healthy individuals. We investigate the impact of mobility on the scaling properties of disease spreading near the extinction threshold by introducing two generalizations of GEP, where the mobility of susceptible and recovered individuals is examined independently. In both cases, including mobility violates GEP’s rapidity reversal symmetry and alters the number of absorbing states. The critical dynamics of the models are analyzed through a perturbative renormalization group (RG) approach and large-scale stochastic simulations using a Gillespie algorithm. The RG analysis predicts both models to belong to the same novel universality class describing the critical dynamics of epidemic spreading when the infected individuals interact with a diffusive species and gain immunization upon recovery. At the associated RG fixed point, the immobile species decouples from the dynamics of the infected species, dominated by the coupling with the diffusive species. Numerical simulations in two dimensions affirm our RG results by identifying the same set of critical exponents for both models. Violation of the rapidity reversal symmetry is confirmed by breaking the associated hyperscaling relation. Our study underscores the significance of mobility in shaping population spreading dynamics near the extinction threshold.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 10.1088/1751-8121/ad754e
M V Berry and Pragya Shukla
Classical curl forces are position-dependent Newtonian forces (accelerations) that are not the gradient of a scalar potential, and in general cannot be described by Hamiltonians. However, a special class of curl forces can be described by Hamiltonians, with the unusual feature that the kinetic energy is anisotropic in the momentum components. Therefore they can be quantised conventionally. We quantise the simplest such case: motion in the plane, with a curl force azimuthally directed and linear. As expected, the quantum propagator, and the way this drives Gaussian wavepackets, directly reflects the spiralling classical curl force dynamics. Two classes of stationary states—eigenfunctions of a continuous spectrum for the unbounded Hamiltonian—are described. They possess unusual singularities and an unfamiliar quantisation condition; their explanation requires asymptotics and unfamiliar singularities in the underlying families of classical trajectories. The analysis is supported and illustrated numerically.
{"title":"Quantising a Hamiltonian curl force","authors":"M V Berry and Pragya Shukla","doi":"10.1088/1751-8121/ad754e","DOIUrl":"https://doi.org/10.1088/1751-8121/ad754e","url":null,"abstract":"Classical curl forces are position-dependent Newtonian forces (accelerations) that are not the gradient of a scalar potential, and in general cannot be described by Hamiltonians. However, a special class of curl forces can be described by Hamiltonians, with the unusual feature that the kinetic energy is anisotropic in the momentum components. Therefore they can be quantised conventionally. We quantise the simplest such case: motion in the plane, with a curl force azimuthally directed and linear. As expected, the quantum propagator, and the way this drives Gaussian wavepackets, directly reflects the spiralling classical curl force dynamics. Two classes of stationary states—eigenfunctions of a continuous spectrum for the unbounded Hamiltonian—are described. They possess unusual singularities and an unfamiliar quantisation condition; their explanation requires asymptotics and unfamiliar singularities in the underlying families of classical trajectories. The analysis is supported and illustrated numerically.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"53 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 10.1088/1751-8121/ad776a
Pieter W Claeys and Austen Lamacraft
Many-body quantum dynamics defined on a spatial lattice and in discrete time—either as stroboscopic Floquet systems or quantum circuits—has been an active area of research for several years. Being discrete in space and time, a natural question arises: when can such a model be viewed as evolving unitarily in space as well as in time? Models with this property, which sometimes goes by the name space-time duality, have been shown to have a number of interesting features related to entanglement growth and correlations. One natural way in which the property arises in the context of (brickwork) quantum circuits is by choosing dual unitary gates: two site operators that are unitary in both the space and time directions. We introduce a class of models with q states per site, defined on the square lattice by a complex partition function and paremeterized in terms of q × q Hadamard matrices, that have the property of space-time duality. These may interpreted as particular dual unitary circuits or stroboscopically evolving systems, and generalize the well studied self-dual kicked Ising model. We explore the operator dynamics in the case of Clifford circuits, making connections to Clifford cellular automata (Schlingemann et al 2008 J. Math. Phys.49 112104) and in the limit to the classical spatiotemporal cat model of many body chaos (Gutkin et al 2021 Nonlinearity34 2800). We establish integrability and the corresponding conserved charges for a large subfamily and show how the long-range entanglement protocol discussed in the recent paper (Lotkov et al 2022 Phys. Rev. B 105 144306) can be reinterpreted in purely graphical terms and directly applied here.
在空间晶格和离散时间中定义的多体量子动力学--无论是频闪弗洛凯系统还是量子电路--几年来一直是一个活跃的研究领域。由于空间和时间都是离散的，自然会产生一个问题：什么时候可以把这样的模型看作是在空间和时间上都在单元地演化？具有这种特性（有时也称为时空二重性）的模型已被证明具有许多与纠缠增长和相关性有关的有趣特征。在（砖砌）量子电路的背景下，该特性产生的一种自然方式是选择双重单元门：在空间和时间方向上都是单元的两个站点算子。我们介绍了一类每个位点有 q 个状态的模型，这些状态在方格上由复数分割函数定义，并以 q × q 哈达玛矩阵来表示，具有时空对偶性。它们可以被解释为特殊的对偶单元电路或频闪演化系统，并概括了研究得很透彻的自偶踢伊辛模型。我们探讨了克利福德电路中的算子动力学，与克利福德蜂窝自动机（Schlingemann et al 2008 J. Math. Phys.49 112104）和多体混沌的经典时空猫模型（Gutkin et al 2021 Nonlinearity34 2800）建立了联系。我们为一个大的亚家族建立了可积分性和相应的守恒电荷，并展示了最近的论文（Lotkov et al 2022 Phys.
{"title":"Operator dynamics and entanglement in space-time dual Hadamard lattices","authors":"Pieter W Claeys and Austen Lamacraft","doi":"10.1088/1751-8121/ad776a","DOIUrl":"https://doi.org/10.1088/1751-8121/ad776a","url":null,"abstract":"Many-body quantum dynamics defined on a spatial lattice and in discrete time—either as stroboscopic Floquet systems or quantum circuits—has been an active area of research for several years. Being discrete in space and time, a natural question arises: when can such a model be viewed as evolving unitarily in space as well as in time? Models with this property, which sometimes goes by the name space-time duality, have been shown to have a number of interesting features related to entanglement growth and correlations. One natural way in which the property arises in the context of (brickwork) quantum circuits is by choosing dual unitary gates: two site operators that are unitary in both the space and time directions. We introduce a class of models with q states per site, defined on the square lattice by a complex partition function and paremeterized in terms of q × q Hadamard matrices, that have the property of space-time duality. These may interpreted as particular dual unitary circuits or stroboscopically evolving systems, and generalize the well studied self-dual kicked Ising model. We explore the operator dynamics in the case of Clifford circuits, making connections to Clifford cellular automata (Schlingemann et al 2008 J. Math. Phys.49 112104) and in the limit to the classical spatiotemporal cat model of many body chaos (Gutkin et al 2021 Nonlinearity34 2800). We establish integrability and the corresponding conserved charges for a large subfamily and show how the long-range entanglement protocol discussed in the recent paper (Lotkov et al 2022 Phys. Rev. B 105 144306) can be reinterpreted in purely graphical terms and directly applied here.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"65 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 10.1088/1751-8121/ad7211
Amos Chan and Andrea De Luca
The projected ensemble is based on the study of the quantum state of a subsystem A conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design, i.e. a system thermalizes when it becomes indistinguishable, up to the kth moment, from a Haar ensemble of uniformly distributed pure states. Here we consider a random unitary circuit with the brick-wall geometry and analyze its convergence to the Haar ensemble through the frame potential and its mapping to a statistical mechanical problem. This approach allows us to highlight a geometric interpretation of the frame potential based on the existence of a fluctuating membrane, similar to those appearing in the study of entanglement entropies. At large local Hilbert space dimension q, we find that all moments converge simultaneously with a time scaling linearly in the size of region A, a feature previously observed in dual unitary models. However, based on the geometric interpretation, we argue that the scaling at finite q on the basis of rare membrane fluctuations, finding the logarithmic scaling of design times . Our results are supported with numerical simulations performed at q = 2.
投影集合基于对子系统 A 的量子态的研究，其条件是对子系统 A 的补集进行投影测量。最近的研究发现，混沌量子系统热化的一个更精细的衡量标准可以在投影集合收敛到量子态设计的基础上定义，即当一个系统与均匀分布的纯态的哈尔集合在第 k 个时刻前变得不可区分时，该系统就热化了。在这里，我们考虑了一个具有砖墙几何形状的随机单元电路，并通过框架势及其与统计力学问题的映射，分析了它向哈尔集合的收敛。通过这种方法，我们可以强调基于波动膜存在的框架势的几何解释，这与纠缠熵研究中出现的情况类似。在较大的局部希尔伯特空间维度 q 下，我们发现所有时刻都会同时收敛，收敛时间与区域 A 的大小成线性比例，这是以前在对偶单元模型中观察到的特征。然而，基于几何解释，我们认为，在有限 q 的基础上的缩放是基于罕见的膜波动，发现了设计时间的对数缩放。我们的结果得到了在 q = 2 条件下进行的数值模拟的支持。
{"title":"Projected state ensemble of a generic model of many-body quantum chaos","authors":"Amos Chan and Andrea De Luca","doi":"10.1088/1751-8121/ad7211","DOIUrl":"https://doi.org/10.1088/1751-8121/ad7211","url":null,"abstract":"The projected ensemble is based on the study of the quantum state of a subsystem A conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design, i.e. a system thermalizes when it becomes indistinguishable, up to the kth moment, from a Haar ensemble of uniformly distributed pure states. Here we consider a random unitary circuit with the brick-wall geometry and analyze its convergence to the Haar ensemble through the frame potential and its mapping to a statistical mechanical problem. This approach allows us to highlight a geometric interpretation of the frame potential based on the existence of a fluctuating membrane, similar to those appearing in the study of entanglement entropies. At large local Hilbert space dimension q, we find that all moments converge simultaneously with a time scaling linearly in the size of region A, a feature previously observed in dual unitary models. However, based on the geometric interpretation, we argue that the scaling at finite q on the basis of rare membrane fluctuations, finding the logarithmic scaling of design times . Our results are supported with numerical simulations performed at q = 2.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"94 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-09-15DOI: 10.1088/1751-8121/ad77fe
Mbavhalelo Mulokwe and Konstantinos Zoubos
With a view towards higher-spin applications, we study the partition function of a free complex fermion in 2d conformal field theory, restricted to the neutral (zero fermion number) sector. This restriction leads to a partial theta function with a combinatoric interpretation in terms of Dyson’s crank of a partition. More crucially, this partition function can be expressed in terms of a q-hypergeometric function with quantum modular properties. This allows us to find its high-temperature asymptotics, including subleading terms which agree with, but also go beyond, what one obtains by imposing neutrality thermodynamically through a chemical potential. We evaluate the asymptotic density of states for this neutral partition function, including the first few subleading terms. Our results should be extendable to more fermions, as well as to higher-spin chemical potentials, which would be of relevance to the higher-spin/minimal model correspondence.
{"title":"Free fermions, neutrality and modular transformations","authors":"Mbavhalelo Mulokwe and Konstantinos Zoubos","doi":"10.1088/1751-8121/ad77fe","DOIUrl":"https://doi.org/10.1088/1751-8121/ad77fe","url":null,"abstract":"With a view towards higher-spin applications, we study the partition function of a free complex fermion in 2d conformal field theory, restricted to the neutral (zero fermion number) sector. This restriction leads to a partial theta function with a combinatoric interpretation in terms of Dyson’s crank of a partition. More crucially, this partition function can be expressed in terms of a q-hypergeometric function with quantum modular properties. This allows us to find its high-temperature asymptotics, including subleading terms which agree with, but also go beyond, what one obtains by imposing neutrality thermodynamically through a chemical potential. We evaluate the asymptotic density of states for this neutral partition function, including the first few subleading terms. Our results should be extendable to more fermions, as well as to higher-spin chemical potentials, which would be of relevance to the higher-spin/minimal model correspondence.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"16 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-09-15DOI: 10.1088/1751-8121/ad742b
Guido Mazzuca
In recent years, a lot of effort has been put in describing the hydrodynamic behavior of integrable systems. In this paper, we describe such picture for the Volterra lattice. Specifically, we are able to explicitly compute the susceptibility matrix and the current-field correlation matrix in terms of the density of states of the Volterra lattice endowed with a Generalized Gibbs ensemble. Furthermore, we apply the theory of linear Generalized Hydrodynamics (GHDs) to describe the Euler scale behavior of the correlation functions. We anticipate that the solution to the GHDs equations develops shocks at ; so this linear approximation does not fully describe the behavior of correlation functions. Intrigued by this fact, we performed several numerical investigations which show that, exactly when the solution to the hydrodynamic equations develops shock, the correlation functions show an highly oscillatory behavior. In view of this empirical observation, we believe that at this point ξ0 the diffusive contribution are not sub-leading corrections to the ballistic transport, but they are of the same order.
{"title":"Generalized hydrodynamics for the volterra lattice: ballistic and non-ballistic behavior of correlation functions","authors":"Guido Mazzuca","doi":"10.1088/1751-8121/ad742b","DOIUrl":"https://doi.org/10.1088/1751-8121/ad742b","url":null,"abstract":"In recent years, a lot of effort has been put in describing the hydrodynamic behavior of integrable systems. In this paper, we describe such picture for the Volterra lattice. Specifically, we are able to explicitly compute the susceptibility matrix and the current-field correlation matrix in terms of the density of states of the Volterra lattice endowed with a Generalized Gibbs ensemble. Furthermore, we apply the theory of linear Generalized Hydrodynamics (GHDs) to describe the Euler scale behavior of the correlation functions. We anticipate that the solution to the GHDs equations develops shocks at ; so this linear approximation does not fully describe the behavior of correlation functions. Intrigued by this fact, we performed several numerical investigations which show that, exactly when the solution to the hydrodynamic equations develops shock, the correlation functions show an highly oscillatory behavior. In view of this empirical observation, we believe that at this point ξ0 the diffusive contribution are not sub-leading corrections to the ballistic transport, but they are of the same order.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"28 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-09-15DOI: 10.1088/1751-8121/ad77fd
N I Stoilova and J Van der Jeugt
We propose a new generalization of the standard (anti-)commutation relations for creation and annihilation operators of bosons and fermions. These relations preserve the usual symmetry properties of bosons and fermions. Only the standard (anti-)commutator relation involving one creation and one annihilation operator is deformed by introducing fractional coefficients, containing a positive integer parameter p. The Fock space is determined by the classical definition. The new relations are chosen in such a way that the total occupation number in the system has the maximum value p. From the actions of creation and annihilation operators in the Fock space, a group theoretical framework is determined, and from here the correspondence with known particle statistics is established.
{"title":"Generalized boson and fermion operators with a maximal total occupation property","authors":"N I Stoilova and J Van der Jeugt","doi":"10.1088/1751-8121/ad77fd","DOIUrl":"https://doi.org/10.1088/1751-8121/ad77fd","url":null,"abstract":"We propose a new generalization of the standard (anti-)commutation relations for creation and annihilation operators of bosons and fermions. These relations preserve the usual symmetry properties of bosons and fermions. Only the standard (anti-)commutator relation involving one creation and one annihilation operator is deformed by introducing fractional coefficients, containing a positive integer parameter p. The Fock space is determined by the classical definition. The new relations are chosen in such a way that the total occupation number in the system has the maximum value p. From the actions of creation and annihilation operators in the Fock space, a group theoretical framework is determined, and from here the correspondence with known particle statistics is established.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"10 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 10.1088/1751-8121/ad770f
Thomas E Baker and Negar Seif
We consider a set of density matrices. All of which are written in the same orbital basis, but the orbital basis size is less than the total Hilbert space size. We ask how each density matrix is related to each of the others by establishing a norm between density matrices based on the truncation error in a partial trace for a small set of orbitals. We find that states with large energy differences must have large differences in their density matrices. Small energy differences are divided into two groups, one where two density matrices have small differences and another where they are very different, as is the case of symmetry. We extend these ideas to a bundle of matrix product states and show that bond dimension of the wavefunction ansatz for two states with large energy differences are larger. Meanwhile, low energy differences can have nearly the same bond dimensions for similar states.
{"title":"Bundled matrix product states represent low-energy excitations faithfully","authors":"Thomas E Baker and Negar Seif","doi":"10.1088/1751-8121/ad770f","DOIUrl":"https://doi.org/10.1088/1751-8121/ad770f","url":null,"abstract":"We consider a set of density matrices. All of which are written in the same orbital basis, but the orbital basis size is less than the total Hilbert space size. We ask how each density matrix is related to each of the others by establishing a norm between density matrices based on the truncation error in a partial trace for a small set of orbitals. We find that states with large energy differences must have large differences in their density matrices. Small energy differences are divided into two groups, one where two density matrices have small differences and another where they are very different, as is the case of symmetry. We extend these ideas to a bundle of matrix product states and show that bond dimension of the wavefunction ansatz for two states with large energy differences are larger. Meanwhile, low energy differences can have nearly the same bond dimensions for similar states.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"33 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 10.1088/1751-8121/ad7427
Eli Hawkins, Christoph Minz and Kasia Rejzner
Geometric quantization is a natural way to construct quantum models starting from classical data. In this work, we start from a symplectic vector space with an inner product and—using techniques of geometric quantization—construct the quantum algebra and equip it with a distinguished state. We compare our result with the construction due to Sorkin—which starts from the same input data—and show that our distinguished state coincides with the Sorkin-Johnson state. Sorkin’s construction was originally applied to the free scalar field over a causal set (locally finite, partially ordered set). Our perspective suggests a natural generalization to less linear examples, such as an interacting field.
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