Pub Date : 2023-11-14DOI: 10.1088/1751-8121/ad0c72
Ismagil Talgatovich Habibullin, Kira Igorevna Faizulina, Aigul Rinatovna Khakimova
Abstract It is well known that the Laplace cascade method is an effective tool for constructing solutions to linear equations of hyperbolic type, as well as nonlinear equations of the Liouville type. The connection between the Laplace method and soliton equations of hyperbolic type remains less studied. The article shows that the Laplace cascade also has important applications in the theory of hyperbolic equations of the soliton type. Laplace’s method provides a simple way to construct such fundamental objects related to integrability theory as the recursion operator, the Lax pair and Dubrovin-type equations, allowing one to find algebro-geometric solutions. As an application of this approach, previously unknown recursion operators and Lax pairs are found for two nonlinear integrable equations of the sine-Gordon type.
{"title":"Laplace transformations and sine-Gordon type integrable PDE","authors":"Ismagil Talgatovich Habibullin, Kira Igorevna Faizulina, Aigul Rinatovna Khakimova","doi":"10.1088/1751-8121/ad0c72","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0c72","url":null,"abstract":"Abstract It is well known that the Laplace cascade method is an effective tool for constructing solutions to linear equations of hyperbolic type, as well as nonlinear equations of the Liouville type. The connection between the Laplace method and soliton equations of hyperbolic type remains less studied. The article shows that the Laplace cascade also has important applications in the theory of hyperbolic equations of the soliton type. Laplace’s method provides a simple way to construct such fundamental objects related to integrability theory as the recursion operator, the Lax pair and Dubrovin-type equations, allowing one to find algebro-geometric solutions. As an application of this approach, previously unknown recursion operators and Lax pairs are found for two nonlinear integrable equations of the sine-Gordon type.
","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"15 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134954732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.1088/1751-8121/ad04a3
Michael V Berry, Pragya Shukla
Abstract Classical nonhamiltonian dynamics, driven by external ‘curl forces’ (which are not the gradient of a potential) is extended to the quantum domain. This is a generalisation of the two-stage Madelung procedure for the quantum Hamiltonian case: (i) considering not individual trajectories but families of them, characterised by their velocity and density fields (both functions of position and in general time); and (ii) adding the gradient of the quantum potential to the external curl force. Curl forces require the velocity field to have nonzero vorticity, so there is no underlying singlevalued wavefunction. Two explicit examples are presented. A possible experiment would be the motion of small particles with complex polarisability, influenced by forces from optical fields.
{"title":"Quantum curl forces","authors":"Michael V Berry, Pragya Shukla","doi":"10.1088/1751-8121/ad04a3","DOIUrl":"https://doi.org/10.1088/1751-8121/ad04a3","url":null,"abstract":"Abstract Classical nonhamiltonian dynamics, driven by external ‘curl forces’ (which are not the gradient of a potential) is extended to the quantum domain. This is a generalisation of the two-stage Madelung procedure for the quantum Hamiltonian case: (i) considering not individual trajectories but families of them, characterised by their velocity and density fields (both functions of position and in general time); and (ii) adding the gradient of the quantum potential to the external curl force. Curl forces require the velocity field to have nonzero vorticity, so there is no underlying singlevalued wavefunction. Two explicit examples are presented. A possible experiment would be the motion of small particles with complex polarisability, influenced by forces from optical fields.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"4 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134993765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-10DOI: 10.1088/1751-8121/ad0347
Fay Dowker, R D Sorkin
Abstract Relativistic causality (RC) is the principle that no cause can act outside its future light cone, but any attempt to formulate this principle more precisely will depend on the foundational framework that one adopts for quantum theory. Adopting a histories-based (or ‘path integral’) framework, we relate RC to a condition we term ‘Persistence of Zero’ (PoZ), according to which an event E of measure zero remains forbidden if one forms its conjunction with any other event associated to a spacetime region that is later than or spacelike to that of E . We also relate PoZ to the Bell inequalities by showing that, in combination with a second, more technical condition it leads to the quantal counterpart of Fine’s patching theorem in much the same way as Bell’s condition of local causality leads to Fine’s original theorem. We then argue that RC per se has very little to say on the matter of which correlations can occur in nature and which cannot. From the point of view we arrive at, histories-based quantum theories are nonlocal in spacetime , and fully in compliance with RC .
{"title":"An intrinsic causality principle in histories-based quantum theory: a proposal","authors":"Fay Dowker, R D Sorkin","doi":"10.1088/1751-8121/ad0347","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0347","url":null,"abstract":"Abstract Relativistic causality (RC) is the principle that no cause can act outside its future light cone, but any attempt to formulate this principle more precisely will depend on the foundational framework that one adopts for quantum theory. Adopting a histories-based (or ‘path integral’) framework, we relate RC to a condition we term ‘Persistence of Zero’ (PoZ), according to which an event E of measure zero remains forbidden if one forms its conjunction with any other event associated to a spacetime region that is later than or spacelike to that of E . We also relate PoZ to the Bell inequalities by showing that, in combination with a second, more technical condition it leads to the quantal counterpart of Fine’s patching theorem in much the same way as Bell’s condition of local causality leads to Fine’s original theorem. We then argue that RC per se has very little to say on the matter of which correlations can occur in nature and which cannot. From the point of view we arrive at, histories-based quantum theories are nonlocal in spacetime , and fully in compliance with RC .","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"74 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135088360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-10DOI: 10.1088/1751-8121/ad0bcb
Ansgar Siemens, Peter Schmelcher
Abstract We investigate the ground state properties of rectangular dipole lattices on curved surfaces. The curved geometry can `distort' the lattice and lead to dipole equilibrium configurations that strongly depend on the local geometry of the surface. We find that the system's ground state can exhibit domain-walls separating domains with different dipole configurations. Furthermore, we show how, regardless of the surface geometry, the domain-walls locate along the lattice sites for which the (Euclidean) distances to nearest and next-nearest neighbors are equal. We analyze the response of the domain-walls to an external electric field and observe displacements and splittings thereof below and above a critical electric field, respectively. We further show that the domain-wall acts as a boundary that traps low-energy excitations within a domain.
{"title":"Geometry induced domain-walls of dipole lattices on curved structures","authors":"Ansgar Siemens, Peter Schmelcher","doi":"10.1088/1751-8121/ad0bcb","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0bcb","url":null,"abstract":"Abstract We investigate the ground state properties of rectangular dipole lattices on curved surfaces. The curved geometry can `distort' the lattice and lead to dipole equilibrium configurations that strongly depend on the local geometry of the surface. We find that the system's ground state can exhibit domain-walls separating domains with different dipole configurations. Furthermore, we show how, regardless of the surface geometry, the domain-walls locate along the lattice sites for which the (Euclidean) distances to nearest and next-nearest neighbors are equal. We analyze the response of the domain-walls to an external electric field and observe displacements and splittings thereof below and above a critical electric field, respectively. We further show that the domain-wall acts as a boundary that traps low-energy excitations within a domain.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"82 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135092096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-10DOI: 10.1088/1751-8121/ad0804
Shingo Kukita, Haruki Kiya, Yasushi Kondo
Abstract Precise control of quantum systems is a cornerstone for realizing high-quality quantum technology such as quantum computing and quantum communication. The performance of control of systems often deteriorates due to systematic errors. In one-qubit control, the pulse length error (PLE) is a typical systematic error, which is often caused by deviation of the strength of the control field. A composite quantum gate (CQG) is a method for suppressing effects of such systematic errors at the cost of a long operation time. A longer operation time implies stronger decoherence, and thus a shorter CQG is preferable from the viewpoint of noise immunity. However, it has not been clear how short CQG can be implemented. This problem can be regarded as an optimization problem under constraints: optimizing the operation time while requiring the error robustness. In this paper, we find a lower bound on operation time of all CQGs with first-order robustness against the PLE, in which effects of the error are eliminated up to its first order. The derivation of this bound is based on a geometric property of robustness against the PLE. This can be used for search after high-performance CQGs.
{"title":"Lower bound on operation time of composite quantum gates robust against pulse length error","authors":"Shingo Kukita, Haruki Kiya, Yasushi Kondo","doi":"10.1088/1751-8121/ad0804","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0804","url":null,"abstract":"Abstract Precise control of quantum systems is a cornerstone for realizing high-quality quantum technology such as quantum computing and quantum communication. The performance of control of systems often deteriorates due to systematic errors. In one-qubit control, the pulse length error (PLE) is a typical systematic error, which is often caused by deviation of the strength of the control field. A composite quantum gate (CQG) is a method for suppressing effects of such systematic errors at the cost of a long operation time. A longer operation time implies stronger decoherence, and thus a shorter CQG is preferable from the viewpoint of noise immunity. However, it has not been clear how short CQG can be implemented. This problem can be regarded as an optimization problem under constraints: optimizing the operation time while requiring the error robustness. In this paper, we find a lower bound on operation time of all CQGs with first-order robustness against the PLE, in which effects of the error are eliminated up to its first order. The derivation of this bound is based on a geometric property of robustness against the PLE. This can be used for search after high-performance CQGs.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"67 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-10DOI: 10.1088/1751-8121/ad0bcc
Rafael Wagner, Roberto D. Baldijão, Alisson Tezzin, Bárbara Amaral
Abstract We employ the resource theory of generalized contextuality as a tool for analyzing the structure of prepare-and-measure scenarios. We argue that this framework simplifies proofs of quantum contextuality in complex scenarios and strengthens existing arguments regarding robustness of experimental implementations. As a case study, we demonstrate quantum contextuality associated with any nontrivial noncontextuality inequality for a class of useful scenarios by noticing a connection between the resource theory and measurement simulability. Additionally, we expose a formal composition rule that allows engineering complex scenarios from simpler ones. This approach provides insights into the noncontextual polytope structure for complex scenarios and facilitates the identification of possible quantum violations of noncontextuality inequalities.
{"title":"Using a resource theoretic perspective to witness and engineer quantum generalized contextuality for prepare-and-measure scenarios","authors":"Rafael Wagner, Roberto D. Baldijão, Alisson Tezzin, Bárbara Amaral","doi":"10.1088/1751-8121/ad0bcc","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0bcc","url":null,"abstract":"Abstract We employ the resource theory of generalized contextuality as a tool for analyzing the structure of prepare-and-measure scenarios. We argue that this framework simplifies proofs of quantum contextuality in complex scenarios and strengthens existing arguments regarding robustness of experimental implementations. As a case study, we demonstrate quantum contextuality associated with any nontrivial noncontextuality inequality for a class of useful scenarios by noticing a connection between the resource theory and measurement simulability. Additionally, we expose a formal composition rule that allows engineering complex scenarios from simpler ones. This approach provides insights into the noncontextual polytope structure for complex scenarios and facilitates the identification of possible quantum violations of noncontextuality inequalities.
","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"84 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-10DOI: 10.1088/1751-8121/ad0822
Marina A Ferreira, Eugenia Franco, Jani Lukkarinen, Alessia Nota, Juan J L Velazquez
Abstract We study the long-time behaviour of the solutions to Smoluchowski coagulation equations with a source term of small clusters. The source drives the system out-of-equilibrium, leading to a rich range of different possible long-time behaviours, including anomalous self-similarity. The coagulation kernel is non-gelling, homogeneous, with homogeneity γ⩽−1 , and behaves like xγ+λy−λ when y≪x with γ+2λ>1 . Our analysis shows that the long-time behaviour of the solutions depends on the parameters γ and λ . More precisely, we argue that the long-time behaviour is self-similar, although the scaling of the self-similar solutions depends on the sign of γ+λ and on whether γ=−1 or γ<−1 . In all these cases, the scaling differs from the usual one that has been previously obtained when γ+2λ<1 or γ+2λ⩾1,γ>−1 . In the last part of the paper, we present some conjectures supporting the self-similar ansatz also for the critical case
{"title":"Coagulation equations with source leading to anomalousself-similarity","authors":"Marina A Ferreira, Eugenia Franco, Jani Lukkarinen, Alessia Nota, Juan J L Velazquez","doi":"10.1088/1751-8121/ad0822","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0822","url":null,"abstract":"Abstract We study the long-time behaviour of the solutions to Smoluchowski coagulation equations with a source term of small clusters. The source drives the system out-of-equilibrium, leading to a rich range of different possible long-time behaviours, including anomalous self-similarity. The coagulation kernel is non-gelling, homogeneous, with homogeneity <?CDATA $gamma unicode{x2A7D} -1 $?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>γ</mml:mi> <mml:mtext>⩽</mml:mtext> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:math> , and behaves like <?CDATA $x^{gamma+lambda} y^{-lambda} $?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:msup> <mml:mi>x</mml:mi> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mo>+</mml:mo> <mml:mi>λ</mml:mi> </mml:mrow> </mml:msup> <mml:msup> <mml:mi>y</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi>λ</mml:mi> </mml:mrow> </mml:msup> </mml:math> when <?CDATA $y ll x$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>y</mml:mi> <mml:mo>≪</mml:mo> <mml:mi>x</mml:mi> </mml:math> with <?CDATA $gamma+2lambda gt 1$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>γ</mml:mi> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> <mml:mi>λ</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:math> . Our analysis shows that the long-time behaviour of the solutions depends on the parameters γ and λ . More precisely, we argue that the long-time behaviour is self-similar, although the scaling of the self-similar solutions depends on the sign of <?CDATA $gamma+lambda$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>γ</mml:mi> <mml:mo>+</mml:mo> <mml:mi>λ</mml:mi> </mml:math> and on whether <?CDATA $gamma = -1$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>γ</mml:mi> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:math> or <?CDATA $gamma lt -1$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>γ</mml:mi> <mml:mo><</mml:mo> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:math> . In all these cases, the scaling differs from the usual one that has been previously obtained when <?CDATA $gamma+2lambda lt 1$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>γ</mml:mi> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> <mml:mi>λ</mml:mi> <mml:mo><</mml:mo> <mml:mn>1</mml:mn> </mml:math> or <?CDATA $gamma+2lambda unicode{x2A7E} 1, gamma gt -1$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>γ</mml:mi> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> <mml:mi>λ</mml:mi> <mml:mtext>⩾</mml:mtext> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>γ</mml:mi> <mml:mo>></mml:mo> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:math> . In the last part of the paper, we present some conjectures supporting the self-similar ansatz also for the critical case <?CDATA $gamma+2lambda = ","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"69 20","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-10DOI: 10.1088/1751-8121/ad0bcd
Pascal Grange
Abstract The voter model is a toy model of consensus formation based on nearest-neighbor interactions. A voter sits at each vertex in a hypercubic lattice (of dimension $d$) and is in one of two possible opinion states. The opinion state of each voter flips randomly, at a rate proportional to the fraction of the nearest neighbors that disagree with the voter. If the voters are initially independent and undecided, the model is known to lead to a consensus if and only if $dleq 2$. In this paper the model is subjected to stochastic resetting: the voters revert independently to their initial opinion according to a Poisson process of fixed intensity (the resetting rate). This resetting prescription induces kinetic equations for the average opinion state and for the two-point function of the model. For initial conditions consisting of undecided voters except for one decided voter at the origin, the one-point function evolves as the probability of presence of a diffusive random walker on the lattice, whose position is stochastically reset to the origin. The resetting prescription leads to a non-equilibrium steady state. For an initial state consisting of independent undecided voters, the density of domain walls in the steady state is expressed in closed form as a function of the resetting rate. This function is differentiable at zero if and only if $dgeq 5$.
{"title":"Voter model under stochastic resetting","authors":"Pascal Grange","doi":"10.1088/1751-8121/ad0bcd","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0bcd","url":null,"abstract":"Abstract The voter model is a toy model of consensus formation based on nearest-neighbor interactions. A voter sits at each vertex in a hypercubic lattice (of dimension $d$) and is in one of two possible opinion states. The opinion state of each voter flips randomly, at a rate proportional to the fraction of the nearest neighbors that disagree with the voter. If the voters are initially independent and undecided, the model is known to lead to a consensus if and only if $dleq 2$. In this paper the model is subjected to stochastic resetting: the voters revert independently to their initial opinion according to a Poisson process of fixed intensity (the resetting rate). This resetting prescription induces kinetic equations for the average opinion state and for the two-point function of the model. For initial conditions consisting of undecided voters except for one decided voter at the origin, the one-point function evolves as the probability of presence of a diffusive random walker on the lattice, whose position is stochastically reset to the origin. The resetting prescription leads to a non-equilibrium steady state. For an initial state consisting of independent undecided voters, the density of domain walls in the steady state is expressed in closed form as a function of the resetting rate. This function is differentiable at zero if and only if $dgeq 5$.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"88 18","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135091591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-10DOI: 10.1088/1751-8121/ad0bca
Ko Sanders
Abstract We initiate an investigation into separable, but physically reasonable, states in relativistic quantum field theory. In particular we will consider the minimum amount of energy density needed to ensure the existence of separable states between given spacelike separated regions. This is a first step towards improving our understanding of the balance between entanglement entropy and energy (density), which is of great physical interest in its own right and also in the context of black hole thermodynamics. We will focus concretely on a linear scalar quantum field in a topologically trivial, four-dimensional globally hyperbolic spacetime. For rather general spacelike separated regions A and B we prove the existence of a separable quasi-free Hadamard state. In Minkowski spacetime we provide a tighter construction for massive free scalar fields: given any R>0 we construct a quasi-free Hadamard state which is stationary, homogeneous, spatially isotropic and separable between any two regions in an inertial time slice t= const. all of whose points have a distance >R . We also show that the normal ordered energy density of these states can be made ≦10 31 m 4 (mR) -8 e -mR/4 (in Planck units). To achieve these results we use a rather explicit construction of test-functions f of positive type for which we can get sufficient control on lower bounds on the Fourier transform.
摘要本文对相对论量子场论中可分离但物理上合理的态进行了研究。特别是，我们将考虑确保在给定的类空间分离区域之间存在可分离状态所需的最小能量密度。这是提高我们对纠缠熵和能量(密度)之间平衡的理解的第一步，这在其本身和黑洞热力学的背景下都具有很大的物理意义。我们将具体关注拓扑平凡的四维全局双曲时空中的线性标量量子场。对于一般的类空间分离区域A和B，证明了可分离的拟自由Hadamard态的存在性。在Minkowski时空中，我们为大质量自由标量场提供了一个更严格的构造:给定任意R>0，我们构造了一个准自由Hadamard状态，它在惯性时间片t= const中任意两个区域之间是平稳的、均匀的、空间各向同性的和可分离的。所有点的距离都是>R。我们也证明了这些态的正常有序能量密度可以达到≦10 31 m 4 (mR) -8 e -mR/4(普朗克单位)。为了得到这些结果，我们使用了一个相当显式的正型测试函数f的构造，这样我们就可以充分控制傅里叶变换的下界。
{"title":"On separable states in relativistic quantum field theory","authors":"Ko Sanders","doi":"10.1088/1751-8121/ad0bca","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0bca","url":null,"abstract":"Abstract We initiate an investigation into separable, but physically reasonable, states in relativistic quantum field theory. In particular we will consider the minimum amount of energy density needed to ensure the existence of separable states between given spacelike separated regions. This is a first step towards improving our understanding of the balance between entanglement entropy and energy (density), which is of great physical interest in its own right and also in the context of black hole thermodynamics. We will focus concretely on a linear scalar quantum field in a topologically trivial, four-dimensional globally hyperbolic spacetime. For rather general spacelike separated regions A and B we prove the existence of a separable quasi-free Hadamard state. In Minkowski spacetime we provide a tighter construction for massive free scalar fields: given any R>0 we construct a quasi-free Hadamard state which is stationary, homogeneous, spatially isotropic and separable between any two regions in an inertial time slice t= const. all of whose points have a distance >R . We also show that the normal ordered energy density of these states can be made ≦10 31 m 4 (mR) -8 e -mR/4 (in Planck units). To achieve these results we use a rather explicit construction of test-functions f of positive type for which we can get sufficient control on lower bounds on the Fourier transform.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"33 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135093117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-09DOI: 10.1088/1751-8121/ad0b5a
Adway Kumar Das, Anandamohan Ghosh
Abstract We introduce a two-parameter ensemble of generalized 2 × 2 real symmetric random matrices called the β-Rosenzweig-Porter ensemble (β-RPE), parameterized by β, a fictitious inverse temperature of the analogous Coulomb gas model, and γ, controlling the relative strength of disorder. β-RPE encompasses RPE from all of the Dyson’s threefold symmetry classes: orthogonal, unitary and symplectic for β = 1, 2, 4. Firstly, we study the energy correlations by calculating the density and 2nd moment of the Nearest Neighbor Spacing (NNS) and robustly quantify the crossover among various degrees of level repulsions. Secondly, the dynamical properties are determined from an exact calculation of the temporal evolution of the fidelity enabling an identification of the characteristic Thouless and the equilibration timescales. The relative depth of the correlation hole in the average fidelity serves as a dynamical signature of the crossover from chaos to integrability and enables us to construct the phase diagram of β-RPE in the γ-β plane. Our results are in qualitative agreement with numerically computed fidelity for N ≫ 2 matrix ensembles. Furthermore, we observe that for large N the 2nd moment of NNS and the relative depth of the correlation hole exhibit a second order phase transition at γ = 2.
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