Pub Date : 2023-11-09DOI: 10.1088/1751-8121/ad0b59
Alexander Flegel
Abstract Representations for products of two Airy functions with different complex arguments in the form of one-dimensional contour integrals are obtained. These representations are used for analysis of the Green’s function for a charged particle in a uniform static electric field. The integral relation between the stationary and time-dependent Green’s functions is discussed in the sense of its analytical properties for complex energy and field strength. It is shown that the Green’s function can be divided into analytic and non-analytic parts with respect to the field strength near its zero.
{"title":"Integral representations for products of Airy functions and their application for analysis of the Green’s function for a particle in a uniform static field","authors":"Alexander Flegel","doi":"10.1088/1751-8121/ad0b59","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0b59","url":null,"abstract":"Abstract Representations for products of two Airy functions with different complex arguments in the form of one-dimensional contour integrals are obtained. These representations are used for analysis of the Green’s function for a charged particle in a uniform static electric field. The integral relation between the stationary and time-dependent Green’s functions is discussed in the sense of its analytical properties for complex energy and field strength. It is shown that the Green’s function can be divided into analytic and non-analytic parts with respect to the field strength near its zero.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":" 20","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135192574","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/ad0b5c
Galina Filipuk, Alexander Stokes
Abstract We describe the quasi-Painlevé property of a system of ordinary differential equations in terms of a global Hamiltonian structure on an analogue of Okamoto’s space of initial conditions for the Painlevé equations. In the quasi-Painlevé case, the Hamiltonian structure is with respect to a two-form which is allowed to have certain zeroes on the surfaces forming the space of initial conditions, as opposed to holomorphic symplectic forms in the case of the Painlevé equations. We provide the spaces and Hamiltonian structures for several known quasi-Painlevé equations and also for a new example, which we prove to have the quasi-Painlevé property via the Hamiltonian structure and construction of an appropriate auxiliary function which remains bounded on solutions.
{"title":"On Hamiltonian structures of quasi-Painlevé equations","authors":"Galina Filipuk, Alexander Stokes","doi":"10.1088/1751-8121/ad0b5c","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0b5c","url":null,"abstract":"Abstract We describe the quasi-Painlevé property of a system of ordinary differential equations in terms of a global Hamiltonian structure on an analogue of Okamoto’s space of initial conditions for the Painlevé equations. In the quasi-Painlevé case, the Hamiltonian structure is with respect to a two-form which is allowed to have certain zeroes on the surfaces forming the space of initial conditions, as opposed to holomorphic symplectic forms in the case of the Painlevé equations. We provide the spaces and Hamiltonian structures for several known quasi-Painlevé equations and also for a new example, which we prove to have the quasi-Painlevé property via the Hamiltonian structure and construction of an appropriate auxiliary function which remains bounded on solutions.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":" 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135192978","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/ad0b5b
Marllos E F Fernandes, Felipe F Fanchini, Emanuel de Lima, Leonardo Kleber Castelano
Abstract We apply the Krotov method for open and closed quantum systems to find optimized controls to manipulate qubit/qutrit systems in the presence of the external environment. In the case of unitary optimization, the Krotov method is first applied to a quantum system neglecting its interaction with the environment. The resulting controls from the unitary optimization are then used to drive the system along with the environmental noise. In the case of non-unitary optimization, the Krotov method already takes into account the noise during the optimization process. We consider two distinct computational tasks: target-state preparation and quantum gate implementation. These tasks are carried out in simple qubit/qutrit systems and also in systems presenting leakage states. For the state preparation cases, the controls from the non-unitary optimization outperform the controls from the unitary optimization. However, as we show here, this is not always true for the implementation of quantum gates. There are some situations where the unitary optimization performs equally well compared to the non-unitary optimization. We verify that these situations correspond to either the absence of leakage states or to the effects of dissipation being spread uniformly over the system, including non-computational levels. For such cases, the quantum gate implementation must cover the entire Hilbert space and there is no way to dodge dissipation. On the other hand, if the subspace containing the computational levels and its complement are differently affected by dissipation, the non-unitary optimization becomes effective.
{"title":"Effectiveness of the Krotov method in finding controls for open quantum systems","authors":"Marllos E F Fernandes, Felipe F Fanchini, Emanuel de Lima, Leonardo Kleber Castelano","doi":"10.1088/1751-8121/ad0b5b","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0b5b","url":null,"abstract":"Abstract We apply the Krotov method for open and closed quantum systems to find optimized controls to manipulate qubit/qutrit systems in the presence of the external environment. In the case of unitary optimization, the Krotov method is first applied to a quantum system neglecting its interaction with the environment. The resulting controls from the unitary optimization are then used to drive the system along with the environmental noise. In the case of non-unitary optimization, the Krotov method already takes into account the noise during the optimization process. We consider two distinct computational tasks: target-state preparation and quantum gate implementation. These tasks are carried out in simple qubit/qutrit systems and also in systems presenting leakage states. For the state preparation cases, the controls from the non-unitary optimization outperform the controls from the unitary optimization. However, as we show here, this is not always true for the implementation of quantum gates. There are some situations where the unitary optimization performs equally well compared to the non-unitary optimization. We verify that these situations correspond to either the absence of leakage states or to the effects of dissipation being spread uniformly over the system, including non-computational levels. For such cases, the quantum gate implementation must cover the entire Hilbert space and there is no way to dodge dissipation. On the other hand, if the subspace containing the computational levels and its complement are differently affected by dissipation, the non-unitary optimization becomes effective.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":" 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135192026","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 : 2023-11-08DOI: 10.1088/1751-8121/ad0ac8
Matteo Casati, Danda Zhang
Abstract In a recent series of papers by Lou et al., it was conjectured that higher dimensional integrable equations may be constructed by utilizing some conservation laws of (1 + 1)-dimensional systems. We prove that the deformation algorithm introduced in JHEP03(2023)018, applied to Lax integrable (1 + 1)-dimensional systems, produces Lax integrable higher dimensional systems. The same property is enjoyed by the generalized deformation algorithm introduced in [Chinese Phys. Lett 40(2023)]; we present a novel example of a (2+1)-dimensional deformation of KdV equation obtained by generalized deformation. The deformed systems obtained by such procedure, however, pose a serious challenge because most of the mathematical structures that the (1 + 1)-dimensional systems possess is lost.
{"title":"Multidimensional integrable deformations of integrable PDEs","authors":"Matteo Casati, Danda Zhang","doi":"10.1088/1751-8121/ad0ac8","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0ac8","url":null,"abstract":"Abstract In a recent series of papers by Lou et al., it was conjectured that higher dimensional integrable equations may be constructed by utilizing some conservation laws of (1 + 1)-dimensional systems. We prove that the deformation algorithm introduced in JHEP03(2023)018, applied to Lax integrable (1 + 1)-dimensional systems, produces Lax integrable higher dimensional systems. The same property is enjoyed by the generalized deformation algorithm introduced in [Chinese Phys. Lett 40(2023)]; we present a novel example of a (2+1)-dimensional deformation of KdV equation obtained by generalized deformation. The deformed systems obtained by such procedure, however, pose a serious challenge because most of the mathematical structures that the (1 + 1)-dimensional systems possess is lost.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":" 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135341401","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 : 2023-11-08DOI: 10.1088/1751-8121/ad0a82
Michele Aldé, Michel Berthier, Edoardo Provenzi
Abstract The classification of qubit channels is known since 2002. However, that of rebit channels has never been studies so far, maybe because of the scarcity of concrete rebit examples. In this paper we point out that the strategy used to classify qubit channels cannot be pursued in the rebit case and we propose an alternative which allows us to complete the rebit channel classification. This mathematical result has not only a purely abstract interest: as we shall briefly mention, it may have applications in the analysis of local properties and temporal evolution of real quantum systems and also in a recent color vision model based on quantum information.
{"title":"The classification of rebit quantum channels","authors":"Michele Aldé, Michel Berthier, Edoardo Provenzi","doi":"10.1088/1751-8121/ad0a82","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0a82","url":null,"abstract":"Abstract The classification of qubit channels is known since 2002. However, that of rebit channels has never been studies so far, maybe because of the scarcity of concrete rebit examples. In this paper we point out that the strategy used to classify qubit channels cannot be pursued in the rebit case and we propose an alternative which allows us to complete the rebit channel classification. This mathematical result has not only a purely abstract interest: as we shall briefly mention, it may have applications in the analysis of local properties and temporal evolution of real quantum systems and also in a recent color vision model based on quantum information.
","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"80 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135342530","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 : 2023-11-08DOI: 10.1088/1751-8121/ad0af5
Max A Lohe
Abstract We consider scalar field theories in $1+1$ dimensions with $N$ fields $varphi_1, dots varphi_N$ which interact through a potential
$V=V(varphi_1, dots varphi_N)$, which is defined in terms of an explicit superpotential $W$. We construct $W$ for any $N$ in terms of a known superpotential $w$ for a single-scalar model, such as that for the sine-Gordon equation or the $varphi^4$ model, leading to an expression for $V$ which has multiple minima that supports solitons. Static solitons which minimize the total energy in each soliton sector appear as solutions of first-order Bogomolny equations, which have a gradient structure. These are identical in form to equations which arise in the context of synchronization phenomena in complex systems, with the space and time variables interchanged. The sine-Gordon superpotential, for example, leads to an explicit periodic superpotential $W$ for $N$ scalar fields, with associated Bogomolny equations that are equivalent to the well-known Kuramoto equations which describe the synchronization of identical phase oscillators on the unit circle. The known asymptotic properties of the Kuramoto system, for both positive and negative coupling constants, ensure that finite-energy solitons exist for any given set of intermediate values imposed at the origin. Besides the models derived from the sine-Gordon equation, we investigate $varphi^4$ and $varphi^6$ models with $N$ scalar fields and show numerically that solitons again exist over a wide range of parameters. We also derive general properties of the elementary meson excitations of the system, in particular we show that meson-soliton bound states exist over a restricted range of mass parameters with respect to an exact solution of the $varphi^6$ system for $N=3$.
{"title":"Multisoliton complex systems with explicit superpotential interactions","authors":"Max A Lohe","doi":"10.1088/1751-8121/ad0af5","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0af5","url":null,"abstract":"Abstract We consider scalar field theories in $1+1$ dimensions with $N$ fields $varphi_1, dots varphi_N$ which interact through a potential
$V=V(varphi_1, dots varphi_N)$, which is defined in terms of an explicit superpotential $W$. We construct $W$ for any $N$ in terms of a known superpotential $w$ for a single-scalar model, such as that for the sine-Gordon equation or the $varphi^4$ model, leading to an expression for $V$ which has multiple minima that supports solitons. Static solitons which minimize the total energy in each soliton sector appear as solutions of first-order Bogomolny equations, which have a gradient structure. These are identical in form to equations which arise in the context of synchronization phenomena in complex systems, with the space and time variables interchanged. The sine-Gordon superpotential, for example, leads to an explicit periodic superpotential $W$ for $N$ scalar fields, with associated Bogomolny equations that are equivalent to the well-known Kuramoto equations which describe the synchronization of identical phase oscillators on the unit circle. The known asymptotic properties of the Kuramoto system, for both positive and negative coupling constants, ensure that finite-energy solitons exist for any given set of intermediate values imposed at the origin. Besides the models derived from the sine-Gordon equation, we investigate $varphi^4$ and $varphi^6$ models with $N$ scalar fields and show numerically that solitons again exist over a wide range of parameters. We also derive general properties of the elementary meson excitations of the system, in particular we show that meson-soliton bound states exist over a restricted range of mass parameters with respect to an exact solution of the $varphi^6$ system for $N=3$.
","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":" 23","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135340353","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 : 2023-11-08DOI: 10.1088/1751-8121/ad0a71
Lachlan Bennett, Phillip Simon Isaac, Jon Links
Abstract A recently proposed extended Bose-Hubbard model, one that is a quantum integrable model, provides a framework for a NOON state generation protocol. Here we derive a Bethe Ansatz solution for the model. The form of the solution provides the means to obtain exact asymptotic expressions for the energies and eigenstates. These results are used to derive formulae for measurement probabilities and outcome fidelities. We benchmark these results against numerical calculations.
{"title":"NOON state measurement probabilities and outcome fidelities: a Bethe Ansatz approach","authors":"Lachlan Bennett, Phillip Simon Isaac, Jon Links","doi":"10.1088/1751-8121/ad0a71","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0a71","url":null,"abstract":"Abstract A recently proposed extended Bose-Hubbard model, one that is a quantum integrable model, provides a framework for a NOON state generation protocol. Here we derive a Bethe Ansatz solution for the model. The form of the solution provides the means to obtain exact asymptotic expressions for the energies and eigenstates. These results are used to derive formulae for measurement probabilities and outcome fidelities. We benchmark these results against numerical calculations.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"6 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135390907","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 : 2023-11-08DOI: 10.1088/1751-8121/ad0ac7
Jonathan Foldager, Bálint Koczor
Abstract Shallow quantum circuits are believed to be the most promising candidates for achieving early practical quantum advantage -- this has motivated the development of a broad range of error mitigation techniques whose performance generally improves when the quantum state is well approximated by a global depolarising (white) noise model. While it has been crucial for demonstrating quantum supremacy that random circuits scramble local noise into global white noise---a property that has been proved rigorously---we investigate to what degree practical shallow quantum circuits scramble local noise into global white noise. We define two key metrics as (a) density matrix eigenvalue uniformity and (b) commutator norm. While the former determines the distance from white noise, the latter determines the performance of purification based error mitigation. We derive analytical approximate bounds on their scaling and find in most cases they nicely match numerical results. On the other hand, we simulate a broad class of practical quantum circuits and find that white noise is in certain cases a bad approximation posing significant limitations on the performance of some of the simpler error mitigation schemes. On a positive note, we find in all cases that the commutator norm is sufficiently small guaranteeing a very good performance of purification-based error mitigation. Lastly, we identify techniques that may decrease both metrics, such as increasing the dimensionality of the dynamical Lie algebra by gate insertions or randomised compiling.
{"title":"Can shallow quantum circuits scramble local noise into global white noise?","authors":"Jonathan Foldager, Bálint Koczor","doi":"10.1088/1751-8121/ad0ac7","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0ac7","url":null,"abstract":"Abstract Shallow quantum circuits are believed to be the most promising candidates for achieving early practical quantum advantage -- this has motivated the development of a broad range of error mitigation techniques whose performance generally improves when the quantum state is well approximated by a global depolarising (white) noise model. While it has been crucial for demonstrating quantum supremacy that random circuits scramble local noise into global white noise---a property that has been proved rigorously---we investigate to what degree practical shallow quantum circuits scramble local noise into global white noise. We define two key metrics as (a) density matrix eigenvalue uniformity and (b) commutator norm. While the former determines the distance from white noise, the latter determines the performance of purification based error mitigation. We derive analytical approximate bounds on their scaling and find in most cases they nicely match numerical results. On the other hand, we simulate a broad class of practical quantum circuits and find that white noise is in certain cases a bad approximation posing significant limitations on the performance of some of the simpler error mitigation schemes. On a positive note, we find in all cases that the commutator norm is sufficiently small guaranteeing a very good performance of purification-based error mitigation. Lastly, we identify techniques that may decrease both metrics, such as increasing the dimensionality of the dynamical Lie algebra by gate insertions or randomised compiling.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":" 26","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135341417","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 : 2023-11-08DOI: 10.1088/1751-8121/ad0af4
Keppler, H., Krajewski, T., Muller, T., Tanasa, A.
Abstract In a recent series of papers, a duality between orthogonal and symplectic random tensor models has been proven, first for quartic models and then for models with interactions of arbitrary order. However, the tensor models considered so far in the literature had no symmetry under permutation of the indices. In this paper, we generalize these results for tensors models with interactions of arbitrary order which further have non-trivial symmetry under the permutation of the indices. Totally symmetric and anti-symmetric tensors are thus treated as a particular case of our result.
{"title":"Duality of O(N) and Sp(N) random tensor models: tensors with symmetries","authors":"Keppler, H., Krajewski, T., Muller, T., Tanasa, A.","doi":"10.1088/1751-8121/ad0af4","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0af4","url":null,"abstract":"Abstract In a recent series of papers, a duality between orthogonal and symplectic random tensor models has been proven, first for quartic models and then for models with interactions of arbitrary order. However, the tensor models considered so far in the literature had no symmetry under permutation of the indices. In this paper, we generalize these results for tensors models with interactions of arbitrary order which further have non-trivial symmetry under the permutation of the indices. Totally symmetric and anti-symmetric tensors are thus treated as a particular case of our result.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":" 22","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135293656","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 : 2023-11-07DOI: 10.1088/1751-8121/ad0a43
Ivar Lyberg, Vladimir Korepin, Jacopo Viti
Abstract We consider the six-vertex model with Domain Wall Boundary Conditions in $Ntimes N$ square lattice. Our main interest is the study of the fluctuations of the extremal lattice path about the arctic curves. We address the problem through Monte Carlo simulations. At $Delta=0$, the fluctuations of the extremal path along any line parallel to the square diagonal were rigorously proven to follow the Tracy-Widom distribution. We provide strong numerical evidence that this is true also for other values of the anisotropy parameter $Delta$ ($0leq Delta<1$). We argue that the typical width of the fluctuations of the extremal path about the arctic curves scales as $N^{1/3}$ and provide a numerical estimate for the parameters of the scaling random variable.
{"title":"Fluctuation of the phase boundary in the six-vertex model with Domain Wall Boundary Conditions: a Monte Carlo study","authors":"Ivar Lyberg, Vladimir Korepin, Jacopo Viti","doi":"10.1088/1751-8121/ad0a43","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0a43","url":null,"abstract":"Abstract We consider the six-vertex model with Domain Wall Boundary Conditions in $Ntimes N$ square lattice. Our main interest is the study of the fluctuations of the extremal lattice path about the arctic curves. We address the problem through Monte Carlo simulations. At $Delta=0$, the fluctuations of the extremal path along any line parallel to the square diagonal were rigorously proven to follow the Tracy-Widom distribution. We provide strong numerical evidence that this is true also for other values of the anisotropy parameter $Delta$ ($0leq Delta<1$). We argue that the typical width of the fluctuations of the extremal path about the arctic curves scales as $N^{1/3}$ and provide a numerical estimate for the parameters of the scaling random variable.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"318 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135475062","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}
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