Pub Date : 2023-10-16DOI: 10.1088/1751-8121/ad009e
Luca Angelani
Abstract The motion of run-and-tumble particles in one-dimensional finite domains are analyzed in the presence of generic boundary conditions. These describe accumulation at walls, where particles can either be absorbed at a given rate, or tumble, with a rate that may be, in general, different from that in the bulk. This formulation allows us to treat in a unified way very different boundary conditions (fully and partially absorbing/reflecting, sticky, sticky-reactive and sticky-absorbing boundaries) which can be recovered as appropriate limits of the general case. We report the general expression of the mean exit time, valid for generic boundaries, discussing many case studies, from equal boundaries to more interesting cases of different boundary conditions at the two ends of the domain, resulting in nontrivial expressions of mean exit times.
{"title":"One-dimensional run-and-tumble motions with generic boundary conditions","authors":"Luca Angelani","doi":"10.1088/1751-8121/ad009e","DOIUrl":"https://doi.org/10.1088/1751-8121/ad009e","url":null,"abstract":"Abstract The motion of run-and-tumble particles in one-dimensional finite domains are analyzed in the presence of generic boundary conditions. These describe accumulation at walls, where particles can either be absorbed at a given rate, or tumble, with a rate that may be, in general, different from that in the bulk. This formulation allows us to treat in a unified way very different boundary conditions (fully and partially absorbing/reflecting, sticky, sticky-reactive and sticky-absorbing boundaries) which can be recovered as appropriate limits of the general case. We report the general expression of the mean exit time, valid for generic boundaries, discussing many case studies, from equal boundaries to more interesting cases of different boundary conditions at the two ends of the domain, resulting in nontrivial expressions of mean exit times.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136077902","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 : 2023-10-16DOI: 10.1088/1751-8121/ad03a4
Elizabeth Melville, Gamal Mograby, Nikhil Nagabandi, Luke G Rogers, Alexander Teplyaev
Abstract Motivated by the appearance of fractals in several areas of physics, especially in solid state physics and the physics of aperiodic order, and in other sciences, including the quantum information theory, we present a detailed spectral analysis for a new class of fractal-type diamond graphs, referred to as bubble-diamond graphs, and provide a gap-labeling theorem in the sense of Bellissard for the corresponding probabilistic graph Laplacians using the technique of spectral decimation. Labeling the gaps in the Cantor set by the normalized eigenvalue counting function, also known as the integrated density of states, we describe the gap labels as orbits of a second dynamical system that reflects the branching parameter of the bubble construction and the decimation structure. The spectrum of the natural Laplacian on limit graphs is shown generically to be pure point supported on a Cantor set, though one particular graph has a mixture of pure point and singularly continuous components.
{"title":"Gaps labeling theorem for the bubble-diamond self-similar graphs","authors":"Elizabeth Melville, Gamal Mograby, Nikhil Nagabandi, Luke G Rogers, Alexander Teplyaev","doi":"10.1088/1751-8121/ad03a4","DOIUrl":"https://doi.org/10.1088/1751-8121/ad03a4","url":null,"abstract":"Abstract Motivated by the appearance of fractals in several areas of physics, especially in solid state physics and the physics of aperiodic order, and in other sciences, including the quantum information theory, we present a detailed spectral analysis for a new class of fractal-type diamond graphs, referred to as bubble-diamond graphs, and provide a gap-labeling theorem in the sense of Bellissard for the corresponding probabilistic graph Laplacians using the technique of spectral decimation. Labeling the gaps in the Cantor set by the normalized eigenvalue counting function, also known as the integrated density of states, we describe the gap labels as orbits of a second dynamical system that reflects the branching parameter of the bubble construction and the decimation structure. The spectrum of the natural Laplacian on limit graphs is shown generically to be pure point supported on a Cantor set, though one particular graph has a mixture of pure point and singularly continuous components.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136078643","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 : 2023-10-16DOI: 10.1088/1751-8121/ad00ed
Laurent Delisle
Abstract This article presents a novel application of the Hirota bilinear formalism to the N = 2 supersymmetric Korteweg–de Vries and Burgers equations. This new approach avoids splitting N = 2 equations into two N = 1 equations. We use the super Bell polynomials to obtain bilinear representations and present multi-soliton solutions.
{"title":"A novel Hirota bilinear approach to <i>N</i> = 2 supersymmetric equations","authors":"Laurent Delisle","doi":"10.1088/1751-8121/ad00ed","DOIUrl":"https://doi.org/10.1088/1751-8121/ad00ed","url":null,"abstract":"Abstract This article presents a novel application of the Hirota bilinear formalism to the N = 2 supersymmetric Korteweg–de Vries and Burgers equations. This new approach avoids splitting N = 2 equations into two N = 1 equations. We use the super Bell polynomials to obtain bilinear representations and present multi-soliton solutions.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136077733","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 : 2023-10-13DOI: 10.1088/1751-8121/acff51
H Koizumi
Superconductivity is reformulated as a phenomenon in which a stable velocity field is created by a U(1) phase neglected by Dirac in the Schrödinger representation of quantum mechanics. The neglected phase gives rise to a U(1) gauge field expressed as the Berry connection from many-body wave functions. The inclusion of this gauge field transforms the standard particle-number non-conserving formalism of superconductivity to a particle-number conserving one with many results of the former unaltered. In other words, the new formalism indicates that the current standard one is an approximation that effectively takes into account this neglected U(1) gauge field by employing the particle-number non-conserving formalism. Since the standard and new formalisms are physically different, conflicting results are predicted in some cases. We reexamine the Josephson relation and show that a capacitance contribution of the Josephson junction to the U(1) phase is missing in the standard formalism, and inclusion of it indicates that the standard theory actually does not agree with the experiment while the new one does. It is also shown that the dissipative quantum phase transition in Josephson junctions predicted in the standard theory does not exist in the new one in accordance with a recent experiment (Murani et al 2020 Phys. Rev. X 10 021003).
超导被重新表述为一种现象，在量子力学Schrödinger表示中，由Dirac忽略的U(1)相产生稳定的速度场。被忽略的相位产生U(1)规范场，表示为多体波函数的贝里连接。该规范场的加入将超导的标准粒子数非守恒形式转化为粒子数守恒形式，而前者的许多结果不变。换句话说，新的形式表明，目前的标准形式是一个近似值，它通过采用粒子数非守恒形式有效地考虑了这个被忽视的U(1)规范场。由于标准形式和新形式在物理上不同，在某些情况下预测的结果会相互冲突。我们重新考察了约瑟夫森关系，并表明约瑟夫森结对U(1)相的电容贡献在标准的形式主义中是缺失的，它的包含表明标准理论实际上与实验不一致，而新的理论与实验一致。根据最近的一项实验，也表明标准理论中预测的约瑟夫森结的耗散量子相变在新理论中不存在(Murani et al 2020 Phys。Rev. X 10 021003)。
{"title":"Neglected U(1) phase in the Schrödinger representation of quantum mechanics and particle number conserving formalisms for superconductivity","authors":"H Koizumi","doi":"10.1088/1751-8121/acff51","DOIUrl":"https://doi.org/10.1088/1751-8121/acff51","url":null,"abstract":"Superconductivity is reformulated as a phenomenon in which a stable velocity field is created by a U(1) phase neglected by Dirac in the Schrödinger representation of quantum mechanics. The neglected phase gives rise to a U(1) gauge field expressed as the Berry connection from many-body wave functions. The inclusion of this gauge field transforms the standard particle-number non-conserving formalism of superconductivity to a particle-number conserving one with many results of the former unaltered. In other words, the new formalism indicates that the current standard one is an approximation that effectively takes into account this neglected U(1) gauge field by employing the particle-number non-conserving formalism. Since the standard and new formalisms are physically different, conflicting results are predicted in some cases. We reexamine the Josephson relation and show that a capacitance contribution of the Josephson junction to the U(1) phase is missing in the standard formalism, and inclusion of it indicates that the standard theory actually does not agree with the experiment while the new one does. It is also shown that the dissipative quantum phase transition in Josephson junctions predicted in the standard theory does not exist in the new one in accordance with a recent experiment (Murani et al 2020 Phys. Rev. X 10 021003).","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135805452","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 : 2023-10-13DOI: 10.1088/1751-8121/ad0349
Ryan Requist
Abstract The covariant derivative suitable for differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent adiabatic quantum eigenstate is introduced. It is proved to be covariant under gauge and coordinate transformations and compatible with the quantum geometric tensor. For a quantum system driven by a Hamiltonian $H=H(x)$ depending on slowly-varying parameters $x={x_1(epsilon t),x_2(epsilon t),ldots}$, $epsilonll 1$, the quantum covariant derivative is used to derive a recurrence relation that determines an asymptotic series for the wave function to all orders in $epsilon$. This adiabatic perturbation theory provides an efficient tool for calculating nonlinear response properties.
{"title":"Quantum covariant derivative: a tool for deriving adiabatic perturbation theory to all orders","authors":"Ryan Requist","doi":"10.1088/1751-8121/ad0349","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0349","url":null,"abstract":"Abstract The covariant derivative suitable for differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent adiabatic quantum eigenstate is introduced. It is proved to be covariant under gauge and coordinate transformations and compatible with the quantum geometric tensor. For a quantum system driven by a Hamiltonian $H=H(x)$ depending on slowly-varying parameters $x={x_1(epsilon t),x_2(epsilon t),ldots}$, $epsilonll 1$, the quantum covariant derivative is used to derive a recurrence relation that determines an asymptotic series for the wave function to all orders in $epsilon$. This adiabatic perturbation theory provides an efficient tool for calculating nonlinear response properties.&#xD;","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135853735","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 : 2023-10-13DOI: 10.1088/1751-8121/acfeb7
Ludovico Lami, Daniel Goldwater, Gerardo Adesso
Abstract Associative memories are devices storing information that can be fully retrieved given partial disclosure of it. We examine a toy model of associative memory and the ultimate limitations to which it is subjected within the framework of general probabilistic theories (GPTs), which represent the most general class of physical theories satisfying some basic operational axioms. We ask ourselves how large the dimension of a GPT should be so that it can accommodate 2 m states with the property that any N of them are perfectly distinguishable. Call d(N,m) the minimal such dimension. Invoking an old result by Danzer and Grünbaum, we prove that d(2,m)=m+1 , to be compared with O(2m) when the GPT is required to be either classical or quantum. This yields an example of a task where GPTs outperform both classical and quantum theory exponentially. More generally, we resolve the case of fixed N and asymptotically large m , proving that d(N,m)⩽m1+oN(1) (as m→∞ ) for every N⩾2 , which yields again an exponential improvement over classical and quantum theories. Finally, we develop a numerical approach to the general problem of finding the largest N -wise mutually distinguishable set for a given GPT, which can be seen as an instance of th
联想记忆是一种存储信息的装置，它可以在部分披露的情况下被完全检索。我们研究了联想记忆的一个玩具模型，以及它在一般概率论(GPTs)框架内受到的最终限制，GPTs代表了满足一些基本操作公理的最一般的物理理论。我们问自己，GPT的维度应该有多大，才能容纳2m个状态，并且其中任意N个状态都是完全可区分的。称d (N, m)为最小维数。引用Danzer和gr nbaum的旧结果，我们证明了d (2, m) = m + 1，当GPT被要求是经典的或量子的时，与O (2 m)进行比较。这就产生了一个任务的例子，其中gpt的表现都以指数方式优于经典理论和量子理论。更一般地说，我们解决了固定N和渐近大m的情况，证明对于每个N大于或等于2,d (N, m)≥m 1 + o N(1)(作为m→∞)，这再次产生了比经典理论和量子理论的指数改进。最后，我们提出了一种求解给定GPT的最大N -明智互可分辨集的一般问题的数值方法，这可以看作是N -正则超图上最大团问题的一个实例。
{"title":"A post-quantum associative memory","authors":"Ludovico Lami, Daniel Goldwater, Gerardo Adesso","doi":"10.1088/1751-8121/acfeb7","DOIUrl":"https://doi.org/10.1088/1751-8121/acfeb7","url":null,"abstract":"Abstract Associative memories are devices storing information that can be fully retrieved given partial disclosure of it. We examine a toy model of associative memory and the ultimate limitations to which it is subjected within the framework of general probabilistic theories (GPTs), which represent the most general class of physical theories satisfying some basic operational axioms. We ask ourselves how large the dimension of a GPT should be so that it can accommodate 2 m states with the property that any N of them are perfectly distinguishable. Call <?CDATA $d(N,m)$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>d</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>N</mml:mi> <mml:mo>,</mml:mo> <mml:mi>m</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:math> the minimal such dimension. Invoking an old result by Danzer and Grünbaum, we prove that <?CDATA $d(2,m) = m+1$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>d</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mi>m</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:math> , to be compared with <?CDATA $O(2^m)$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>O</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mi>m</mml:mi> </mml:msup> <mml:mo stretchy=\"false\">)</mml:mo> </mml:math> when the GPT is required to be either classical or quantum. This yields an example of a task where GPTs outperform both classical and quantum theory exponentially. More generally, we resolve the case of fixed N and asymptotically large m , proving that <?CDATA $d(N,m) unicode{x2A7D} m^{1+o_N(1)}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>d</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>N</mml:mi> <mml:mo>,</mml:mo> <mml:mi>m</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mtext>⩽</mml:mtext> <mml:msup> <mml:mi>m</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>o</mml:mi> <mml:mi>N</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> </mml:msup> </mml:math> (as <?CDATA $mtoinfty$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>m</mml:mi> <mml:mo stretchy=\"false\">→</mml:mo> <mml:mi mathvariant=\"normal\">∞</mml:mi> </mml:math> ) for every <?CDATA $Nunicode{x2A7E} 2$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>N</mml:mi> <mml:mtext>⩾</mml:mtext> <mml:mn>2</mml:mn> </mml:math> , which yields again an exponential improvement over classical and quantum theories. Finally, we develop a numerical approach to the general problem of finding the largest N -wise mutually distinguishable set for a given GPT, which can be seen as an instance of th","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"136 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135805668","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 : 2023-10-13DOI: 10.1088/1751-8121/ad02ec
Fabio Bagarello, Francesco Gargano, L Saluto
In this paper we consider squares of pseudo-bosonic ladder operators and we use them to produce explicit examples of eigenstates of certain operators satisfying a deformed $mathfrak{su}(1,1)$ Lie algebra. We show how these eigenstates may, or may not, be square-integrable. In both cases, a notion of biorthonormality can be introduced and analyzed. Some examples are discussed in details. We also propose some preliminary results on bi-squeezed states arising from our operators.
{"title":"Extended coupled SUSY, pseudo-bosons and weak squeezed states","authors":"Fabio Bagarello, Francesco Gargano, L Saluto","doi":"10.1088/1751-8121/ad02ec","DOIUrl":"https://doi.org/10.1088/1751-8121/ad02ec","url":null,"abstract":"In this paper we consider squares of pseudo-bosonic ladder operators and we use them to produce explicit examples of eigenstates of certain operators satisfying a deformed $mathfrak{su}(1,1)$ Lie algebra. We show how these eigenstates may, or may not, be square-integrable. In both cases, a notion of biorthonormality can be introduced and analyzed. Some examples are discussed in details. We also propose some preliminary results on bi-squeezed states arising from our operators.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"159 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135858288","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 : 2023-10-13DOI: 10.1088/1751-8121/acff9d
Rafał Bistroń, Wojciech Śmiałek, Karol Życzkowski
Abstract The notion of convolution of two probability vectors, corresponding to a coincidence experiment can be extended to a family of binary operations determined by (tri)stochastic tensors, to describe Markov chains of a higher order. The problem of associativity, commutativity, and the existence of neutral elements and inverses for such operations acting on classical states is analyzed. For a more general setup of multi-stochastic tensors, we present the characterization of their probability eigenvectors. Similar results are obtained for the quantum case: we analyze tristochastic channels, which induce binary operations defined in the space of quantum states. Studying coherifications of tristochastic tensors we propose a quantum analogue of the convolution of probability vectors defined for two arbitrary density matrices of the same size. Possible applications of this notion to construct schemes of error mitigation or building blocks in quantum convolutional neural networks are discussed.
{"title":"Tristochastic operations and products of quantum states","authors":"Rafał Bistroń, Wojciech Śmiałek, Karol Życzkowski","doi":"10.1088/1751-8121/acff9d","DOIUrl":"https://doi.org/10.1088/1751-8121/acff9d","url":null,"abstract":"Abstract The notion of convolution of two probability vectors, corresponding to a coincidence experiment can be extended to a family of binary operations determined by (tri)stochastic tensors, to describe Markov chains of a higher order. The problem of associativity, commutativity, and the existence of neutral elements and inverses for such operations acting on classical states is analyzed. For a more general setup of multi-stochastic tensors, we present the characterization of their probability eigenvectors. Similar results are obtained for the quantum case: we analyze tristochastic channels, which induce binary operations defined in the space of quantum states. Studying coherifications of tristochastic tensors we propose a quantum analogue of the convolution of probability vectors defined for two arbitrary density matrices of the same size. Possible applications of this notion to construct schemes of error mitigation or building blocks in quantum convolutional neural networks are discussed.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"250 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135804902","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 : 2023-10-13DOI: 10.1088/1751-8121/acff9c
Eldad Bettelheim
Abstract We employ a mathematical framework based on the Riemann-Hilbert approach developed by Bettelheim et al (2022 J. Phys. A: Math. Gen. 55 135001) to study logarithmic negativity of two intervals of free fermions in the case where the size of the intervals as well as the distance between them is macroscopic. We find that none of the eigenvalues of the density matrix become negative, but rather they develop a small imaginary value, leading to non-zero logarithmic negativity. As an example, we compute negativity at half-filling and for intervals of equal size we find a result of order (log(N))−1 , where N is the typical length scale in units of the lattice spacing. One may compute logarithmic negativity in further situations, but we find that the results are non-universal, depending non-smoothly on the Fermi level and the size of the intervals in units of the lattice spacing.
我们采用了一个基于Riemann-Hilbert方法的数学框架，该方法由Bettelheim等人(2022 J. Phys)开发。答:数学。(gen 55 135001)来研究两个自由费米子区间的对数负性，在这种情况下，区间的大小以及它们之间的距离是宏观的。我们发现密度矩阵的特征值都不是负的，而是形成一个小的虚值，导致非零对数负。作为一个例子，我们在半填充时计算负性，对于相同大小的间隔，我们发现结果为(log (N))−1阶，其中N是晶格间距单位的典型长度尺度。人们可以在进一步的情况下计算对数负性，但我们发现结果是非普遍的，非平滑地依赖于费米能级和晶格间距单位间隔的大小。
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Pub Date : 2023-10-13DOI: 10.1088/1751-8121/acfc07
Vincenzo Emilio Marotta, Richard J Szabo
Abstract We study the geometry of foliated non-Lorentzian spacetimes in terms of the Godbillon-Vey class of the foliation. We relate the intrinsic torsion of a foliated Aristotelian manifold to its Godbillon-Vey class, and interpret it as a measure of the local spin of the spatial leaves in the time direction. With this characterisation, the Godbillon-Vey class is an obstruction to integrability of the G -structure defining the Aristotelian spacetime. We use these notions to formulate a new geometric approach to hydrodynamics of fluid flows by endowing them with Aristotelian structures. We establish conditions under which the Godbillon-Vey class represents an obstruction to steady flow of the fluid and prove new conservation laws.
{"title":"Godbillon-Vey invariants of non-Lorentzian spacetimes and Aristotelian hydrodynamics","authors":"Vincenzo Emilio Marotta, Richard J Szabo","doi":"10.1088/1751-8121/acfc07","DOIUrl":"https://doi.org/10.1088/1751-8121/acfc07","url":null,"abstract":"Abstract We study the geometry of foliated non-Lorentzian spacetimes in terms of the Godbillon-Vey class of the foliation. We relate the intrinsic torsion of a foliated Aristotelian manifold to its Godbillon-Vey class, and interpret it as a measure of the local spin of the spatial leaves in the time direction. With this characterisation, the Godbillon-Vey class is an obstruction to integrability of the <?CDATA ${mathsf{G}}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"sans-serif\">G</mml:mi> </mml:mrow> </mml:mrow> </mml:math> -structure defining the Aristotelian spacetime. We use these notions to formulate a new geometric approach to hydrodynamics of fluid flows by endowing them with Aristotelian structures. We establish conditions under which the Godbillon-Vey class represents an obstruction to steady flow of the fluid and prove new conservation laws.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"370 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135804735","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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