Journal of Physics A最新文献

{"title":"Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble","authors":"Gernot Akemann, Sung-Soo Byun, Markus Ebke, Gregory Schehr","doi":"10.1088/1751-8121/ad0885","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0885","url":null,"abstract":"Abstract In this article, we compute and compare the statistics of the number of eigenvalues in a centred disc of radius $R$ in all three Ginibre ensembles. We determine the mean and variance as functions of $R$ in the vicinity of the origin, where the real and symplectic ensembles exhibit respectively an additional attraction to or repulsion from the real axis, leading to different results. In the large radius limit, all three ensembles coincide and display a universal bulk behaviour of $O(R^2)$ for the mean, and $O(R)$ for the variance. We present detailed conjectures for the bulk and edge scaling behaviours of the real Ginibre ensemble, having real and complex eigenvalues. For the symplectic ensemble we can go beyond the Gaussian case (corresponding to the Ginibre ensemble) and prove the universality of the full counting statistics both in the bulk and at the edge of the spectrum for rotationally invariant potentials, extending a recent work which considered the mean and the variance. This statistical behaviour coincides with the universality class of the complex Ginibre ensemble, which has been shown to be associated with the ground state of non-interacting fermions in a two-dimensional rotating harmonic trap. All our analytical results and conjectures are corroborated by numerical simulations.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"98 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135870901","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}

{"title":"Ultra-quantum coherent states in a single finite quantum system","authors":"Apostol Vourdas","doi":"10.1088/1751-8121/ad0438","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0438","url":null,"abstract":"Abstract A set of n coherent states is introduced in a quantum system with d -dimensional Hilbert space H ( d ). It is shown that they resolve the identity, and also have a discrete isotropy property. A finite cyclic group acts on the set of these coherent states, and partitions it into orbits. A n -tuple representation of arbitrary states in H ( d ), analogous to the Bargmann representation, is defined. There are two other important properties of these coherent states which make them ‘ultra-quantum’. The first property is related to the Grothendieck formalism which studies the ‘edge’ of the Hilbert space and quantum formalisms. Roughly speaking the Grothendieck theorem considers a ‘classical’ quadratic form <?CDATA ${mathfrak C}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"fraktur\">C</mml:mi> </mml:mrow> </mml:mrow> </mml:math> that uses complex numbers in the unit disc, and a ‘quantum’ quadratic form <?CDATA ${mathfrak Q}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"fraktur\">Q</mml:mi> </mml:mrow> </mml:mrow> </mml:math> that uses vectors in the unit ball of the Hilbert space. It shows that if <?CDATA ${mathfrak C}unicode{x2A7D} 1$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"fraktur\">C</mml:mi> </mml:mrow> </mml:mrow> <mml:mtext>⩽</mml:mtext> <mml:mn>1</mml:mn> </mml:math> , the corresponding <?CDATA ${mathfrak Q}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"fraktur\">Q</mml:mi> </mml:mrow> </mml:mrow> </mml:math> might take values greater than 1, up to the complex Grothendieck constant <?CDATA $k_mathrm{G}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:msub> <mml:mi>k</mml:mi> <mml:mrow> <mml:mi mathvariant=\"normal\">G</mml:mi> </mml:mrow> </mml:msub> </mml:math> . <?CDATA ${mathfrak Q}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"fraktur\">Q</mml:mi> </mml:mrow> </mml:mrow> </mml:math> related to these coherent states is shown to take values in the ‘Grothendieck region’ <?CDATA $(1,k_mathrm{G})$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>k</mml:mi> <mml:mrow> <mml:mi mathvariant=\"normal\">G</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> </mml:math> , which is classically forbidden in the sense that <?CDATA ${mathfrak C}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"fraktur\">C</mml:mi> </mml:mrow> </mml:mrow> </mml:math> does not take values in it. The second property complements this, showing that these coheren","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136019119","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}

{"title":"Transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations","authors":"Ba Phi Nguyen, Kihong Kim","doi":"10.1088/1751-8121/ad03cd","DOIUrl":"https://doi.org/10.1088/1751-8121/ad03cd","url":null,"abstract":"Abstract We present a numerical study of the transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations. The model is characterized by the modulation period κ and the disorder strength W . We calculate the disorder averages <?CDATA $langle Trangle$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mo fence=\"false\" stretchy=\"false\">⟨</mml:mo> <mml:mi>T</mml:mi> <mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo> </mml:math> , <?CDATA $langle ln Trangle$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mrow> <mml:mo>〈</mml:mo> <mml:mi>ln</mml:mi> <mml:mi>T</mml:mi> <mml:mo>〉</mml:mo> </mml:mrow> </mml:math> , and <?CDATA $langle Prangle$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mo fence=\"false\" stretchy=\"false\">⟨</mml:mo> <mml:mi>P</mml:mi> <mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo> </mml:math> , where T is the transmittance and P is the participation ratio, as a function of energy E and system size L , for different values of κ and W . For excitations at quasiresonance energies determined by κ , we find power-law scaling behaviors of the form <?CDATA $langle T rangle propto L^{-gamma_{a}}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mo fence=\"false\" stretchy=\"false\">⟨</mml:mo> <mml:mi>T</mml:mi> <mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo> <mml:mo>∝</mml:mo> <mml:msup> <mml:mi>L</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>γ</mml:mi> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msup> </mml:math> , <?CDATA $langle ln T rangle approx -gamma_g ln L$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mo fence=\"false\" stretchy=\"false\">⟨</mml:mo> <mml:mo form=\"prefix\">ln</mml:mo> <mml:mi>T</mml:mi> <mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo> <mml:mo>≈</mml:mo> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mo form=\"prefix\">ln</mml:mo> <mml:mi>L</mml:mi> </mml:math> , and <?CDATA $langle P rangle propto L^{beta}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mo fence=\"false\" stretchy=\"false\">⟨</mml:mo> <mml:mi>P</mml:mi> <mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo> <mml:mo>∝</mml:mo> <mml:msup> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> </mml:msup> </mml:math> , as L increases to a large value. In the strong disorder limit, the exponents are seen to saturate at the values <?CDATA $gamma_a sim 0.5$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>a</mml:mi> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>0.5</mml:mn> </mml:math> , <?CDATA $gamma_g sim 1$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>g</mml:mi> </mml:msub> <mml:mo>∼</mml:","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"22 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136019105","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}

{"title":"Direct Poisson neural networks: learning non-symplectic mechanical systems","authors":"Martin Šípka, Michal Pavelka, Oğul Esen, M Grmela","doi":"10.1088/1751-8121/ad0803","DOIUrl":"https://doi.org/10.1088/1751-8121/ad0803","url":null,"abstract":"Abstract In this paper, we present neural networks learning mechanical systems that are both symplectic&amp;#xD;(for instance particle mechanics) and non-symplectic (for instance rotating rigid body). Mechanical&amp;#xD;systems have Hamiltonian evolution, which consists of two building blocks: a Poisson bracket and an&amp;#xD;energy functional. We feed a set of snapshots of a Hamiltonian system to our neural network models&amp;#xD;which then find both the two building blocks. In particular, the models distinguish between symplectic&amp;#xD;systems (with non-degenerate Poisson brackets) and non-symplectic systems (degenerate brackets).&amp;#xD;In contrast with earlier works, our approach does not assume any further a priori information about&amp;#xD;the dynamics except its Hamiltonianity, and it returns Poisson brackets that satisfy Jacobi identity.&amp;#xD;Finally, the models indicate whether a system of equations is Hamiltonian or not.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"11 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136019191","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}

{"title":"Closed form expressions for the Green’s function of a quantum graph – a scattering approach","authors":"Tristan Lawrie, Sven Gnutzmann, Gregor K Tanner","doi":"10.1088/1751-8121/ad03a5","DOIUrl":"https://doi.org/10.1088/1751-8121/ad03a5","url":null,"abstract":"Abstract In this work we present a three step procedure for generating a closed form expression of the Green’s function on both closed and open finite quantum graphs with general self-adjoint matching conditions. We first generalize and simplify the approach by Barra and Gaspard (2001 Phys. Rev. E 65 016205) and then discuss the validity of the explicit expressions. For compact graphs, we show that the explicit expression is equivalent to the spectral decomposition as a sum over poles at the discrete energy eigenvalues with residues that contain projector kernel onto the corresponding eigenstate. The derivation of the Green’s function is based on the scattering approach, in which stationary solutions are constructed by treating each vertex or subgraph as a scattering site described by a scattering matrix. The latter can then be given in a simple closed form from which the Green’s function is derived. The relevant scattering matrices contain inverse operators which are not well defined for wave numbers at which bound states in the continuum exists. It is shown that the singularities in the scattering matrix related to these bound states or perfect scars can be regularised. Green’s functions or scattering matrices can then be expressed as a sum of a regular and a singular part where the singular part contains the projection kernel onto the perfect scar.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"73 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136019237","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}

{"title":"Hankel determinants for a Gaussian weight with Fisher-Hartwig singularities and generalized Painlevé IV equation","authors":"Xinyu Mu, Shulin Lyu","doi":"10.1088/1751-8121/ad04a6","DOIUrl":"https://doi.org/10.1088/1751-8121/ad04a6","url":null,"abstract":"Abstract We study the Hankel determinant generated by a Gaussian weight with Fisher–Hartwig singularities of root type at t j , <?CDATA $j = 1,cdots ,N$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>j</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>,</mml:mo> <mml:mi>N</mml:mi> </mml:math> . It characterizes a type of average characteristic polynomial of matrices from Gaussian unitary ensembles. We derive the ladder operators satisfied by the associated monic orthogonal polynomials and three compatibility conditions. By using them and introducing 2 N auxiliary quantities <?CDATA ${R_{n,j}, r_{n,j}, j = 1,cdots,N}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo> <mml:msub> <mml:mi>R</mml:mi> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mi>j</mml:mi> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mi>j</mml:mi> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>j</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>,</mml:mo> <mml:mi>N</mml:mi> <mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo> </mml:math> , we build a series of difference equations. Furthermore, we prove that <?CDATA ${R_{n,j}, r_{n,j}}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo> <mml:msub> <mml:mi>R</mml:mi> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mi>j</mml:mi> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mi>j</mml:mi> </mml:mrow> </mml:msub> <mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo> </mml:math> satisfy Riccati equations. From them we deduce a system of second order PDEs satisfied by <?CDATA ${R_{n,j}, j = 1,cdots,N}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo> <mml:msub> <mml:mi>R</mml:mi> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mi>j</mml:mi> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>j</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>,</mml:mo> <mml:mi>N</mml:mi> <mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo> </mml:math> , which reduces to a Painlevé IV equation for N = 1. We also show that the logarithmic derivative of the Hankel determinant satisfies the generalized σ -form of a Painlevé IV equation.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"69 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136018875","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}

{"title":"Four-wave mixing in all degrees of freedom","authors":"Filippus Stefanus Roux","doi":"10.1088/1751-8121/acfcf5","DOIUrl":"https://doi.org/10.1088/1751-8121/acfcf5","url":null,"abstract":"Abstract A Wigner functional approach is used to derive an evolution equation for a photonic state propagating through a Kerr medium. The resulting evolution equation incorporates all the spatiotemporal degrees of freedom together with the photon-number degrees of freedom and thus allows thorough analyses of the effects of experimental parameters in physical quantum information systems. We then use the evolution equation to consider four-wave mixing as a spontaneous process and finally we impose some approximations to obtain an expression for the optical field due to self-phase modulation.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"58 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136018673","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}

{"title":"Influence of cumulative damage on synchronizationof Kuramoto oscillators on networks","authors":"L K Eraso-Hernandez, Alejandro P Riascos","doi":"10.1088/1751-8121/ad043b","DOIUrl":"https://doi.org/10.1088/1751-8121/ad043b","url":null,"abstract":"Abstract In this paper, we study the synchronization of identical Kuramoto phase oscillators under cumulative stochastic damage to the edges of networks. We analyze the capacity of coupled oscillators to reach a coherent state from initial random phases. The process of synchronization is a global function performed by a system that gradually changes when the damage weakens individual connections of the network. We explore diverse structures characterized by different topologies. Among these are deterministic networks as a wheel or the lattice formed by the movements of the knight on a chess board, and random networks generated with the Erdős–Rényi and Barabási–Albert algorithms. In addition, we study the synchronization times of 109 non-isomorphic graphs with six nodes. The synchronization times and other introduced quantities are sensitive to the impact of damage, allowing us to measure the reduction of the capacity of synchronization and classify the effect of damage in the systems under study. This approach is general and paves the way for the exploration of the effect of damage accumulation in diverse dynamical processes in complex systems.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"53 S2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136018987","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}

{"title":"Local minimizers of the distances to the majorization flows","authors":"María José Benac, Pedro Massey, Noelia Belén Rios, Mariano Ruiz","doi":"10.1088/1751-8121/ad07c6","DOIUrl":"https://doi.org/10.1088/1751-8121/ad07c6","url":null,"abstract":"Abstract Let $mathcal{D}(d)$ denote the convex set of density matrices of size $d$ and let $rho,,sigmainmathcal{D}(d)$ be such that $rhonotprec sigma$. Consider the majorization flows $mathcal{L}(sigma)={mu inmathcal{D}(d) : muprec sigma}$ and $mathcal{U}(rho)={nuinmathcal{D}(d) : rhoprec nu}$, where $prec$ stands for the majorization pre-order relation. We endow $mathcal{L}(sigma)$ and $mathcal{U}(rho)$ with the metric induced by the spectral norm. Let $N(cdot)$ be a strictly convex unitarily invariant norm and let $mu_0in mathcal{L}(sigma)$ and $nu_0inmathcal{U}(rho)$ be local minimizers of the distance functions &amp;#xD;$Phi_N(mu)=N(rho-mu)$, for $muinmathcal{L}(sigma)$ and $Psi_N(nu)=N(sigma-nu)$, for $nuinmathcal{U}(rho)$. In this work we show that, for every unitarily invariant norm $tilde N(cdot)$ we have that &amp;#xD;$$&amp;#xD;tilde N(rho-mu_0)leq tilde N(rho-mu), , , muinmathcal{L}(sigma)peso{and} &amp;#xD;tilde N(sigma-nu_0)leq tilde N(sigma-nu), , , nuinmathcal{U}(rho),.&amp;#xD;$$ That is, $mu_0$ and $nu_0$ are global minimizers of the distances to the corresponding majorization flows, with respect to every unitarily invariant norm. We describe the (unique) spectral structure (eigenvalues) of $mu_0$ and $nu_0$ in terms of a simple finite step algorithm; we also describe the geometrical structure (eigenvectors) of $mu_0$ and $nu_0$ in terms of the geometrical structure of $sigma$ and $rho$, respectively. We include a discussion of the physical and computational implications of our results. We also compare our results to some recent related results in the context of quantum information theory.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"14 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136317243","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}

{"title":"Two-dimensional integrable systems with position-dependent mass via complex holomorphic functions","authors":"Hai Zhang, Kai Wu, Delong Wang","doi":"10.1088/1751-8121/ad07c7","DOIUrl":"https://doi.org/10.1088/1751-8121/ad07c7","url":null,"abstract":"We study the relationship between integrable systems with a position-dependent mass (PDM) and complex holomorphic functions and the potential applications of the latter to deduce the former. For a prescribed mass term the associated complex function is derived. The complex function and related plane transformation are used to generate the PDM systems of three integrable Hénon–Heiles systems and a Holt system as well. We also figure out a holomorphic function, which ensures separability of the corresponding PDM systems in the polar-like coordinates. The holomorphic function together with Jacobi method have yielded a variety of generalized separable systems. At last we put forward an example of a family of separable systems to show that not all PDM systems can be deduced through some holomorphic function.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136234986","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}