Reviews in Mathematical Physics最新文献

{"title":"Classical limits of Hilbert bimodules as symplectic dual pairs","authors":"Benjamin H. Feintzeig, Jer Steeger","doi":"10.1142/s0129055x24500260","DOIUrl":"https://doi.org/10.1142/s0129055x24500260","url":null,"abstract":"<p>Hilbert bimodules are morphisms between C*-algebraic models of quantum systems, while symplectic dual pairs are morphisms between Poisson geometric models of classical systems. Both of these morphisms preserve representation-theoretic structures of the relevant types of models. Previously, it has been shown that one can functorially associate certain symplectic dual pairs to Hilbert bimodules through strict deformation quantization. We show that, in the inverse direction, strict deformation quantization also allows one to functorially take the classical limit of a Hilbert bimodule to reconstruct a symplectic dual pair.</p>","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"25 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Scattering theory for some non-self-adjoint operators","authors":"Nicolas Frantz","doi":"10.1142/s0129055x24500235","DOIUrl":"https://doi.org/10.1142/s0129055x24500235","url":null,"abstract":"&lt;p&gt;We consider a non-self-adjoint &lt;span&gt;&lt;math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; acting on a complex Hilbert space. We suppose that &lt;span&gt;&lt;math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; is of the form &lt;span&gt;&lt;math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo stretchy=\"false\"&gt;+&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; is a bounded, positive definite and relatively compact with respect to &lt;span&gt;&lt;math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; is bounded. We suppose that &lt;span&gt;&lt;math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo stretchy=\"false\"&gt;−&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; is uniformly bounded in &lt;span&gt;&lt;math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;ℂ&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;∖&lt;/mo&gt;&lt;mi&gt;ℝ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;. We define the regularized wave operators associated to &lt;span&gt;&lt;math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; and &lt;span&gt;&lt;math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt; by &lt;span&gt;&lt;math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;±&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mstyle&gt;&lt;mtext mathvariant=\"normal\"&gt;s-lim&lt;/mtext&gt;&lt;/mstyle&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;±&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;∓&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi mathvariant=\"normal\"&gt;Π&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mstyle&gt;&lt;mtext mathvariant=\"normal\"&gt;p&lt;/mtext&gt;&lt;/mstyle&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;⋆&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo stretchy=\"false\"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;⊥&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo stretchy=\"false\"&gt;∓&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"67 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Renormalization on the DFR quantum spacetime","authors":"Juan F. López, Andrés F. Reyes-Lega","doi":"10.1142/s0129055x24600055","DOIUrl":"https://doi.org/10.1142/s0129055x24600055","url":null,"abstract":"<p>An approach to renormalization of scalar fields on the Doplicher–Fredenhagen–Roberts (DFR) quantum spacetime is presented. The effective nonlocal theory obtained through the use of states of optimal localization for the quantum spacetime is reformulated in the language of (perturbative) Algebraic Quantum Field Theory. The structure of the singularities associated to the nonlocal kernel that codifies the effects of non-commutativity is analyzed using the tools of microlocal analysis.</p>","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"113 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Perturbation theory and canonical coordinates in celestial mechanics","authors":"Gabriella Pinzari","doi":"10.1142/s0129055x24300061","DOIUrl":"https://doi.org/10.1142/s0129055x24300061","url":null,"abstract":"<p>KAM theory owes most of its success to its initial motivation: the application to problems of celestial mechanics. The masterly application was offered by Arnold in the 60s who worked out a theorem, that he named the “Fundamental Theorem” (FT), especially designed for the planetary problem. However, FT could be really used at that purpose only when, about 50 years later, a set of coordinates constructively taking the invariance by rotation and close-to-integrability into account was used. Since then, some progress has been done in the symplectic assessment of the problem, and here we review such results.</p>","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"77 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140611559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Feynman checkers: External electromagnetic field and asymptotic properties","authors":"Fedor Ozhegov","doi":"10.1142/s0129055x2450017x","DOIUrl":"https://doi.org/10.1142/s0129055x2450017x","url":null,"abstract":"<p>In this paper, we study Feynman checkers, one of the most elementary models of electron motion. It is also known as a one-dimensional quantum walk or an Ising model at an imaginary temperature. We add the simplest non-trivial electromagnetic field and find the limits of the resulting model for small lattice step and large time, analogous to the results by Narlikar from 1972 and Grimmet–Jason–Scudo from the 2000s. It turns out that the limits in the model with the added field are obtained from the ones without field by mass renormalization. Also, we find an exact solution of the resulting model.</p>","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"300 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some contributions to k-contact Lagrangian field equations, symmetries and dissipation laws","authors":"Xavier Rivas, Modesto Salgado, Silvia Souto","doi":"10.1142/s0129055x24500193","DOIUrl":"https://doi.org/10.1142/s0129055x24500193","url":null,"abstract":"<p>It is well known that <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>k</mi></math></span><span></span>-contact geometry is a suitable framework to deal with non-conservative field theories. In this paper, we study some relations between solutions of the <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>k</mi></math></span><span></span>-contact Euler–Lagrange equations, symmetries, dissipation laws and Newtonoid vector fields. We review the <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>k</mi></math></span><span></span>-contact Euler–Lagrange equations written in terms of <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>k</mi></math></span><span></span>-vector fields and sections and provide new results relating the solutions in both approaches. We also study different kinds of symmetries depending on the structures they preserve: natural (preserving the Lagrangian function), dynamical (preserving the solutions), and <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>k</mi></math></span><span></span>-contact (preserving the underlying geometric structures) symmetries. For some of these symmetries, we provide Noether-like theorems relating symmetries and dissipation laws. We also analyze the relation between <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>k</mi></math></span><span></span>-contact symmetries and Newtonoid vector fields. Throughout the paper, we will use the damped vibrating string as our main illustrative example.</p>","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"80 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Complex translation methods and its application to resonances for quantum walks","authors":"Kenta Higuchi, Hisashi Morioka","doi":"10.1142/s0129055x24500181","DOIUrl":"https://doi.org/10.1142/s0129055x24500181","url":null,"abstract":"<p>In this paper, some properties of resonances for multi-dimensional quantum walks are studied. Resonances for quantum walks are defined as eigenvalues of complex translated time evolution operators in the pseudo momentum space. For some typical cases, we show some results of existence or nonexistence of resonances. One is a perturbation of an elastic scattering of a quantum walk which is an analogue of classical mechanics. Another one is a shape resonance model which is a perturbation of a quantum walk with a non-penetrable barrier.</p>","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"21 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Homotopical foundations of parametrized quantum spin systems","authors":"Agnès Beaudry, Michael Hermele, Juan Moreno, Markus J. Pflaum, Marvin Qi, Daniel D. Spiegel","doi":"10.1142/s0129055x24600031","DOIUrl":"https://doi.org/10.1142/s0129055x24600031","url":null,"abstract":"<p>In this paper, we present a homotopical framework for studying invertible gapped phases of matter from the point of view of infinite spin lattice systems, using the framework of algebraic quantum mechanics. We define the notion of <i>quantum state types</i>. These are certain lax-monoidal functors from the category of finite-dimensional Hilbert spaces to the category of topological spaces. The universal example takes a finite-dimensional Hilbert space <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"cal\">ℋ</mi></math></span><span></span> to the pure state space of the quasi-local algebra of the quantum spin system with Hilbert space <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"cal\">ℋ</mi></math></span><span></span> at each site of a specified lattice. The lax-monoidal structure encodes the tensor product of states, which corresponds to stacking for quantum systems. We then explain how to formally extract parametrized phases of matter from quantum state types, and how they naturally give rise to <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi mathvariant=\"script\">ℰ</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span><span></span>-spaces for an operad we call the “multiplicative” linear isometry operad. We define the notion of invertible quantum state types and explain how the passage to phases for these is related to group completion. We also explain how invertible quantum state types give rise to loop-spectra. Our motivation is to provide a framework for constructing Kitaev’s loop-spectrum of bosonic invertible gapped phases of matter. Finally, as a first step toward understanding the homotopy types of the loop-spectra associated to invertible quantum state types, we prove that the pure state space of any UHF algebra is simply connected.</p>","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"55 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140165643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lattice Green functions for pedestrians: Exponential decay","authors":"Wojciech Dybalski, Alexander Stottmeister, Yoh Tanimoto","doi":"10.1142/s0129055x2430005x","DOIUrl":"https://doi.org/10.1142/s0129055x2430005x","url":null,"abstract":"<p>The exponential decay of lattice Green functions is one of the main technical ingredients of the Bałaban’s approach to renormalization. We give here a self-contained proof, whose various ingredients were scattered in the literature. The main sources of exponential decay are the Combes–Thomas method and the analyticity of the Fourier transforms. They are combined using a renormalization group equation and the method of images.</p>","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"156 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140165917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A result about the classification of quantum covariance matrices based on their eigenspectra","authors":"Arik Avagyan","doi":"10.1142/s0129055x2460002x","DOIUrl":"https://doi.org/10.1142/s0129055x2460002x","url":null,"abstract":"<p>The set of covariance matrices of a continuous-variable quantum system with a finite number of degrees of freedom is a strict subset of the set of real positive-definite matrices (PDMs) due to Heisenberg’s uncertainty principle. This has the implication that, in general, not every orthogonal transform of a quantum covariance matrix (CM) produces a PDM that obeys the uncertainty principle. A natural question thus arises, to find the set of quantum covariance matrices consistent with a given eigenspectrum. For the special class of pure Gaussian states the set of quantum covariance matrices with a given eigenspectrum consists of a single orbit of the action of the orthogonal symplectic group. The eigenspectrum of a CM of a state in this class is composed of pairs that each multiply to one. Our main contribution is finding a non-trivial class of eigenspectra with the property that the set of quantum covariance matrices corresponding to any eigenspectrum in this class are related by orthogonal symplectic transformations. We show that all non-degenerate eigenspectra with this property must belong to this class, and that the set of such eigenspectra coincides with the class of non-degenerate eigenspectra that identify the physically relevant thermal and squeezing parameters of a Gaussian state.</p>","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"24 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140165647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}