讨论班和报告
当前位置:首页  讨论班和报告
Vladimir Al. Osipov——Integrability in random matrix theory and its applications
发布人:王斯萌  发布时间:2022-08-26   浏览次数:147

题目:Integrability in random matrix theory and its applications


报告人:Vladimir Al. Osipov (Faculty of Sciences, Holon Institute of Technology)


时间:2022年8月31日(星期),16:00-17:30


Zoom会议:会议号:882 8540 7533,会议密码:028422

会议链接:https://zoom.us/j/88285407533pwd=NFlsWlZlb2F3c3VmMHBqOXVud1NpQT09


摘要:Random matrices are widely used to model quantum systems with chaos and disorder. In such models, the observable is expressed as a quantum operator averaged over an ensemble of random matrices with a given probability measure. In my talk, I demonstrate a general approach, “the random matrix integrable theory”, to the nonperturbative calculation of the random-matrix integrals. With this approach, the internal symmetries of the integration measure, expressed in terms of highly non-trivial nonlinear relations for the original integral (the Toda lattice hierarchy, the Kadomtsev-Petviashvili hierarchy) and the relations following from the deformation of the integration measure (Virasoro constraints), are used to represent the integral as a solution of differential equations, where the differentials are taken over the internal (physical) parameters of the model [1,2]. This method represents a particular implementation of results obtained within a more general theory of τ -functions. In particular, the central theorem of this theory states the existence of the Toda lattice and Kadomtsev-Petviashvili hierarchies for the typical random-matrix integrals.The particular implementation of the integrable theory will be discussed in the example of the physical problem of quantum transport in chaotic cavities [3,4]. A brief introduction to the physics of the problem and the advantage of the integrable theory method for calculation of the conductance cumulants, and of the shot-noise-conductance joint cumulants are going to be presented. In particular, we demonstrate how the conductance cumulant generation function can be expressed in terms of the solution of the Painleve V transcendent equation. In addition, the results of the integrable theory implementation to the averaged random-matrix characteristic polynomials [1], and also for the problem of the power spectrum of the eigenlevel sequences in the quantum chaotic system [2,5] will be discussed.

[1] V.Al.Osipov, E.Kanzieper, “Correlations of RMT characteristic polynomials and integrability: Random Hermitian matrices”, Annals of Physics
325 (2010) 2251
[2] R.Riser, V.Al.Osipov, E.Kanzieper, “Nonperturbative theory of power spectrum in complex systems”, Annals of Physics 413 (2020) 168065
[3] V.Al.Osipov, E.Kanzieper, “Integrable theory of quantum transport in chaotic cavities”, Phys.Rev.Let. 101 (2008) 176804
[4] V.Al.Osipov, E.Kanzieper, “Statistics of thermal to shot noise crossover in chaotic cavities”, J.Phys.A:Math.Theor. 42 (2009) 475101

[5] R.Riser, V.Al.Osipov, E.Kanzieper, “Power-spectrum of long eigenlevel sequences in quantum chaology”, Phys.Rev.Let. 118 (2017) 204101



Integrability in random matrix theory and its applications.pdf


更多相关信息请参见泛函分析研讨班网页