Diagnosing Thermalization Dynamics of Non-Hermitian Quantum Systems via GKSL Master Equations

The application of the eigenstate thermalization hypothesis to non-Hermitian quantum systems has become one of the most important topics in dissipative quantum chaos, recently giving rise to intense debates. The process of thermalization is intricate, involving many time-evolution trajectories in the reduced Hilbert space of the system. By considering two different expansion forms of the density matrices adopted in the biorthogonal and right-state time evolutions, we derive two versions of the Gorini–Kossakowski–Sudarshan–Lindblad(GKSL)master equations describing the non-Hermitian systems coupled to a bosonic heat bath in thermal equilibrium. By solving the equations, we identify a sufficient condition for thermalization under both time evolutions, resulting in Boltzmann biorthogonal and right-eigenstate statistics, respectively. This finding implies that the recently proposed biorthogonal random matrix theory needs an appropriate revision. Moreover, we exemplify the precise dynamics of thermalization and thermodynamic properties with test models.

Cultural Input in English Vocabulary Teaching

The close relationship between the English words and culture is analyzed in this article.Only by understanding the hidden cultural meanings in the English words,can college students truly have a good command of them and can their communicative ability be improved.

A New Ice Age? None Soon,Snow 2 Miles Deep Implies

冰川学专家认为,全球气候在漫长的地质年代中曾有数次冷暖变化,冰川作用随之重复发生。气候寒冷时,降雪量增加,发育大规模的冰川,巨大的冰盖掩盖地球,称为冰川期(ice age)。地球已经历了四次大冰川期,第五纪冰川期是否即将来临?科学家对此进行了研究。

Acknowledging the Diversity of Modernisation as Foundation of a Common Understanding of Human Rights

Human thinking is apparently caught in dichotomies:it is about the we and the other,the latter often seen as barbarians;it is about the now and then;and all this thinking is characterised by a tension:while the grass seems to be greener on the other side,we are often inclined to refer to our own time,space and organisation as superior.This implies not only the rejection of the notion of equality,but also that there is no equality so between different patterns;it also proves difficult to truly accept diversity,or in other words:to accept that something is different,at least initially,without any valuation.

The Chinese Vision for Digital Human Rights

Under the tremendous impetus of the information revolution,humanity is transitioning from an industrial society to a digital society,and digital human rights have become a prominent global issue.Guided by the strategies of“Rule of Law in China”and“Digital China,”China’s digital legal construction has made significant achievements with distinctive features.This implies that China will also play a more important role and have a greater impact in the field of digital human rights.

一口锅里盛满的幸福味道

Everyone knows that cookware,as the name implies,cooks meals,but it can also incite an appetite and utmost joy.On December16,2022,a special event was held to showcase various multi-use,high-pressure cookware(designed for highland use)in Yaou Village of Changlong Township in Gangpa County,Shigatse City.

Decompesition of Kernel and Maximal Generalized Bochner-Riesz Means

设l∈N,δ=k/p-k+1/2,以及<p<1.本文的主要结果是建立广义BochnerRiesz平均的核的某种分解: ((1-|ξ|~l)~σ+)^(x)=sum from f=1 to J(k,l,p) b_f((1-|ξ|~2)ь+ζ)^(x)+T(|x|),其中T满足 T^(n+1)(s)≤cmin{(1+s)_(k-n-2),(1+s)^(-k,p)},0<s<∞以及n=[K(1/p-1)]·作为上述分解的一个直接结果,我们得到:临界阶广义Bochner-Riesz平均在H^p(R^k)上的a.e.收敛性。

广义Young不等式及其逆(英文)

本文给出一种广义Young不等式,并且通过建立函数不等式证明了它的逆。

盘锦城市文化展示馆,盘锦,中国

项目以稳重的建筑形态塑造了一个具有仪式感的场所空间,幻化的建筑表皮再现了＂红海滩＂地域景观,内向的空间布局隐喻着＂天圆地方＂的传统内涵,将城市开放空间融入建筑主导空间,诠释了建筑对城市空间的尊重与回应。

Instability from Steady and Axisymmetric to Steady and Asymmetric Floating Half Zone Convection in a Fat Liquid Bridge of Larger Prandtl Number

The linear instability analysis of the present paper shows that the thermocapillary convection in a half floating zone of larger Prandtl number has a steady instability mode ωi = 0 and m = 1 for a fat liquid bridge V = 1.2 with small geometrical aspect ratio A = 0.6. This conclusion is different from the usual idea of hydrothermal instability, and implies that the instability of the system may excite a steady and axial asymmetric state before the onset of oscillation in the case of large Prandtl number.

On Black Hole Thermodynamics and Back-reaction

It is shown in this paper that there is a difficulty in conventional black hole thermodynamics.To overcome the difficulty we introduce a“surface”near the event horizon as an additional thermodynamical object.The mass and entropy of the additional“surface”are the same as the correction of mass of Schwarzschild black hole obtained in the back-reaction program up to a constant factor.This implies that some effects of back reaction an automatically considered in our thermodynamic phenomenological treatment.

Cyclic load testing of pre-stressed rock anchors for slope stabilization

The objective of this research was to assess the characteristics of seismic induced damage and the deformation patterns of pre-stressed cement-grouted cables that are used for rock slope stabilization projects subjected to quasi-static cyclic loading.The experimental configuration includes the installation of 15 pre-stressed cables in a slope model made of concrete blocks(theoretically rigid rock mass) on top of a pre-existing sliding surface.The study showed that:(i) The pre-stressed cables exhibited great seismic performance.Rapid displacement of the model blocks was observed after the complete loss of the initial pre-stress load under continued applied cyclic loads and exceedance of the state of equilibrium,which implies the higher the initial pre-stress load,the better the seismic performance of the rock anchor;(ii) The failure of the pre-stressed cables was due to fracture at the connection of the tendons and cable heads under cyclic loading.The sequence of failure had a distinct pattern.Failure was first observed at the upper row of cables,which experienced the most severe damage,including the ejection of cable heads.No evidence of de-bonding was observed during the cyclic loading;(iii) The stress distribution of the bond length for pre-stressed cables was highly non-uniform.High stress concentrations were observed at both the fixed end and the free end of the bond length both before and immediately after the state of equilibrium is exceeded.The results obtained can be used to evaluate the overall performance of pre-stressed rock anchors subject to seismic loading and their potential as rockfall prevention and stabilization measures.

The Linearization Principle for Fully Nonlinear Perturbation Equations

本文讨论方程u_i=a(t,εu,ε▽u,ε▽u)·▽u+f(t,x,u,▽u)带第一初边值条件的解的存在性,其中a(t,0,0,0)】0,当|ξ|【p,1λ≤λ【2时,|f(t,x,ξ,η)|≤c(p)(1+|η|~2),本文还讨论了方程u_i=a(x,u,▽u,△u)·△u+f(t,x,u,▽u)带小初值、小边值条件的解的存在性。在适当的条件下,上述两个问题都有整体古典解。

On thermoelastic diffusion thin plate theory

The effect of diffusion on thermoelastic thin plates is investigated. The governing equations for thin thermoelastic diffusion plates under three different laws of heat and diffusion transmission are derived. By the C0-semigroup theory, the well-posedness of the proposed equations is shown.

Recovering implied risk-neutral probability density function using SVR

Using support vector regression （SVR）, a novel non-parametric method for recovering implied risk-neutral probability density function （IRNPDF） is investigated by solving linear operator equations. First, the SVR principle for function approximation is introduced, and an SVR method for solving linear operator equations with knowing some values of the right-hand function and without knowing its form is depicted. Then, the principle for solving the IRNPDF based on SVR and the method for constructing cross-kernel functions are proposed. Finally, an empirical example is given to verify the validity of the method. The results show that the proposed method can overcome the shortcomings of the traditional parametric methods, which have strict restrictions on the option exercise price; meanwhile, it requires less data than other non-parametric methods, and it is a promising method for the recover of IRNPDF.

Interest rate swap pricing with default risk under variance gamma process

Under the assumption that the dynamic assets price follows the variance gamma process, we establish a new bilateral pricing model of interest rate swap by integrating the reduced form model for swap pricing and the structural model for default risk measurement.Our pricing model preserves the simplicity of the reduced form model and also considers the dynamic evolution of the counterparty assets price by incorporating with the structural model for default risk measurement. We divide the swap pricing framework into two parts, simplifying the pricing model relatively. Simulation results show that, for a one year interest rate swap, a bond spread of one hundred basis points implies a swap credit spread about 0.1054 basis point.

Brett:Women's Tragedy and Values in the 1920s

Traditionally,Brett from Hemingway’s The Sun Also Rises is criticized for her embodiment of various decaying indications.In appearance,that is the very conclusion a plain reader can draw from the text.But taking the specific historic and literal background into the inter-textual reading,a critic reader will surely discern a series of qualities in Brett to argue for her inner innocent self which was so damaged by the reality.The author implies his"iceberg"to the effect that most readers are liable to ignore or neglect.Close reading reveals the deep-rooted sympathy in the author’s inner heart.This sympathy is not only directed to Brett,but all those in tragedies in that historic era and this sympathy later functions to highlight women’s values in the author’s viewpoint.

Copyright

Submission of a manuscript implies:that the work described has not been published before(except in the form of an abstract or as part of a published lecture,review,or thesis);that it is not under consideration for publication elsewhere;that its publication has been approved by all co-authors,if any,as well as-tacitly or explicitly-by the responsible authorities at the institution where the work was carried

Copyright

Submission of a manuscript implies:that the work described has not been published before(except in the form of an abstract or as part of a published lecture,review,or thesis);that it is not under consideration for publication elsewhere;that its publication has been approved by all co-authors,if any,as well as--tacitly or explicitly--by the responsible authorities at the institution where the work was carried out.The author warrants that his/her contribution is original