scholarly journals Perturbation Theory Near Degenerate Exceptional Points

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1309
Author(s):  
Miloslav Znojil
Keyword(s):  
Perturbation Theory ◽  
Quantum Phase Transitions ◽  
Geometric Multiplicity ◽  
Exceptional Points ◽  
Time Symmetry ◽  
The Matrix ◽  
Approximation Analysis ◽  
The Stability ◽  
Complicated Nature ◽  
Perturbation Approximation

In an overall framework of quantum mechanics of unitary systems a rather sophisticated new version of perturbation theory is developed and described. The motivation of such an extension of the list of the currently available perturbation-approximation recipes was four-fold: (1) its need results from the quick growth of interest in quantum systems exhibiting parity-time symmetry (PT-symmetry) and its generalizations; (2) in the context of physics, the necessity of a thorough update of perturbation theory became clear immediately after the identification of a class of quantum phase transitions with the non-Hermitian spectral degeneracies at the Kato’s exceptional points (EP); (3) in the dedicated literature, the EPs are only being studied in the special scenarios characterized by the spectral geometric multiplicity L equal to one; (4) apparently, one of the decisive reasons may be seen in the complicated nature of mathematics behind the L≥2 constructions. In our present paper we show how to overcome the latter, purely technical obstacle. The temporarily forgotten class of the L>1 models is shown accessible to a feasible perturbation-approximation analysis. In particular, an emergence of a counterintuitive connection between the value of L, the structure of the matrix elements of perturbations, and the possible loss of the stability and unitarity of the processes of the unfolding of the singularities is given a detailed explanation.

scholarly journals Chiral correlators in $$ \mathcal{N} $$ = 2 superconformal quivers

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Francesco Galvagno ◽  
Michelangelo Preti
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Flat Space ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
Yang Mills ◽  
The Matrix ◽  
Superspace Formalism ◽  
Model Approach

Abstract We consider a family of $$ \mathcal{N} $$ N = 2 superconformal field theories in four dimensions, defined as ℤq orbifolds of $$ \mathcal{N} $$ N = 4 Super Yang-Mills theory. We compute the chiral/anti-chiral correlation functions at a perturbative level, using both the matrix model approach arising from supersymmetric localisation on the four-sphere and explicit field theory calculations on the flat space using the $$ \mathcal{N} $$ N = 1 superspace formalism. We implement a highly efficient algorithm to produce a large number of results for finite values of N , exploiting the symmetries of the quiver to reduce the complexity of the mixing between the operators. Finally the interplay with the field theory calculations allows to isolate special observables which deviate from $$ \mathcal{N} $$ N = 4 only at high orders in perturbation theory.

scholarly journals Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case

2010 ◽  
Vol 2010 ◽  
pp. 1-23 ◽  
Author(s):  
Josef Diblík ◽  
Denys Ya. Khusainov ◽  
Irina V. Grytsay ◽  
Zdenĕk Šmarda
Keyword(s):  
Lyapunov Functions ◽  
Critical Case ◽  
Autonomous Systems ◽  
Discrete Systems ◽  
Simple Eigenvalue ◽  
Discrete Equations ◽  
The Matrix ◽  
The Stability ◽  
Important Characterization

Many processes are mathematically simulated by systems of discrete equations with quadratic right-hand sides. Their stability is thought of as a very important characterization of the process. In this paper, the method of Lyapunov functions is used to derive classes of stable quadratic discrete autonomous systems in a critical case in the presence of a simple eigenvalueλ=1of the matrix of linear terms. In addition to the stability investigation, we also estimate stability domains.

scholarly journals Coupled THM and Matrix Stability Modeling of Hydroshearing Stimulation in a Coupled Fracture-Matrix Hot Volcanic System

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Yong Xiao ◽  
Jianchun Guo ◽  
Hehua Wang ◽  
Lize Lu ◽  
John McLennan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conduction ◽  
Dominant Role ◽  
Injection Well ◽  
Time Step ◽  
Volcanic System ◽  
Induced Stress ◽  
The Matrix ◽  
Matrix Stability ◽  
The Stability

A coupled thermal-hydraulic-mechanical (THM) model is developed to simulate the combined effect of fracture fluid flow, heat transfer from the matrix to injected fluid, and shearing dilation behaviors in a coupled fracture-matrix hot volcanic reservoir system. Fluid flows in the fracture are calculated based on the cubic law. Heat transfer within the fracture involved is thermal conduction, thermal advection, and thermal dispersion; within the reservoir matrix, thermal conduction is the only mode of heat transfer. In view of the expansion of the fracture network, deformation and thermal-induced stress model are added to the matrix node’s in situ stress environment in each time step to analyze the stability of the matrix. A series of results from the coupled THM model, induced stress, and matrix stability indicate that thermal-induced aperture plays a dominant role near the injection well to enhance the conductivity of the fracture. Away from the injection well, the conductivity of the fracture is contributed by shear dilation. The induced stress has the maximum value at the injection point; the deformation-induced stress has large value with smaller affected range; on the contrary, thermal-induced stress has small value with larger affected range. Matrix stability simulation results indicate that the stability of the matrix nodes may be destroyed; this mechanism is helpful to create complex fracture networks.

Investigation of Thermochemical Hydrogen Production via the Novel Thermo-Mechanical Stabilized Iron Oxide-Zirconia Porous Structure

2013 ◽  
Author(s):  
Ayyoub M. Mehdizadeh ◽  
Kelvin Randhir ◽  
James F. Klausner ◽  
Nicholas AuYeung ◽  
Fotouh Al-Raqom ◽  
...  
Keyword(s):  
Hydrogen Production ◽  
Porous Structure ◽  
Chemical Reactivity ◽  
Thermal Reduction ◽  
The Novel ◽  
Concentrated Solar Energy ◽  
The Matrix ◽  
Unique Method ◽  
Laboratory Scale Reactor ◽  
The Stability

In this study we have developed a unique method for synthesizing very reactive water splitting materials that will remain stable at temperatures as high as 1450 °C to efficiently produce clean hydrogen from concentrated solar energy. The hydrogen production for a laboratory scale reactor using a “Thermo-mechanical Stabilized Porous Structure” (TSPS) is experimentally investigated for oxidation and thermal reduction temperatures of 1200 and 1450 °C, respectively. The stability and reactivity of a 10 g TSPS over many consecutive oxidation and thermal reduction cycles for different particle size ranges has been investigated. The novel thermo-mechanical stabilization exploits sintering and controls the geometry of the matrix of particles inside the structure in a favorable manner so that the chemical reactivity of the structure remains intact. The experimental results demonstrate that this structure yields peak hydrogen production rates of 1–2 cm3/(min.gFe3O4) during the oxidation step at 1200 °C and the 30 minute thermal reduction step at 1450 ° C without noticeable degradation over many consecutive cycles. The hydrogen production rate is one of the highest yet reported in the open literature for thermochemical looping processes using thermal reduction. This novel process has strong potential for developing an enabling technology for efficient and commercially viable solar fuel production.

Occurrence and persistence of bacterial and viral faecal indicators in wastewater biofilms

2007 ◽  
Vol 55 (8-9) ◽  
pp. 377-385 ◽  
Author(s):  
S. Skraber ◽  
K. Helmi ◽  
R. Willame ◽  
M. Ferréol ◽  
C. Gantzer ◽  
...  
Keyword(s):  
Dynamic Equilibrium ◽  
Wastewater Treatment Plants ◽  
Plate Count ◽  
Cryptosporidium Oocysts ◽  
The Matrix ◽  
Thermotolerant Coliforms ◽  
Viral Indicators ◽  
The Stability ◽  
Faecal Indicators ◽  
Giardia Cysts

Biofilms within wastewater treatment plants can capture enteric microorganisms initially present in the water phase immobilising them either definitively or temporarily. Consequently, fates of microorganisms may totally change depending on whether they interact or not with biofilms. In this study, we assessed the stability of wastewater biofilms comparing the evolution of the concentrations of bacteria (heterotrophic plate count [HPC], thermotolerant coliforms [TC]) and viral (somatic coliphages [SC] and F-specific phages [F+]) indicators in the biofilms and in the corresponding wastewaters at 4 and 20 °C. Additionally, we assessed the monthly occurrence of these bacterial and viral indicators as well as of pathogenic protozoa (Cryptosporidium oocysts and Giardia cysts) in three native wastewater biofilms for four months. Our results show that viral indicators (SC and F+) persist longer in biofilms than in the corresponding wastewaters at 4 °C as well as at 20 °C. In contrast, persistence of bacterial indicators (TC and HPC) depends on both the temperature and the matrix. Differences between viral and bacterial persistence are discussed. Monthly analysis of native wastewater biofilms shows that bacterial and viral indicators, as well as Cryptosporidium oocysts and Giardia cysts, attach to wastewater biofilms to a concentration that remains stable in time, probably as a result of a dynamic equilibrium between attachment and detachment processes.

scholarly journals Paths of unitary access to exceptional points

2021 ◽  
Vol 2038 (1) ◽  
pp. 012026
Author(s):  
Miloslav Znojil
Keyword(s):  
Hilbert Space ◽  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Systems ◽  
Point Of View ◽  
Explicit Description ◽  
Direct Access ◽  
Exceptional Point ◽  
Exceptional Points ◽  
Innovative Idea

Abstract With an innovative idea of acceptability and usefulness of the non-Hermitian representations of Hamiltonians for the description of unitary quantum systems (dating back to the Dyson’s papers), the community of quantum physicists was offered a new and powerful tool for the building of models of quantum phase transitions. In this paper the mechanism of such transitions is discussed from the point of view of mathematics. The emergence of the direct access to the instant of transition (i.e., to the Kato’s exceptional point) is attributed to the underlying split of several roles played by the traditional single Hilbert space of states ℒ into a triplet (viz., in our notation, spaces K and ℋ besides the conventional ℒ ). Although this explains the abrupt, quantum-catastrophic nature of the change of phase (i.e., the loss of observability) caused by an infinitesimal change of parameters, the explicit description of the unitarity-preserving corridors of access to the phenomenologically relevant exceptional points remained unclear. In the paper some of the recent results in this direction are summarized and critically reviewed.

scholarly journals Interactions of the matrix attachment region of DNA with the matrix proteins from the copper preincubated liver nuclei.

1995 ◽  
Vol 42 (2) ◽  
pp. 205-210 ◽  
Author(s):  
P Widłak ◽  
J Rogoliński ◽  
J Rzeszowska-Wolny
Keyword(s):  
Rat Liver ◽  
Copper Ions ◽  
Specific Interaction ◽  
Protein Composition ◽  
Matrix Proteins ◽  
Matrix Attachment Region ◽  
The Matrix ◽  
Attachment Region ◽  
Liver Nuclei ◽  
The Stability

Preincubation of rat liver nuclei with copper ions influenced the stability and protein composition of the nuclear matrices isolated by a "high salt" method. Also the specific interaction between matrix proteins and the kappa Ig matrix attachment region of DNA was affected.

scholarly journals Non-Hermitian physics for optical manipulation uncovers inherent instability of large clusters

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Xiao Li ◽  
Yineng Liu ◽  
Zhifang Lin ◽  
Jack Ng ◽  
C. T. Chan
Keyword(s):  
Large Scale ◽  
Critical Role ◽  
Optical Forces ◽  
Exceptional Points ◽  
Complex Eigenvalues ◽  
Microscopic World ◽  
The Stability ◽  
The Many ◽  
Large Clusters ◽  
Conventional Systems

AbstractIntense light traps and binds small particles, offering unique control to the microscopic world. With incoming illumination and radiative losses, optical forces are inherently nonconservative, thus non-Hermitian. Contrary to conventional systems, the operator governing time evolution is real and asymmetric (i.e., non-Hermitian), which inevitably yield complex eigenvalues when driven beyond the exceptional points, where light pumps in energy that eventually “melts” the light-bound structures. Surprisingly, unstable complex eigenvalues are prevalent for clusters with ~10 or more particles, and in the many-particle limit, their presence is inevitable. As such, optical forces alone fail to bind a large cluster. Our conclusion does not contradict with the observation of large optically-bound cluster in a fluid, where the ambient damping can take away the excess energy and restore the stability. The non-Hermitian theory overturns the understanding of optical trapping and binding, and unveils the critical role played by non-Hermiticity and exceptional points, paving the way for large-scale manipulation.

Effect of Heat-Treatment Time on Microstructure and Mechanical Properties of Mg-5Gd-2Y-2Zn-0.5Zr Alloy

2012 ◽  
Vol 482-484 ◽  
pp. 1384-1389 ◽  
Author(s):  
Ling Gang Meng ◽  
Can Feng Fang ◽  
Peng Peng ◽  
Nai Pu Li ◽  
Qiong Zhu ◽  
...  
Keyword(s):  
Heat Treatment ◽  
Grain Boundary ◽  
Treatment Time ◽  
Time Range ◽  
Lpso Phase ◽  
High Temperature Heat Treatment ◽  
Lpso Structure ◽  
The Matrix ◽  
New Type ◽  
The Stability

Microstructure evolution of Mg-5Gd-2Y-2Zn-0.5Zr alloy during high temperature heat-treatment at 500°C in the time range 10-70h was investigated. The results show that after adding the element Y, the as-cast Mg-5Gd-2Y-2Zn-0.5Zr alloy forms the Mg12Zn(Y,Gd) phase with 18R-LPSO structure at the grain boundary. During heat-treatment at 500°C, the stability of 18R-LPSO structure is weakened by Gd atoms, parts of LPSO phases dissolve gradually into the matrix with time prolonged and a new type Mg(Y,Gd)Zn phase come into being. LPSO phase in the grain boundary can ensure the ultimate tensile strength and elongation of the alloy, and effect of dissevering on the LPSO phase by Mg(Gd,Y)Zn phase results the decrease of UTS and elongation.

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