scholarly journals Non-Hermitian Bulk-Boundary Correspondence and Singular Behaviors of Generalized Brillouin Zone

2021 ◽  
Author(s):  
Gang-Feng Guo ◽  
Xi-Xi Bao ◽  
Lei Tan
Keyword(s):  
Brillouin Zone ◽  
Closed Loop ◽  
Boundary Energy ◽  
Topological Invariant ◽  
Open Boundary ◽  
Band Theory ◽  
Boundary Correspondence ◽  
Bloch Band ◽  
Definition Of ◽  
The Continuum

Abstract The bulk boundary correspondence, which connects the topological invariant, the continuum band and energies under different boundary conditions, is the core concept in the non-Bloch band theory, in which the generalized Brillouin zone (GBZ), appearing as a closed loop generally, is a fundamental tool to rebuild it. In this work, it can be shown that the recovery of the open boundary energy spectrum by the continuum band remains unchanged even if the GBZ itself shrinks into a point. Contrastively, if the bizarreness of the GBZ occurs, the winding number will become illness. Namely, we find that the bulk boundary correspondence can still be established whereas the GBZ has singularities from the perspective of the energy, but not from the topological invariant. Meanwhile, regardless of the fact that the GBZ comes out with the closed loop, the bulk boundary correspondence can not be well characterized yet because of the ill-definition of the topological number. Here, the results obtained may be useful for improving the existing non-Bloch band theory.

scholarly journals Generalized Bloch band theory for non-Hermitian bulk–boundary correspondence

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Ken-Ichiro Imura ◽  
Yositake Takane
Keyword(s):  
Boundary Condition ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Open Boundary ◽  
Fundamental Relation ◽  
Band Theory ◽  
Boundary Correspondence ◽  
Boundary Properties ◽  
Bloch Band ◽  
Topological Number

Abstract Bulk–boundary correspondence is the cornerstone of topological physics. In some non-Hermitian topological systems this fundamental relation is broken in the sense that the topological number calculated for the Bloch energy band under the periodic boundary condition fails to reproduce the boundary properties under the open boundary. To restore the bulk–boundary correspondence in such non-Hermitian systems a framework beyond the Bloch band theory is needed. We develop a non-Hermitian Bloch band theory based on a modified periodic boundary condition that allows a proper description of the bulk of a non-Hermitian topological insulator in a manner consistent with its boundary properties. Taking a non-Hermitian version of the Su–Schrieffer–Heeger model as an example, we demonstrate our scenario, in which the concept of bulk–boundary correspondence is naturally generalized to non-Hermitian topological systems.

scholarly journals Non-Bloch band theory and bulk–edge correspondence in non-Hermitian systems

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Kazuki Yokomizo ◽  
Shuichi Murakami
Keyword(s):  
Brillouin Zone ◽  
Tight Binding ◽  
Topological Invariant ◽  
Edge States ◽  
Energy Bands ◽  
Open Chain ◽  
Band Theory ◽  
Continuum Energy ◽  
Bloch Band ◽  
Simple Models

Abstract In this paper, we review our non-Bloch band theory in 1D non-Hermitian tight-binding systems. In our theory, it is shown that in non-Hermitian systems, the Brillouin zone is determined so as to reproduce continuum energy bands in a large open chain. By using simple models, we explain the concept of the non-Bloch band theory and the method to calculate the Brillouin zone. In particular, for the non-Hermitian Su–Schrieffer–Heeger model, the bulk–edge correspondence can be established between the topological invariant defined from our theory and existence of the topological edge states.

ГЕРМЕНЕВТИКА ЛИЧНОСТИ КАК МЕТОД СОВРЕМЕННОЙ ПЕРСОНОЛОГИИ

1970 ◽  
Vol 6 (1) ◽  
pp. 32-42
Author(s):  
Елена Старовойтенко
Keyword(s):  
Text Setting ◽  
Research Setting ◽  
Textual Representations ◽  
General Scientific ◽  
Definition Of ◽  
The Individual ◽  
The Continuum

Персонологическая интерпретация текстов предполагает реализацию общенаучных, а также специфических для персонологии, герменевтических установок, к которым относятся: установка на интерпретацию текста как исследование, установка на разнообразие герменевтических действий с текстом, установка на выявление неисследованных содержаний текста, установка на творческое постижение тайн текста, установка на целостное отношение к личности и "Я" автора текста, установка на выявление способности автора быть "практикующим феноменологом", установка на определение места изучаемого текста в континууме текстовых репрезентаций "личности", установка на соотнесение своего понимания текста с другими интерпретациями и их интеграцию, установка на раскрытие сущности авторской "идеи личности", возможное только в единстве интерпретаций, установка на построение и применение герменевтической модели, определяющей процедуру интерпретации как исследования и творчества, установка на определение места проделанного герменевтического поиска в культуре познания и жизни личности, установка на интерпретацию различных видов "текстов личности". Personological interpretation of texts suggests the implementation of the general scientific and also hermeneutical settings specific for Personology which include the setting of the interpretation of the text as a research, setting of a variety of hermeneutical actions with the text, setting to identify unexplored contents of the text, setting of the creative comprehension of the mysteries of the text, setting of the integrity of the attitude of the individual and the "I" of the author of the text, setting to reveal the author's ability to be "practicing phenomenologist", setting of the definition of the place in the text in the continuum of textual representations of the "personality", setting in the correlation of the understanding of the text with other interpretations and their integration, setting of the disclosure of the author's "ideas person" is possible only in the unity of interpretation, setting of the construction and usage of hermeneutical models defining the procedure for the interpretation of both studies and work, the setting to determine the place of hermeneutical research in culture and knowledge of a person's life, setting of the interpretation of various types of "texts of the individual."

scholarly journals Non-Bloch band theory in bosonic Bogoliubov–de Gennes systems

2021 ◽  
Vol 103 (16) ◽  
Author(s):  
Kazuki Yokomizo ◽  
Shuichi Murakami
Keyword(s):  
Band Theory ◽  
Bloch Band

Impedance Reduction Controller Design for Mechanical Systems

2013 ◽  
Author(s):  
Hanseung Woo ◽  
Kyoungchul Kong
Keyword(s):  
Case Studies ◽  
Closed Loop ◽  
Controller Design ◽  
Mechanical Impedance ◽  
Open Loop ◽  
Mechatronic Systems ◽  
Closed Loop Systems ◽  
Guaranteed Stability ◽  
Reaction Forces ◽  
Definition Of

Safety is one of important factors in control of mechatronic systems interacting with humans. In order to evaluate the safety of such systems, mechanical impedance is often utilized as it indicates the magnitude of reaction forces when the systems are subjected to motions. Namely, the mechatronic systems should have low mechanical impedance for improved safety. In this paper, a methodology to design controllers for reduction of mechanical impedance is proposed. For the proposed controller design, the mathematical definition of the mechanical impedance for open-loop and closed-loop systems is introduced. Then the controllers are designed for stable and unstable systems such that they effectively lower the magnitude of mechanical impedance with guaranteed stability. The proposed method is verified through case studies including simulations.

The theory of conditional invariance. I

1968 ◽  
Vol 305 (1482) ◽  
pp. 405-427 ◽  
Keyword(s):  
Bound States ◽  
General Relation ◽  
Variable Parameter ◽  
Geometric Invariance ◽  
Hermitian Conjugate ◽  
New Type ◽  
Definition Of ◽  
Conditional Invariance ◽  
Conditional Constant ◽  
The Continuum

In order to extend the use of group theoretical arguments to the problem of accidental degeneracy in quantum mechanics, a new type of constant of the motion, known as a conditional constant of the motion, is introduced. Such a quantity, instead of commuting with the Hamiltonian H for the system, satisfies the more general relation H A = A † H , where A † denotes the hermitian conjugate (adjoint) of the conditional constant of the motion A . This expression reduces, if A is hermitian, to the usual definition of a constant of the motion. Otherwise it defines a new type of invariance, and it is this which will be referred to as conditional invariance. A discussion of the difficulties arising from the lack of hermiticity of A , which is of course essential to its definition, is given. In particular it is shown, under fairly general conditions, that the process of introducing a variable parameter in the Hamiltonian enabling it to have simultaneous eigenfunctions with A , gives rise to an eigenvalue equation in this parameter with respect to which A may be chosen to be hermitian. Conditional invariance is contrasted with both dynamical and geometric invariance. It is found to be sometimes replaceable by either of the latter forms of invariance and for such, explicit conditions are given. Some applications of conditional invariance are discussed. These include a study of the crossing of potential energy curves, a new model of symmetry breaking, a possible means of calculating the exact number of bound states for certain potentials and conditions for the existence of bound states near to the continuum.

scholarly journals Optimizing the Definition of a Sudden Stratospheric Warming

2018 ◽  
Vol 31 (6) ◽  
pp. 2337-2344 ◽  
Author(s):  
Amy H. Butler ◽  
Edwin P. Gerber
Keyword(s):  
Stratospheric Warming ◽  
Sudden Stratospheric Warming ◽  
Systematic Analysis ◽  
Wave Forcing ◽  
Zonal Winds ◽  
Stratospheric Temperature ◽  
Stratospheric Wind ◽  
Definition Of ◽  
Access To Data ◽  
The Continuum

Various criteria exist for determining the occurrence of a major sudden stratospheric warming (SSW), but the most common is based on the reversal of the climatological westerly zonal-mean zonal winds at 60° latitude and 10 hPa in the winter stratosphere. This definition was established at a time when observations of the stratosphere were sparse. Given greater access to data in the satellite era, a systematic analysis of the optimal parameters of latitude, altitude, and threshold for the wind reversal is now possible. Here, the frequency of SSWs, the strength of the wave forcing associated with the events, changes in stratospheric temperature and zonal winds, and surface impacts are examined as a function of the stratospheric wind reversal parameters. The results provide a methodical assessment of how to best define a standard metric for major SSWs. While the continuum nature of stratospheric variability makes it difficult to identify a decisively optimal threshold, there is a relatively narrow envelope of thresholds that work well—and the original focus at 60° latitude and 10 hPa lies within this window.

Defining Man as Animal Religiosum in English Religious Writing ca. 1650–ca. 1700

2019 ◽  
Vol 88 (4) ◽  
pp. 925-952 ◽  
Author(s):  
R. J. W. Mills
Keyword(s):  
Eighteenth Century ◽  
Early Modern ◽  
Human Nature ◽  
Relationship With God ◽  
Rational Animal ◽  
Cambridge Platonism ◽  
Definition Of ◽  
The Relationship ◽  
Subsequent Incorporation ◽  
The Continuum

This article surveys the emergence and usage of the redefinition of man not as animal rationale (rational animal) but as animal religiosum (religious animal) by numerous English theologians between 1650 and 1700. Across the continuum of English Protestant thought, human nature was being redescribed as unique due to its religious, not primarily its rational, capabilities. This article charts said appearance as a contribution to debates over man's relationship with God; then its subsequent incorporation into the discussion over the theological consequences of arguments in favor of animal rationality, as well as its uses in anti-atheist apologetics; and then the sudden disappearance of the definition of man as animal religiosum at the beginning of the eighteenth century. In doing so, the article hopes to make a useful contribution to our understanding of changing early modern understandings of human nature by reasserting the significance of theological writing in the dispute over the relationship between humans and beasts. As a consequence, it offers a more wide-ranging account of man as animal religiosum than the current focus on “Cambridge Platonism” and “Latitudinarianism” allows.

scholarly journals Thermal Simulations, Open Boundary Conditions and Switches

2018 ◽  
Vol 175 ◽  
pp. 07004 ◽  
Author(s):  
Yannis Burnier ◽  
Adrien Florio ◽  
Olaf Kaczmarek ◽  
Lukas Mazur
Keyword(s):  
Boundary Conditions ◽  
Topological Charge ◽  
Finite Size ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Finite Size Effects ◽  
Compact Spaces ◽  
Integral Current ◽  
Thermal Simulations ◽  
The Continuum

SU(N) gauge theories on compact spaces have a non-trivial vacuum structure characterized by a countable set of topological sectors and their topological charge. In lattice simulations, every topological sector needs to be explored a number of times which reflects its weight in the path integral. Current lattice simulations are impeded by the so-called freezing of the topological charge problem. As the continuum is approached, energy barriers between topological sectors become well defined and the simulations get trapped in a given sector. A possible way out was introduced by Lüscher and Schaefer using open boundary condition in the time extent. However, this solution cannot be used for thermal simulations, where the time direction is required to be periodic. In this proceedings, we present results obtained using open boundary conditions in space, at non-zero temperature. With these conditions, the topological charge is not quantized and the topological barriers are lifted. A downside of this method are the strong finite-size effects introduced by the boundary conditions. We also present some exploratory results which show how these conditions could be used on an algorithmic level to reshuffle the system and generate periodic configurations with non-zero topological charge.

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