scholarly journals Local tomography and the role of the complex numbers in quantum mechanics

2020 ◽  
Vol 476 (2238) ◽  
pp. 20200063
Author(s):  
Gerd Niestegge
Keyword(s):  
Quantum Mechanics ◽  
Composite System ◽  
C Algebra ◽  
Local Tomography ◽  
Finite Dimensional ◽  
Logical Definition ◽  
Multipartite System ◽  
State Tomography ◽  
Definition Of

Various reconstructions of finite-dimensional quantum mechanics result in a formally real Jordan algebra A and a last step remains to conclude that A is the self-adjoint part of a C*-algebra. Using a quantum logical setting, it is shown that this can be achieved by postulating that there is a locally tomographic model for a composite system consisting of two copies of the same system. Local tomography is a feature of classical probability theory and quantum mechanics; it means that state tomography for a multipartite system can be performed by simultaneous measurements in all subsystems. The quantum logical definition of local tomography is sufficient, but it is less restrictive than the prevalent definition in the literature and involves some subtleties concerning the so-called spin factors.

scholarly journals Dagger linear logic for categorical quantum mechanics

2021 ◽  
Vol Volume 17, Issue 4 ◽  
Author(s):  
Robin Cockett ◽  
Cole Comfort ◽  
Priyaa Srinivasan
Keyword(s):  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Quantum Physics ◽  
Linear Logic ◽  
Infinite Dimensional ◽  
Graphical Calculus ◽  
Finite Dimensional ◽  
Categorical Quantum Mechanics ◽  
Definition Of ◽  
Categorical Semantics

Categorical quantum mechanics exploits the dagger compact closed structure of finite dimensional Hilbert spaces, and uses the graphical calculus of string diagrams to facilitate reasoning about finite dimensional processes. A significant portion of quantum physics, however, involves reasoning about infinite dimensional processes, and it is well-known that the category of all Hilbert spaces is not compact closed. Thus, a limitation of using dagger compact closed categories is that one cannot directly accommodate reasoning about infinite dimensional processes. A natural categorical generalization of compact closed categories, in which infinite dimensional spaces can be modelled, is *-autonomous categories and, more generally, linearly distributive categories. This article starts the development of this direction of generalizing categorical quantum mechanics. An important first step is to establish the behaviour of the dagger in these more general settings. Thus, these notes simultaneously develop the categorical semantics of multiplicative dagger linear logic. The notes end with the definition of a mixed unitary category. It is this structure which is subsequently used to extend the key features of categorical quantum mechanics.

SUPERSYMMETRY IN QUANTUM MECHANICS

1990 ◽  
Vol 05 (08) ◽  
pp. 1383-1456 ◽  
Author(s):  
ANURADHA LAHIRI ◽  
PRODYOT KUMAR ROY ◽  
BIJAN BAGCHI
Keyword(s):  
Quantum Mechanics ◽  
Mathematical Formulation ◽  
Factorization Method ◽  
Operator Technique ◽  
Shape Invariance ◽  
Ladder Operator ◽  
The Subject ◽  
Definition Of ◽  
The Relationship

A pedagogical review on supersymmetry in quantum mechanis is presented which provides a comprehensive coverage of the subject. First, the key ingredients on the quantization of the systems with anticommuting variables are discussed. The supersymmetric Hamiltotian in quantum mechanics is then constructed by emphasizing the role of partner potentials and the superpotentials. We also make explicit the mathematical formulation of the Hamiltonian by considering in detail the N=1 and N=2 supersymmetric (quantum) mechanics. Supersymmetry is then discussed in the context of one-dimensional problems and the importance of the factorization method is highlighted. We treat in detail the technique of constructing a hierarchy of Hamiltonians employing the so-called ‘shape-invariance’ of potentials. To make transparent the relationship between supersymmetry and solvable potentials, we also solve several examples. We then go over to the formulation of supersymmetry in radial problems, paying a special attention to the Coulomb and isotropic oscillator potentials. We show that the ladder operator technique may be suitably modified in higher dimensions for generating isospectral Hamiltonians. Next, the criteria for the breaking of supersymmetry is considered and their range of applicability is examined by suitably modifying the definition of Witten’s index. Finally, we perform some numerical calculations for a class of potentials to show how a modified WKB approximation works in supersymmetric cases.

scholarly journals Quantum logic as motivated by quantum computing

2005 ◽  
Vol 70 (2) ◽  
pp. 353-359 ◽  
Author(s):  
J. Michael Dunn ◽  
Tobias J. Hagge ◽  
Lawrence S. Moss ◽  
Zhenghan Wang
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Computer Science ◽  
Quantum Logic ◽  
Theoretical Computer Science ◽  
Von Neumann ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Definition Of

§1. Introduction. Our understanding of Nature comes in layers, so should the development of logic. Classic logic is an indispensable part of our knowledge, and its interactions with computer science have recently dramatically changed our life. A new layer of logic has been developing ever since the discovery of quantum mechanics. G. D. Birkhoff and von Neumann introduced quantum logic in a seminal paper in 1936 [1]. But the definition of quantum logic varies among authors (see [2]). How to capture the logic structure inherent in quantum mechanics is very interesting and challenging. Given the close connection between classical logic and theoretical computer science as exemplified by the coincidence of computable functions through Turing machines, recursive function theory, and λ-calculus, we are interested in how to gain some insights about quantum logic from quantum computing. In this note we make some observations about quantum logic as motivated by quantum computing (see [5]) and hope more people will explore this connection.The quantum logic as envisioned by Birkhoff and von Neumann is based on the lattice of closed subspaces of a Hilbert space, usually an infinite dimensional one. The quantum logic of a fixed Hilbert space ℍ in this note is the variety of all the true equations with finitely many variables using the connectives meet, join and negation. Quantum computing is theoretically based on quantum systems with finite dimensional Hilbert spaces, especially the states space of a qubit ℂ2. (Actually the qubit is merely a convenience.

Challenges of Fear Conditioning Research in the Age of RDoC

2017 ◽  
Vol 225 (3) ◽  
pp. 189-199 ◽  
Author(s):  
Tina B. Lonsdorf ◽  
Jan Richter
Keyword(s):  
Fear Conditioning ◽  
Clinical Diagnosis ◽  
Research Domain Criteria ◽  
Major Focus ◽  
The Future ◽  
Definition Of ◽  
Methodological Considerations ◽  
Research Domain

Abstract. As the criticism of the definition of the phenotype (i.e., clinical diagnosis) represents the major focus of the Research Domain Criteria (RDoC) initiative, it is somewhat surprising that discussions have not yet focused more on specific conceptual and procedural considerations of the suggested RDoC constructs, sub-constructs, and associated paradigms. We argue that we need more precise thinking as well as a conceptual and methodological discussion of RDoC domains and constructs, their interrelationships as well as their experimental operationalization and nomenclature. The present work is intended to start such a debate using fear conditioning as an example. Thereby, we aim to provide thought-provoking impulses on the role of fear conditioning in the age of RDoC as well as conceptual and methodological considerations and suggestions to guide RDoC-based fear conditioning research in the future.

Business Model Literature Overview

2014 ◽  
pp. 79-130 ◽  
Author(s):  
Ales Novak
Keyword(s):  
Business Model ◽  
Financial Reporting ◽  
Business Models ◽  
Potential Role ◽  
Financial Instruments ◽  
Business Logic ◽  
Literature Overview ◽  
Ifrs 9 ◽  
Definition Of

The term ?business model' has recently attracted increased attention in the context of financial reporting and was formally introduced into the IFRS literature when IFRS 9 Financial Instruments was published in November 2009. However, IFRS 9 did not fully define the term ‘business model'. Furthermore, the literature on business models is quite diverse. It has been conducted in largely isolated fashion; therefore, no generally accepted definition of ?business model' has emerged. Therefore, a better understanding of the notion itself should be developed before further investigating its potential role within financial reporting. The aim of this paper is to highlight some of the perceived key themes and to identify other bases for grouping/organizing the literature based on business models. The contributions this paper makes to the literature are twofold: first, it complements previous review papers on business models; second, it contains a clear position on the distinction between the notions of the business model and strategy, which many authors identify as a key element in better explaining and communicating the notion of the business model. In this author's opinion, the term ‘strategy' is a dynamic and forward-looking notion, a sort of directional roadmap for future courses of action, whereas, ‘business model' is a more static notion, reflecting the conceptualisation of the company's underlying core business logic. The conclusion contains the author's thoughts on the role of the business model in financial reporting.

The Role of Moral Education on the Dress Code in the Higher Learning Institution

Sains Insani ◽  
2016 ◽  
Vol 1 (1) ◽  
pp. 10-14
Author(s):  
Ira Meilita Ibrahim ◽  
Taufik A. Latif ◽  
Afi Roshezry Abu Bakar ◽  
Muthualagan Thangavelu
Keyword(s):  
Moral Education ◽  
Private University ◽  
Public University ◽  
Higher Learning ◽  
Private Institutions ◽  
Dress Code ◽  
Institutions Of Higher Learning ◽  
The World ◽  
Definition Of

The advancement of European dress to the rest of the world was linked to the definition of civilization as “a stage of social development considered to be more advanced” and “polite and good-mannered”. The widespread of their fashion style in the 19th and 20th centuries influenced the way the rest of the world attire. The fashion trend and dressing style thus change the purpose of dressing through time. The dressing style in campuses especially in private institutions of higher learning is under particular scrutiny, as it is often said to be inappropriate for a learning environment. This study looked at the importance of moral education, and its role in implementing the dress code for students among university students especially between two types of university i.e. public university and private university. It looked on the dressing style of students, both male and female, and the factors that lead to their dressing pattern which is common among students. This study also advocated the students’ understanding of the content of dress codes in their learning institution and the role played by moral education in regard to dress code. The overall study highlighted students’ perception towards the implementation of the dress code and punishment in their learning institution. The methodologies used to carry out this study are questionnaires and interviews. This study will therefore ascertain the important of dress code among students at higher learning institution and the role of moral education in cultivating values in order to dress properly or decently. Key Words: moral education, dress code, higher learning institution, civilization.

Two Representations of the Moscow Art Theater Audience

2020 ◽  
Vol 17 (5) ◽  
pp. 462-476
Author(s):  
Alexander A. Ushkarev ◽  
Galina G. Gedovius ◽  
Tatyana V. Petrushina
Keyword(s):  
Online Community ◽  
Modern Art ◽  
Virtual Space ◽  
Demographic Parameters ◽  
Cultural Consumption ◽  
Cultural Activity ◽  
Behavioral Differences ◽  
Technological Revolution ◽  
Definition Of

The technological revolution of recent decades has already brought art to the broadest masses, and the unexpected intervention of the pandemic has significantly accelerated the process of migration of theatrical art to the virtual space, causing the corresponding dynamics of the audience. What is the theater audience in the era of digitalization and the spread of alternative forms of cultural consumption? How does the theater build its relationship with the audience today? In search of answers, we conducted a series of sociological surveys of the Chekhov Moscow Art Theater’s audience — both at the theater’s performances and in the online community of its fans. The purpose of this phase of the study was to answer the fundamental questions: do spectators surveyed in the theater and those surveyed online represent the same audience; what are their main differences; and what are the drivers of their spectator behavior? The article presents the main results of a comparative analysis of two images of the Moscow Art Theatre’s audience based on a number of content parameters by two types of surveys, as well as the results of a regression analysis of the theater attendance. The study resulted in definition of the qualitative and behavioral differences between the theater visitors and the viewers surveyed online, and identification of the factors of theater attendance for both of the represented audience groups. The study made it possible to clarify the role of age and other socio-demographic parameters in cultural activity, as well as the influence of preferred forms of cultural consumption (live contacts or online views) on one’s attitude to art, motivation and spectator behavior. The conclusions of the study, despite the uniqueness of the object, reflect the general patterns of the modern art audience’s dynamics.

DIGITAL ECONOMY AND GLOBALIZATION: THE IMPORTANCE OF DIGITAL ENTREPRENEURSHIP DEVELOPMENT

2020 ◽  
Vol 6 (3) ◽  
pp. 17-20
Author(s):  
Farxod Tursunov ◽  
Keyword(s):  
Business Models ◽  
Digital Economy ◽  
Management Systems ◽  
Entrepreneurship Development ◽  
New Business ◽  
Definition Of ◽  
Digital Enterprise ◽  
New Business Models ◽  
Digital Entrepreneurship

The article discusses the role of the digital economy in the development of the country, how it becomes the basis of the economy, new business models and management systems. The opinion of scientistsis analyzed, a definition of a digital enterprise is given

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