THE DIFFEOMORPHISM GROUP APPROACH TO ANYONS

1991 ◽  
Vol 05 (16n17) ◽  
pp. 2625-2640 ◽  
Author(s):  
GERALD A. GOLDIN ◽  
DAVID H. SHARP
Keyword(s):  
Quantum Mechanics ◽  
Quantum Systems ◽  
Diffeomorphism Group ◽  
Diffeomorphism Groups ◽  
Group Approach ◽  
Fundamental Properties ◽  
Local Current ◽  
Unified Description ◽  
Particle Statistics ◽  
Insight Into

We explain an approach to quantum mechanics, based on diffeomorphism groups and local current algebras, that predicts many of the fundamental properties of anyons. Our formulation also yields further insight into the meaning of particle statistics, and permits the unified description of a wide variety of quantum systems.

THE DIFFEOMORPHISM GROUP APPROACH TO NONLINEAR QUANTUM SYSTEMS

1992 ◽  
Vol 06 (11n12) ◽  
pp. 1905-1916 ◽  
Author(s):  
GERALD A. GOLDIN
Keyword(s):  
Nonlinear Effects ◽  
Quantum Systems ◽  
Incompressible Fluids ◽  
Diffeomorphism Groups ◽  
Group Approach ◽  
Quantum Vortex ◽  
Nonlinear Quantum ◽  
New Applications ◽  
Fundamental Physical ◽  
Natural Description

Unitary representations of diffeomorphism groups predict some unusual possibilities in quantum theory, including non-standard statistics and certain nonlinear effects. Many of the fundamental physical properties of “anyons” were first derived from their study by R. Menikoff, D.H. Sharp, and the author. This paper surveys new applications in two other domains: first (with Menikoff and Sharp) some surprising conclusions about the nature of quantum vortex configurations in ideal, incompressible fluids; second (with H.-D. Doebner) a natural description of dissipative quantum mechanics by means of a nonlinear Schrödinger equation different from the sort usually studied. Our equation follows from including a diffusion current in the equation of continuity.

scholarly journals Asset–liability modelling in the quantum era

2021 ◽  
Vol 26 ◽  
Author(s):  
T. Berry ◽  
J. Sharpe
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computer ◽  
Quantum Algorithm ◽  
Capital Requirements ◽  
Quantum Computers ◽  
Investment Management ◽  
Asset Liability Management ◽  
Liability Management ◽  
Insight Into ◽  
Current Practices

Abstract This paper introduces and demonstrates the use of quantum computers for asset–liability management (ALM). A summary of historical and current practices in ALM used by actuaries is given showing how the challenges have previously been met. We give an insight into what ALM may be like in the immediate future demonstrating how quantum computers can be used for ALM. A quantum algorithm for optimising ALM calculations is presented and tested using a quantum computer. We conclude that the discovery of the strange world of quantum mechanics has the potential to create investment management efficiencies. This in turn may lead to lower capital requirements for shareholders and lower premiums and higher insured retirement incomes for policyholders.

scholarly journals Wigner's Problem and Alternative Commutation Relations for Quantum Mechanics

1997 ◽  
Vol 11 (10) ◽  
pp. 1281-1296 ◽  
Author(s):  
V. I. Man'ko ◽  
G. Marmo ◽  
F. Zaccaria ◽  
E. C. G. Sudarshan
Keyword(s):  
Quantum Mechanics ◽  
Vector Field ◽  
Equations Of Motion ◽  
Quantum Systems ◽  
Heisenberg Picture ◽  
Commutation Relations

It is shown that for quantum systems the vector field associated with the equations of motion may admit alternative Hamiltonian descriptions, both in the Schrödinger and Heisenberg picture. We illustrate these ambiguities in terms of simple examples.

Would You Like Some World Music with your Latte? Starbucks, Putumayo, and Distributed Tourism

2004 ◽  
Vol 1 (2) ◽  
pp. 209-223 ◽  
Author(s):  
ANAHID KASSABIAN
Keyword(s):  
Quantum Mechanics ◽  
Public Spaces ◽  
World Music ◽  
The Other ◽  
Retail Stores ◽  
Theoretical Perspectives ◽  
The One ◽  
Coffee Shops ◽  
Insight Into

Through an examination of the labels Hear Music and Putumayo and their place in coffee shops and retail stores on the one hand, and of world music scholarship on the other, I argue that listening to world music in public spaces demands new theoretical perspectives. The kinds of tourism that take place in listening to world music inattentively suggest a kind of bi-location. Borrowing from quantum mechanics, I suggest that the term ‘entanglement’ might offer some insight into this bi-location and the ‘distributed tourism’ that I argue is taking place.

scholarly journals Residual Entropy and Critical Behavior of Two Interacting Boson Species in a Double Well

2017 ◽  
Author(s):  
Fabio Lingua ◽  
Andrea Richaud ◽  
Vittorio Penna
Keyword(s):  
Coherent States ◽  
Variational Approach ◽  
Entanglement Entropy ◽  
Quantum Systems ◽  
Residual Entropy ◽  
Zero Temperature ◽  
Temperature Scenario ◽  
Physical Insight ◽  
Insight Into ◽  
Specific Quantum

Motivated by the importance of entanglement and correlation indicators in the analysis of quantum systems, we study the equilibrium and the residual entropy in a two-species Bose Hubbard dimer when the spatial phase separation of the two species takes place. We consider both the zero and non-zero-temperature regime. We present different kinds of residual entropies (each one associated to a different way of partitioning the system), and we show that they strictly depend on the specific quantum phase characterizing the two species (supermixed, mixed or demixed) even at finite temperature. To provide a deeper physical insight into the zero-temperature scenario, we apply the fully-analytical variational approach based on su(2) coherent states and provide a considerbly good approximation of the entanglement entropy. Finally, we show that the effectiveness of residual entropy as a critical indicator at non-zero temperature is unchanged when considering a restricted combination of energy eigenstates.

scholarly journals Using quantum computing to create efficient algorithms

2021 ◽  
Vol 2056 (1) ◽  
pp. 012059
Author(s):  
I N Balaba ◽  
G S Deryabina ◽  
I A Pinchuk ◽  
I V Sergeev ◽  
S B Zabelina
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Computational Model ◽  
Exponential Growth ◽  
Quantum Algorithms ◽  
Quantum Systems ◽  
Efficient Algorithms ◽  
Historical Overview ◽  
Computing Model ◽  
Computational Strategy

Abstract The article presents a historical overview of the development of the mathematical idea of a quantum computing model - a new computational strategy based on the postulates of quantum mechanics and having advantages over the traditional computational model based on the Turing machine; clarified the features of the operation of multi-qubit quantum systems, which ensure the creation of efficient algorithms; the principles of quantum computing are outlined and a number of efficient quantum algorithms are described that allow solving the problem of exponential growth of the complexity of certain problems.

scholarly journals ASSESSING LIDAR TRAINING DATA QUANTITIES FOR CLASSIFICATION MODELS

2021 ◽  
Vol XLVI-4/W4-2021 ◽  
pp. 101-106
Author(s):  
O. Majgaonkar ◽  
K. Panchal ◽  
D. Laefer ◽  
M. Stanley ◽  
Y. Zaki
Keyword(s):  
Point Cloud ◽  
Classification Performance ◽  
Training Data ◽  
Lidar Data ◽  
Data Sets ◽  
Classification Models ◽  
Fundamental Properties ◽  
Point Cloud Classification ◽  
The Impact ◽  
Insight Into

Abstract. Classifying objects within aerial Light Detection and Ranging (LiDAR) data is an essential task to which machine learning (ML) is applied increasingly. ML has been shown to be more effective on LiDAR than imagery for classification, but most efforts have focused on imagery because of the challenges presented by LiDAR data. LiDAR datasets are of higher dimensionality, discontinuous, heterogenous, spatially incomplete, and often scarce. As such, there has been little examination into the fundamental properties of the training data required for acceptable performance of classification models tailored for LiDAR data. The quantity of training data is one such crucial property, because training on different sizes of data provides insight into a model’s performance with differing data sets. This paper assesses the impact of training data size on the accuracy of PointNet, a widely used ML approach for point cloud classification. Subsets of ModelNet ranging from 40 to 9,843 objects were validated on a test set of 400 objects. Accuracy improved logarithmically; decelerating from 45 objects onwards, it slowed significantly at a training size of 2,000 objects, corresponding to 20,000,000 points. This work contributes to the theoretical foundation for development of LiDAR-focused models by establishing a learning curve, suggesting the minimum quantity of manually labelled data necessary for satisfactory classification performance and providing a path for further analysis of the effects of modifying training data characteristics.

scholarly journals PHYSICS OF SINGULAR POINTS IN QUANTUM MECHANICS

2003 ◽  
Vol 01 (04) ◽  
pp. 543-560 ◽  
Author(s):  
IZUMI TSUTSUI ◽  
TAMÁS FÜLÖP
Keyword(s):  
Quantum Mechanics ◽  
Berry Phase ◽  
Singular Points ◽  
One Dimension ◽  
Partition Wall ◽  
Quantum Singularities ◽  
Quantum Force ◽  
Physical Phenomena ◽  
Particle Statistics ◽  
Behavior Characteristic

Defects or junctions in materials serve as a source of interactions for particles, and in idealized limits they may be treated as singular points yielding contact interactions. In quantum mechanics, these singularities accommodate an unexpectedly rich structure and thereby provide a variety of physical phenomena, especially if their properties are controlled properly. Based on our recent studies, we present a brief review on the physical aspects of such quantum singularities in one dimension. Among the intriguing phenomena that the singularities admit, we mention strong versus weak duality, supersymmetry, quantum anholonomy (Berry phase), and a copying process by anomalous caustics. We also show that a partition wall as a singularity in a potential well can give rise to a quantum force which exhibits an interesting temperature behavior characteristic to the particle statistics.

scholarly journals QUANTUM GROUP APPROACH TO A SOLUBLE VERTEX MODEL WITH GENERALIZED ICE RULE

1996 ◽  
Vol 11 (10) ◽  
pp. 1747-1761
Author(s):  
C.L. SOW ◽  
T.T. TRUONG
Keyword(s):  
Free Energy ◽  
Quantum Mechanics ◽  
Positive Integer ◽  
Quantum Group ◽  
Algebraic Structure ◽  
Square Lattice ◽  
Free Fermion ◽  
Vertex Model ◽  
Group Approach ◽  
Operator Structure

Using the representation of the quantum group SL q(2) by the Weyl operators of the canonical commutation relations in quantum mechanics, we construct and solve a new vertex model on a square lattice. Random variables on horizontal bonds are Ising variables, and those on the vertical bonds take half positive integer values. The vertex is subjected to a generalized form of the so-called “ice rule,” its property is studied in detail and its free energy calculated with the method of quantum inverse scattering. Remarkably, in analogy with the usual six-vertex model, there exists a “free-fermion” limit with a novel rich operator structure. The existing algebraic structure suggests a possible connection with a lattice neutral plasma of charges, via the fermion-boson correspondence.

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