THE GEOMETRIC PHASE AND THE SCHWINGER TERM IN SOME MODELS

1992 ◽  
Vol 07 (21) ◽  
pp. 5045-5083 ◽  
Author(s):  
H. GROSSE ◽  
E. LANGMANN
Keyword(s):  
Parameter Space ◽  
Geometric Phase ◽  
Closed Loop ◽  
Parallel Transport ◽  
Quantum Mechanical System ◽  
Second Quantization ◽  
Closed Loops ◽  
Gauge Transformations ◽  
Canonical Anticommutation Relations ◽  
Inequivalent Representations

We discuss the quantization of fermions interacting with external fields and observe the occurrence of equivalent as well as inequivalent representations of the canonical anticommutation relations. Implementability of gauge and axial gauge transformations leads to generators which fulfil an algebra of current with a Schwinger term. This term can be written as a cocycle and leads to the boson-fermion correspondence. Transport of a quantum-mechanical system along a closed loop of parameter space may yield a geometric phase. We discuss models for which nonintegrable phase factors are obtained from the adiabatic parallel transport. After second quantization, one obtains, in addition, a Schwinger term. Depending on the type of transformation, a subtle relationship between these two obstructions can occur. We indicate finally how we may transport density matrices along closed loops in parameter space.

scholarly journals Geometric Phase in Phasing of Antenna Arrays

2002 ◽  
Vol 199 ◽  
pp. 514-515
Author(s):  
Rajendra Bhandari
Keyword(s):  
Parameter Space ◽  
Antenna Arrays ◽  
Geometric Phase ◽  
Singular Points ◽  
Polarization States

The response of a pair of differently polarized antennas is determined by their polarization states and a phase between them which has a geometric part which becomes discontinuous at singular points in the parameter space. Some consequences are described.

scholarly journals Flowering Buds of Globular Proteins: Transpiring Simplicity of Protein Organization

2002 ◽  
Vol 3 (6) ◽  
pp. 525-534 ◽  
Author(s):  
Igor N. Berezovsky ◽  
Edward N. Trifonov
Keyword(s):  
Protein Evolution ◽  
Closed Loop ◽  
Globular Proteins ◽  
Polymer Physics ◽  
Basic Unit ◽  
Amino Acid Residues ◽  
Sequence Motifs ◽  
Closed Loops ◽  
Physical Necessity ◽  
Functional Complexity

Structural and functional complexity of proteins is dramatically reduced to a simple linear picture when the laws of polymer physics are considered. A basic unit of the protein structure is a nearly standard closed loop of 25–35 amino acid residues, and every globular protein is built of consecutively connected closed loops. The physical necessity of the closed loops had been apparently imposed on the early stages of protein evolution. Indeed, the most frequent prototype sequence motifs in prokaryotic proteins have the same sequence size, and their high match representatives are found as closed loops in crystallized proteins. Thus, the linear organization of the closed loop elements is a quintessence of protein evolution, structure and folding.

GEOMETRIC PHASES FOR MIXED STATES DURING UNITARY AND NON-UNITARY EVOLUTIONS

2003 ◽  
Vol 01 (01) ◽  
pp. 135-152 ◽  
Author(s):  
ARUN K. PATI
Keyword(s):  
Geometric Phase ◽  
Parallel Transport ◽  
Quantum Systems ◽  
Mixed States ◽  
Completely Positive Maps ◽  
Initial State ◽  
Unitary Evolution ◽  
Completely Positive ◽  
Quantum Operations ◽  
Positive Maps

Mixed states typically arise when quantum systems interact with the outside world. Evolution of open quantum systems in general are described by quantum operations which are represented by completely positive maps. We elucidate the notion of geometric phase for a quantum system described by a mixed state undergoing unitary evolution and non-unitary evolutions. We discuss parallel transport condition for mixed states both in the case of unitary maps and completely positive maps. We find that the relative phase shift of a system not only depends on the state of the system, but also depends on the initial state of the ancilla with which it might have interacted in the past. The geometric phase change during a sequence of quantum operations is shown to be non-additive in nature. This property can attribute a "memory" to a quantum channel. We explore these ideas and illustrate them with simple examples.

Constraint Wrench Formulation for Closed-Loop Systems Using Two-Level Recursions

2007 ◽  
Vol 129 (12) ◽  
pp. 1234-1242 ◽  
Author(s):  
Himanshu Chaudhary ◽  
Subir Kumar Saha
Keyword(s):  
Lagrange Multipliers ◽  
Spanning Tree ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Minimal Set ◽  
Closed Loops ◽  
Closed Loop Systems ◽  
Subsystem Level ◽  
Body Level

In order to compute the constraint moments and forces, together referred here as wrenches, in closed-loop mechanical systems, it is necessary to formulate a dynamics problem in a suitable manner so that the wrenches can be computed efficiently. A new constraint wrench formulation for closed-loop systems is presented in this paper using two-level recursions, namely, subsystem level and body level. A subsystem is referred here as the serial- or tree-type branches of a spanning tree obtained by cutting the appropriate joints of the closed loops of the system at hand. For each subsystem, unconstrained Newton–Euler equations of motion are systematically reduced to a minimal set in terms of the Lagrange multipliers representing the constraint wrenches at the cut joints and the driving torques/forces provided by the actuators. The set of unknown Lagrange multipliers and the driving torques/forces associated to all subsystems are solved in a recursive fashion using the concepts of a determinate subsystem. Next, the constraint forces and moments at the uncut joints of each subsystem are calculated recursively from one body to another. Effectiveness of the proposed algorithm is illustrated using a multiloop planar carpet scraping machine and the spatial RSSR (where R and S stand for revolute and spherical, respectively) mechanism.

Efficient Parallel Computer Simulation of the Motion Behaviors of Closed-Loop Multibody Systems

2007 ◽  
Author(s):  
Shanzhong Duan ◽  
Andrew Ries
Keyword(s):  
Parallel Computing ◽  
Multibody Systems ◽  
Closed Loop ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Parallel Computer ◽  
Constraint Forces ◽  
Computing Systems ◽  
Closed Loops

This paper presents an efficient parallelizable algorithm for the computer-aided simulation and numerical analysis of motion behaviors of multibody systems with closed-loops. The method is based on cutting certain user-defined system interbody joints so that a system of independent multibody subchains is formed. These subchains interact with one another through associated unknown constraint forces fc at the cut joints. The increased parallelism is obtainable through cutting joints and the explicit determination of associated constraint forces combined with a sequential O(n) method. Consequently, the sequential O(n) procedure is carried out within each subchain to form and solve the equations of motion while parallel strategies are performed between the subchains to form and solve constraint equations concurrently. For multibody systems with closed-loops, joint separations play both a role of creation of parallelism for computing load distribution and a role of opening a closed-loop for use of the O(n) algorithm. Joint separation strategies provide the flexibility for use of the algorithm so that it can easily accommodate the available number of processors while maintaining high efficiency. The algorithm gives the best performance for the application scenarios for n>>1 and n>>m, where n and m are number of degree of freedom and number of constraints of a multibody system with closed-loops respectively. The algorithm can be applied to both distributed-memory parallel computing systems and shared-memory parallel computing systems.

Symmetry and topology

Quantum 20/20 ◽  
2019 ◽  
pp. 225-242
Author(s):  
Ian R. Kenyon
Keyword(s):  
Hilbert Space ◽  
Conservation Laws ◽  
Geometric Phase ◽  
Electromagnetic Coupling ◽  
Charge Symmetry ◽  
Gauge Transformations ◽  
Local Charge ◽  
Classical World ◽  
Bohm Effect ◽  
Aharonov Bohm

Space-time symmetries, conservation laws and Nöther’s theorem are discussed. The Poincaré group, generators and Casimir invariants are outlined. Local charge conservation and the corresponding U(1) charge symmetry underlying electromagnetism are presented, showing the roles of minimal electromagnetic coupling and gauge transformations. Experimental demonstrations of the Aharonov–Bohm effect are described and the topological interpretation is recounted. How the Aharonov–Casher effect survives in the classical world is mentioned. Berry’s revelation of geometric phase is presented. The Bitter–Dubbers experiment confirming this analysis is presented. Some comments are given on a Hilbert space with a simple topology.

scholarly journals INTESTINAL OBSTRUCTION

1913 ◽  
Vol 17 (3) ◽  
pp. 307-324
Author(s):  
G. H. Whiffle ◽  
H. B. Stone ◽  
B. M. Bernheim
Keyword(s):  
Intestinal Mucosa ◽  
Intestinal Tract ◽  
Closed Loop ◽  
Toxic Substance ◽  
Great Part ◽  
Essential Factor ◽  
Closed Loops ◽  
Toxic Material ◽  
Closed Duodenal Loop

The blood of closed duodenal loop dogs is not toxic to normal dogs. The blood of dogs that have been fatally poisoned with duodenal loop fluid is likewise non-toxic to normal dogs. The mucosa of closed or drained duodenal loops contains a toxic substance quite similar to the toxic material found in the lumen of the closed loops. This toxic substance is absorbed from the mucosa itself and not from the lumen of the drained loops. The same is probably true of the closed loops which have an intact mucosa. It seems highly probable that the poison is formed by the mucosa and is in great part absorbed directly from it by the blood. Normal intestinal mucosa contains no toxic substance nor can it neutralize in vitro the toxic substance produced in the closed loops. There is no evidence that the toxic material when given intravenously is excreted by the intestine or held by the intestinal mucosa in any demonstrable form. The toxic substance is not absorbed from the normal intestinal tract. Destruction of the mucosa in a closed loop by means of sodium fluoride prevents the formation of the toxic substance. This fact furnishes the final proof that the mucosa is the essential factor in the elaboration of the poisonous material.

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