VOLKOV'S ALGEBRA AND CASIMIR ELEMENT OF SL2

1995 ◽  
Vol 10 (10) ◽  
pp. 831-835
Author(s):  
SERGEI V. KRYUKOV
Keyword(s):  
Classical Level ◽  
Casimir Element

We construct 3-D module of sl 2 and then obtain the generator of classical Volkov's algebra as Casimir element of sl 2. Only classical level is discussed.

scholarly journals MEASUREMENT-BASED QUANTUM COMPUTATION WITH CLUSTER STATES

2009 ◽  
Vol 07 (06) ◽  
pp. 1053-1203 ◽  
Author(s):  
ROBERT RAUßENDORF
Keyword(s):  
Computational Model ◽  
Quantum Computation ◽  
Quantum Logic ◽  
Network Model ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Cluster State ◽  
Building Blocks ◽  
Network Simulator ◽  
Classical Level

In this thesis, we describe the one-way quantum computer [Formula: see text], a scheme of universal quantum computation that consists entirely of one-qubit measurements on a highly entangled multiparticle state, i.e. the cluster state. We prove the universality of the [Formula: see text], describe the underlying computational model and demonstrate that the [Formula: see text] can be operated fault-tolerantly. In Sec. 2, we show that the [Formula: see text] can be regarded as a simulator of quantum logic networks. In this way, we prove the universality and establish the link to the network model — the common model of quantum computation. We also indicate that the description of the [Formula: see text] as a network simulator is not adequate in every respect. In Sec. 3, we derive the computational model underlying the [Formula: see text], which is very different from the quantum logic network model. The [Formula: see text] has no quantum input, no quantum output and no quantum register, and the unitary gates from some universal set are not the elementary building blocks of [Formula: see text] quantum algorithms. Further, all information that is processed with the [Formula: see text] is the outcomes of one-qubit measurements and thus processing of information exists only at the classical level. The [Formula: see text] is nevertheless quantum-mechanical, as it uses a highly entangled cluster state as the central physical resource. In Sec. 4, we show that there exist nonzero error thresholds for fault-tolerant quantum computation with the [Formula: see text]. Further, we outline the concept of checksums in the context of the [Formula: see text], which may become an element in future practical and adequate methods for fault-tolerant [Formula: see text] computation.

EVALUATION OF TASK ALLOCATION IN MESH-BASED MULTICOMPUTERS USING GENETIC, NEURAL, AND TRADITIONAL ALGORITHMS

1994 ◽  
Vol 03 (01) ◽  
pp. 47-60
Author(s):  
R.A. McCONNELL ◽  
B.L. MENEZES
Keyword(s):  
Task Allocation ◽  
Bin Packing ◽  
Packing Problem ◽  
Allocation Problem ◽  
Hopfield Network ◽  
Processor Allocation ◽  
Classical Level ◽  
Bin Packing Problem ◽  
Residual Space ◽  
Computer Tasks

This article compares three techniques for allocating tasks in a mesh-based multi-computer. Tasks are expressed as rectangles of a certain width and height corresponding to the topology of processors desired. The task allocation problem, is thus a variant of the bin-packing problem, with one major difference: in the bin-packing problem one seeks to minimize the height of the bin, while here we seek to maximize the utilization of processors in a multicomputer. The three techniques compared are a classical level-by-level algorithm, a connectionist simulated annealing variant of the Hopfield network, and a genetic algorithm. An extension to the dynamic processor allocation problem is modeled by fixing some rectangles in place and packing the request rectangles in the residual space on the mesh; this corresponds to a pre-existing condition, i.e., some tasks have already been allocated to the Processor Mesh. Implementation and experimental results are presented.

scholarly journals ENERGY EXTRACTION FROM GRAVITATIONAL COLLAPSE TO STATIC BLACK HOLES

2003 ◽  
Vol 12 (01) ◽  
pp. 121-127 ◽  
Author(s):  
REMO RUFFINI ◽  
LUCA VITAGLIANO
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Extraction Process ◽  
Maximum Efficiency ◽  
Energy Extraction ◽  
Mass Energy ◽  
Classical Level ◽  
Static Black Hole ◽  
Exact Analytic Expression ◽  
Analytic Expression

The mass-energy formula of black holes implies that up to 50% of the energy can be extracted from a static black hole. Such a result is reexamined using the recently established analytic formulas for the collapse of a shell and the expression for the irreducible mass of a static black hole. It is shown that the efficiency of energy extraction process during the formation of the black hole is linked in an essential way to the gravitational binding energy, the formation of the horizon and the reduction of the kinetic energy of implosion. Here a maximum efficiency of 50% in the extraction of the mass energy is shown to be generally attainable in the collapse of a spherically symmetric shell: surprisingly this result holds as well in the two limiting cases of the Schwarzschild and extreme Reissner–Nordström space–times. Moreover, the analytic expression recently found for the implosion of a spherical shell to an already formed black hole leads to a new exact analytic expression for the energy extraction which results in an efficiency strictly less than 100% for any physical implementable process. There appears to be no incompatibility between General Relativity and Thermodynamics at this classical level.

scholarly journals MEDIATION OF SUPERSYMMETRY BREAKING IN EXTRA DIMENSIONS

2005 ◽  
Vol 20 (05) ◽  
pp. 297-312 ◽  
Author(s):  
CLAUDIO A. SCRUCCA
Keyword(s):  
Supersymmetry Breaking ◽  
Effective Field Theory ◽  
Extra Dimensions ◽  
Model Building ◽  
Realistic Model ◽  
Effective Field ◽  
Theory Approach ◽  
Classical Level ◽  
Gravitational Effects ◽  
Gravitational Fields

We review the mechanisms of supersymmetry breaking mediation that occur in sequestered models, where the visible and the hidden sectors are separated by an extra dimension and communicate only via gravitational interactions. By locality, soft breaking terms are forbidden at the classical level and reliably computable within an effective field theory approach at the quantum level. We present a self-contained discussion of these radiative gravitational effects and the resulting pattern of soft masses, and give an overview of realistic model building based on this setup. We consider both flat and warped extra dimensions, as well as the possibility that there be localized kinetic terms for the gravitational fields.

scholarly journals QUANTUM INTEGRABILITY OF COUPLED N=1 SUPER SINE/SINH–GORDON THEORIES AND THE LIE SUPERALGEBRA D(2,1;α)

1999 ◽  
Vol 14 (16) ◽  
pp. 2551-2580 ◽  
Author(s):  
JONATHAN M. EVANS ◽  
JENS OLE MADSEN
Keyword(s):  
Quantum Theory ◽  
Lie Superalgebra ◽  
Field Theories ◽  
Continuous Family ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Classical Level ◽  
Quantum Integrability ◽  
Integrable Quantum ◽  
Conserved Currents

We discuss certain integrable quantum field theories in 1+1 dimensions consisting of coupled sine/sinh–Gordon theories with N=1 supersymmetry, positive kinetic energy, and bosonic potentials which are bounded from below. We show that theories of this type can be constructed as Toda models based on the exceptional affine Lie superalgebra D(2,1;α)(1) (or on related algebras which can be obtained as various limits) provided one adopts appropriate reality conditions for the fields. In particular, there is a continuous family of such models in which the couplings and mass ratios all depend on the parameter α. The structure of these models is analyzed in some detail at the classical level, including the construction of conserved currents with spins up to 4. We then show that these currents generalize to the quantum theory, thus demonstrating quantum-integrability of the models.

scholarly journals LAGRANGIAN FORMULATION OF A MAGNETOSTATIC FIELD IN THE PRESENCE OF A MINIMAL LENGTH SCALE BASED ON THE KEMPF ALGEBRA

2013 ◽  
Vol 28 (30) ◽  
pp. 1350142 ◽  
Author(s):  
S. K. MOAYEDI ◽  
M. R. SETARE ◽  
B. KHOSROPOUR
Keyword(s):  
Integral Form ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Lagrangian Formulation ◽  
Length Scale ◽  
Magnetostatic Field ◽  
Classical Level ◽  
Spatial Dimensions ◽  
Minimal Length Scale ◽  
The Relationship

In the 1990s, Kempf and his collaborators Mangano and Mann introduced a D-dimensional (β, β′)-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length [Formula: see text]. In this work, the Lagrangian formulation of a magnetostatic field in three spatial dimensions (D = 3) described by Kempf algebra is presented in the special case of β′ = 2β up to the first-order over β. We show that at the classical level there is a similarity between magnetostatics in the presence of a minimal length scale (modified magnetostatics) and the magnetostatic sector of the Abelian Lee–Wick model in three spatial dimensions. The integral form of Ampere's law and the energy density of a magnetostatic field in the modified magnetostatics are obtained. Also, the Biot–Savart law in the modified magnetostatics is found. By studying the effect of minimal length corrections to the gyromagnetic moment of the muon, we conclude that the upper bound on the isotropic minimal length scale in three spatial dimensions is 4.42×10-19m. The relationship between magnetostatics with a minimal length and the Gaete–Spallucci nonlocal magnetostatics [J. Phys. A: Math. Theor. 45, 065401 (2012)] is investigated.

scholarly journals Electronic Foreign-Exchange Markets and Passage Events of Independent Subordinators

2005 ◽  
Vol 42 (1) ◽  
pp. 138-152 ◽  
Author(s):  
Matthias Winkel
Keyword(s):  
Stochastic Process ◽  
Foreign Exchange ◽  
Foreign Exchange Markets ◽  
Classical Level ◽  
Jump Size ◽  
Its Analysis ◽  
Exchange Markets ◽  
Set Up

We set up a model for electronic foreign-exchange markets, suggesting subordinators to represent sellers' and buyers' offers. Its analysis naturally leads to the study of level passage events. The classical level passage event concerns the joint law of the time, height, and jump size observed when a real-valued stochastic process first exceeds a given level h. We provide an up-to-date treatment in the case when this process is a subordinator, and extend these results to a multivariate setting.

RICCION AS A COSMIC DARK MATTER CANDIDATE AND LATE COSMIC ACCELERATION

2008 ◽  
Vol 23 (31) ◽  
pp. 2681-2689
Author(s):  
S. K. SRIVASTAVA ◽  
K. P. SINHA
Keyword(s):  
Energy Source ◽  
Dark Matter ◽  
Dark Energy ◽  
Cosmic Acceleration ◽  
Exotic Matter ◽  
Dark Matter Candidate ◽  
Classical Level ◽  
The Past ◽  
Higher Derivative

In the past few years, a possibility is investigated, where curvature itself behaves as a source of dark energy. So, it is natural to think whether curvature can produce dark matter too. It is found that, at classical level, higher-derivative gravity yields curvature inspired particles namely riccions.31 Here, it is probed whether riccion can be a possible source of dark matter. Further, it is found that the late universe accelerates. Here, it is interesting to see that acceleration is obtained from curvature without using any dark energy source of exotic matter.

scholarly journals Dynamics of f(R) gravity models and asymmetry of time

2018 ◽  
Vol 27 (02) ◽  
pp. 1850002 ◽  
Author(s):  
Murli Manohar Verma ◽  
Bal Krishna Yadav
Keyword(s):  
Fixed Points ◽  
Quadratic Forms ◽  
Scale Factor ◽  
Gravity Models ◽  
Field Equations ◽  
Classical Level ◽  
The Matrix ◽  
The Stability ◽  
Effects Of Radiation ◽  
Linear And Quadratic Forms

We solve the field equations of modified gravity for [Formula: see text] model in metric formalism. Further, we obtain the fixed points of the dynamical system in phase-space analysis of [Formula: see text] models, both with and without the effects of radiation. The stability of these points is studied against the perturbations in a smooth spatial background by applying the conditions on the eigenvalues of the matrix obtained in the linearized first-order differential equations. Following this, these fixed points are used for analyzing the dynamics of the system during the radiation, matter and acceleration-dominated phases of the universe. Certain linear and quadratic forms of [Formula: see text] are determined from the geometrical and physical considerations and the behavior of the scale factor is found for those forms. Further, we also determine the Hubble parameter [Formula: see text], the Ricci scalar [Formula: see text] and the scale factor [Formula: see text] for these cosmic phases. We show the emergence of an asymmetry of time from the dynamics of the scalar field exclusively owing to the [Formula: see text] gravity in the Einstein frame that may lead to an arrow of time at a classical level.

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