scholarly journals GEOMETRY OF DEFORMED BOSON ALGEBRAS

1996 ◽  
Vol 08 (07) ◽  
pp. 949-956
Author(s):  
P. CREHAN ◽  
T.G. HO
Keyword(s):  
Phase Space ◽  
Hamiltonian Systems ◽  
Normal Forms ◽  
Parameter Family ◽  
Poisson Structures ◽  
Nonlinear Transformations ◽  
Deformation Parameters ◽  
Special Cases ◽  
Non Linear ◽  
Deformed Algebras

We consider a phase space realisation of an infinite parameter family of deformations of the boson algebra in which the q-deformed algebras arise as special cases. The deformation parameters are identified with coefficients of non-linear terms in the normal forms expansion of a family of classical Hamiltonian systems. These deformations simply correspond to nonlinear transformations of the boson algebra. They are physically interesting, as the deformed commutators consistently quantise a class of noncanonical classical Poisson structures.

scholarly journals DYNAMICAL ASPECTS OF LIE-POISSON STRUCTURES

1993 ◽  
Vol 08 (31) ◽  
pp. 2973-2987 ◽  
Author(s):  
F. LIZZI ◽  
G. MARMO ◽  
G. SPARANO ◽  
P. VITALE
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Poisson Bracket ◽  
Lie Groups ◽  
Hamiltonian Systems ◽  
Quantum Groups ◽  
Equations Of Motion ◽  
Poisson Structures ◽  
Dimensional Phase Space ◽  
Deformation Procedure

Quantum groups can be constructed by applying the quantization by deformation procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to develop an understanding of these structures by investigating dynamical systems which are associated with this bracket. We look at SU(2) and SU(1, 1), as submanifolds of a four-dimensional phase space with constraints, and deal with two classes of problems. In the first set of examples we consider some Hamiltonian systems associated with Lie-Poisson structures and we investigate the equations of motion. In the second set of examples we consider systems which preserve the chosen bracket, but are dissipative. However in this approach, they survive the quantization procedure.

Deformations of Poisson structures on fibered manifolds and adiabatic slow–fast systems

2017 ◽  
Vol 14 (06) ◽  
pp. 1750086 ◽  
Author(s):  
Misael Avendaño-Camacho ◽  
Yury Vorobiev
Keyword(s):  
Perturbation Theory ◽  
Hamiltonian Systems ◽  
Deformation Theory ◽  
Normal Forms ◽  
Geometric Approach ◽  
Fiber Bundles ◽  
Poisson Structures ◽  
Averaging Theorem ◽  
Fibered Manifolds ◽  
Adiabatic Perturbation Theory

In the context of normal forms, we study a class of slow–fast Hamiltonian systems on general Poisson fiber bundles with symmetry. Our geometric approach is motivated by a link between the deformation theory for Poisson structures on fibered manifolds and the adiabatic perturbation theory. We present some normalization results which are based on the averaging theorem for horizontal 2-cocycles on Poisson fiber bundles.

Control of arrivals to a stochastic input–output system

1980 ◽  
Vol 12 (4) ◽  
pp. 972-999 ◽  
Author(s):  
Søren Glud Johansen ◽  
Shaler Stidham
Keyword(s):  
Markov Decision Process ◽  
Decision Process ◽  
Input Output ◽  
Distinctive Features ◽  
Control Models ◽  
Special Cases ◽  
Non Linear ◽  
Markov Decision ◽  
Output System ◽  
Stochastic Input

The problem of controlling input to a stochastic input-output system by accepting or rejecting arriving customers is analyzed as a semi-Markov decision process. Included as special cases are a GI/G/1 model and models with compound input and/or output processes, as well as several previously studied queueing-control models. We establish monotonicity of socially and individually optimal acceptance policies and the more restrictive nature of the former, with random rewards for acceptance and both customer-oriented and system-oriented non-linear waiting costs. Distinctive features of our analysis are (i) that it allows dependent interarrival times and (ii) that the monotonicity proofs do not rely on the standard concavity-preservation arguments.

scholarly journals COVARIANT DESCRIPTION OF PARAMETRIZED NONRELATIVISTIC HAMILTONIAN SYSTEMS

2004 ◽  
Vol 19 (15) ◽  
pp. 2473-2493 ◽  
Author(s):  
MAURICIO MONDRAGÓN ◽  
MERCED MONTESINOS
Keyword(s):  
Phase Space ◽  
Gauge Transformation ◽  
Hamiltonian Systems ◽  
Symplectic Structure ◽  
Canonical Formalism ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Algebra Of Observables ◽  
Covariant Description ◽  
Constraint Surface

The various phase spaces involved in the dynamics of parametrized nonrelativistic Hamiltonian systems are displayed by using Crnkovic and Witten's covariant canonical formalism. It is also pointed out that in Dirac's canonical formalism there exists a freedom in the choice of the symplectic structure on the extended phase space and in the choice of the equations that define the constraint surface with the only restriction that these two choices combine in such a way that any pair (of these two choices) generates the same gauge transformation. The consequence of this freedom on the algebra of observables is also discussed.

scholarly journals Phase Space Homogenization of Noisy Hamiltonian Systems

2018 ◽  
Vol 19 (4) ◽  
pp. 1081-1114 ◽  
Author(s):  
Jeremiah Birrell ◽  
Jan Wehr
Keyword(s):  
Phase Space ◽  
Hamiltonian Systems

scholarly journals Non-Smooth Geodesic Flows and Classical Mechanics

1969 ◽  
Vol 12 (2) ◽  
pp. 209-212 ◽  
Author(s):  
J. E. Marsden
Keyword(s):  
Phase Space ◽  
Kinetic Energy ◽  
Hamiltonian Systems ◽  
Configuration Space ◽  
Smooth Function ◽  
Cotangent Bundle ◽  
Classical Mechanics ◽  
Riemannian Metric ◽  
Geodesic Flows ◽  
Image Position

As is well known, there is an intimate connection between geodesic flows and Hamiltonian systems. In fact, if g is a Riemannian, or pseudo-Riemannian metric on a manifold M (we think of M as q-space or the configuration space), we may define a smooth function Tg on the cotangent bundle T*M (q-p-space, or the phase space). This function is the kinetic energy of q, and locally is given by

scholarly journals PROPERTIES OF THE INVARIANT DISK PACKING IN A MODEL BANDPASS SIGMA–DELTA MODULATOR

2003 ◽  
Vol 13 (03) ◽  
pp. 631-641 ◽  
Author(s):  
PETER ASHWIN ◽  
XIN-CHU FU ◽  
JONATHAN DEANE
Keyword(s):  
Phase Space ◽  
Analytic Functions ◽  
Parameter Family ◽  
Sigma Delta Modulator ◽  
Sigma Delta ◽  
Disk Packing ◽  
Piecewise Isometries ◽  
Map Operations ◽  
Countably Infinite ◽  
Parameter Values

In this paper we discuss the packing properties of invariant disks defined by periodic behavior of a model for a bandpass Σ–Δ modulator. The periodically coded regions form a packing of the forward invariant phase space by invariant disks. For this one-parameter family of PWIs, by introducing codings underlying the map operations we give explicit expressions for the centers of the disks by analytic functions of the parameters, and then show that tangencies between disks in the packings are very rare; more precisely they occur on parameter values that are at most countably infinite. We indicate how similar results can be obtained for other plane maps that are piecewise isometries.

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