scholarly journals The Homological Kähler-de Rham Differential Mechanism: II. Sheaf-Theoretic Localization of Quantum Dynamics

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Anastasios Mallios ◽  
Elias Zafiris
Keyword(s):  
Quantum Dynamics ◽  
Dynamical Behavior ◽  
Quantum Regime ◽  
Commutative Algebras ◽  
Differential Mechanism ◽  
De Rham ◽  
Physical Fields

The homological Kähler-de Rham differential mechanism models the dynamical behavior of physical fields by purely algebraic means and independently of any background manifold substratum. This is of particular importance for the formulation of dynamics in the quantum regime, where the adherence to such a fixed substratum is problematic. In this context, we show that the functorial formulation of the Kähler-de Rham differential mechanism in categories of sheaves of commutative algebras, instantiating generalized localization environments of physical observables, induces a consistent functorial framework of dynamics in the quantum regime.

scholarly journals The Homological Kähler-De Rham Differential Mechanism part I: Application in General Theory of Relativity

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Anastasios Mallios ◽  
Elias Zafiris
Keyword(s):  
Topological Defects ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Dynamical Mechanism ◽  
Geometric Calculus ◽  
Unital Algebra ◽  
Rham Complex ◽  
Differential Mechanism ◽  
De Rham ◽  
Physical Fields

The mechanism of differential geometric calculus is based on the fundamental notion of a connection on a module over a commutative and unital algebra of scalars defined together with the associated de Rham complex. In this communication, we demonstrate that the dynamical mechanism of physical fields can be formulated by purely algebraic means, in terms of the homological Kähler-De Rham differential schema, constructed by connection inducing functors and their associated curvatures, independently of any background substratum. In this context, we show explicitly that the application of this mechanism in General Relativity, instantiating the case of gravitational dynamics, is related with the absolute representability of the theory in the field of real numbers, a byproduct of which is the fixed background manifold construct of this theory. Furthermore, the background independence of the homological differential mechanism is of particular importance for the formulation of dynamics in quantum theory, where the adherence to a fixed manifold substratum is problematic due to singularities or other topological defects.

scholarly journals Simulation of Quantum Dynamics Based on the Quantum Stochastic Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Ming Li
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Quantum Dynamics ◽  
Dynamical Behavior ◽  
Computational Cost ◽  
Quantum Master Equation ◽  
Level System ◽  
Quantum Stochastic Differential Equation ◽  
State Diffusion ◽  
Quantum State Diffusion

The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm.

scholarly journals Effective actions for dual massive (super) p-forms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sergei M. Kuzenko ◽  
Kai Turner
Keyword(s):  
Gauge Theory ◽  
Effective Action ◽  
Quantum Dynamics ◽  
Mass Term ◽  
Four Dimensions ◽  
De Rham ◽  
Form Model ◽  
Compact Expression ◽  
Tensor Multiplet ◽  
Topological Term

Abstract In d dimensions, the model for a massless p-form in curved space is known to be a reducible gauge theory for p > 1, and therefore its covariant quantisation cannot be carried out using the standard Faddeev-Popov scheme. However, adding a mass term and also introducing a Stueckelberg reformulation of the resulting p-form model, one ends up with an irreducible gauge theory which can be quantised à la Faddeev and Popov. We derive a compact expression for the massive p-form effective action, $$ {\Gamma}_p^{(m)} $$ Γ p m , in terms of the functional determinants of Hodge-de Rham operators. We then show that the effective actions $$ {\Gamma}_p^{(m)} $$ Γ p m and $$ {\Gamma}_{d-p-1}^{(m)} $$ Γ d − p − 1 m differ by a topological invariant. This is a generalisation of the known result in the massless case that the effective actions Γp and Γd−p−2 coincide modulo a topological term. Finally, our analysis is extended to the case of massive super p-forms coupled to background $$ \mathcal{N} $$ N = 1 supergravity in four dimensions. Specifically, we study the quantum dynamics of the following massive super p-forms: (i) vector multiplet; (ii) tensor multiplet; and (iii) three-form multiplet. It is demonstrated that the effective actions of the massive vector and tensor multiplets coincide. The effective action of the massive three-form is shown to be a sum of those corresponding to two massive scalar multiplets, modulo a topological term.

The quantum dynamics of a mesoscopic driven RLC circuit consisting of a linear inductor, a linear resistor and a nonlinear capacitor

2021 ◽  
Author(s):  
A. Zamani ◽  
H. Pahlavani
Keyword(s):  
Quantum Dynamics ◽  
Dynamical Behavior ◽  
Electric Circuit ◽  
External Source ◽  
Electrical Circuit ◽  
Persistent Current ◽  
Nonlinear Parameters ◽  
Quantum Dynamical ◽  
Rlc Circuit ◽  
Cubic Polynomial

The nonlinear capacitor that obeys of a cubic polynomial voltage–charge relation (usually a power series in charge) is introduced. The quantum theory for a mesoscopic electric circuit with charge discreteness is investigated, and the Hamiltonian of a quantum mesoscopic electrical circuit comprised by a linear inductor, a linear resistor and a nonlinear capacitor under the influence of a time-dependent external source is expressed. Using the numerical solution approaches, a good analytic approximate solution for the quantum cubic Duffing equation is found. Based on this, the persistent current is obtained antically. The energy spectrum of such nonlinear electrical circuit has been found. The dependency of the persistent current and spectral property equations to linear and nonlinear parameters is discussed by the numerical simulations method, and the quantum dynamical behavior of these parameters is studied.

THE NOTHING THAT REALLY IS!

2016 ◽  
Vol 12 (1) ◽  
pp. 4172-4177
Author(s):  
Abdul Malek
Keyword(s):  
Quantum Dynamics ◽  
Theoretical Physics ◽  
Historical Evolution ◽  
Proper Understanding ◽  
Physical Universe ◽  
Wave Particle Duality ◽  
Negative Effect ◽  
Materialist Interpretation

The denial of the existence of contradiction is at the root of all idealism in epistemology and the cause for alienations.  This alienation has become a hindrance for the understanding of the nature and the historical evolution mathematics itself and its role as an instrument in the enquiry of the physical universe (1). A dialectical materialist approach incorporating  the role of the contradiction of the unity of the opposites, chance and necessity etc., can provide a proper understanding of the historical evolution of mathematics and  may ameliorate  the negative effect of the alienation in modern theoretical physics and cosmology. The dialectical view also offers a more plausible materialist interpretation of the bewildering wave-particle duality in quantum dynamics (2).

THE DE RHAM COHOMOLOGY OF DIFFERENTIAL SPACES

1989 ◽  
Vol 22 (1) ◽  
pp. 249-272 ◽  
Author(s):  
Wiesław Sasin
Keyword(s):  
De Rham Cohomology ◽  
De Rham ◽  
Differential Spaces

Dynamical behavior of a nonlinear rotorcraft model

1989 ◽  
Author(s):  
GEORGE FLOWERS ◽  
BENSONH. TONGUE
Keyword(s):  
Dynamical Behavior
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