scholarly journals Quadratic Tomography Star Product Algebra and its Classical Limit

2018 ◽  
Vol 58 (2) ◽  
pp. 543-557
Author(s):  
A. A. Strakhov ◽  
V. I. Man’ko
Keyword(s):  
Classical Limit ◽  
Star Product ◽  
Product Algebra

scholarly journals Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 684
Author(s):  
Giovani Morales-Hernández ◽  
Juan Castellanos ◽  
José Romero ◽  
Andrei Klimov
Keyword(s):  
Classical Limit ◽  
Quantum Dynamics ◽  
Asymptotic Form ◽  
Star Product ◽  
Spin Systems ◽  
Classical Dynamics ◽  
Classical Dynamic ◽  
Variable Spin ◽  
Long Time ◽  
Dynamic Variables

We apply the semi-classical limit of the generalized SO(3) map for representation of variable-spin systems in a four-dimensional symplectic manifold and approximate their evolution terms of effective classical dynamics on T*S2. Using the asymptotic form of the star-product, we manage to “quantize” one of the classical dynamic variables and introduce a discretized version of the Truncated Wigner Approximation (TWA). Two emblematic examples of quantum dynamics (rotor in an external field and two coupled spins) are analyzed, and the results of exact, continuous, and discretized versions of TWA are compared.

scholarly journals ACTIONS, CHARGES AND OFF-SHELL FIELDS IN THE UNFOLDED DYNAMICS APPROACH

2006 ◽  
Vol 03 (01) ◽  
pp. 37-80 ◽  
Author(s):  
M. A. VASILIEV
Keyword(s):  
Dynamical System ◽  
Closed Form ◽  
Minkowski Space ◽  
Star Product ◽  
Einstein Equations ◽  
Yang Mills ◽  
Conserved Charges ◽  
Zero Curvature ◽  
Product Algebra

Within unfolded dynamics approach, we represent actions and conserved charges as elements of cohomology of the L∞ algebra underlying the unfolded formulation of a given dynamical system. The unfolded off-shell constraints for symmetric fields of all spins in Minkowski space are shown to have the form of zero curvature and covariant constancy conditions for 1-forms and 0-forms taking values in an appropriate star product algebra. Unfolded formulation of Yang–Mills and Einstein equations is presented in a closed form.

Star product and star function

2019 ◽  
pp. 281-292
Author(s):  
Akira YOSHIOKA
Keyword(s):  
Complex Space ◽  
Star Product ◽  
Star Products ◽  
Exponential Functions ◽  
Product Algebra

We give a brief review on star products and star functions [8, 9]. We introduce a star product on polynomials. Extending the product to functions on complex space, we introduce exponential element in the star product algebra. By means of the star exponential functions we can define several functions called star functions in the algebra.We show certain examples.

II. Non adiabatic theory of collisions in a radiative field. Semi-classical limit : Ar + O case

1989 ◽  
Vol 50 (10) ◽  
pp. 1195-1208 ◽  
Author(s):  
A. Spielfiedel ◽  
E. Roueff ◽  
N. Feautrier
Keyword(s):  
Classical Limit ◽  
Adiabatic Theory

Non adiabatic theory of collisions in a radiative field. Semi-classical limit

1988 ◽  
Vol 49 (11) ◽  
pp. 1911-1923 ◽  
Author(s):  
N. Feautrier ◽  
E. Roueff ◽  
A. Spielfiedel
Keyword(s):  
Classical Limit ◽  
Adiabatic Theory

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

scholarly journals Correction to: Star-Product Formalism for the Probability and Mean-Value Representations of Qudits

2021 ◽  
Author(s):  
Peter Adam ◽  
Vladimir A. Andreev ◽  
Margarita A. Man’ko ◽  
Vladimir I. Man’ko ◽  
Matyas Mechler
Keyword(s):  
Star Product ◽  
Mean Value

scholarly journals About the Use of Entropy Production for the Landau–Fermi–Dirac Equation

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
R. Alonso ◽  
V. Bagland ◽  
L. Desvillettes ◽  
B. Lods
Keyword(s):  
Dirac Equation ◽  
Classical Limit ◽  
Large Time ◽  
A Priori Estimates ◽  
Landau Equation ◽  
A Priori ◽  
Time Behaviour ◽  
Entropy Dissipation ◽  
Priori Estimates ◽  
Potential Case

AbstractIn this paper, we present new estimates for the entropy dissipation of the Landau–Fermi–Dirac equation (with hard or moderately soft potentials) in terms of a weighted relative Fisher information adapted to this equation. Such estimates are used for studying the large time behaviour of the equation, as well as for providing new a priori estimates (in the soft potential case). An important feature of such estimates is that they are uniform with respect to the quantum parameter. Consequently, the same estimations are recovered for the classical limit, that is the Landau equation.

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