In this particular case, the terms can actually be obtained more conveniently by an operatorial method, different from that of Appendix I, as shown in Appendix II.
Large amplitude spin waves in ultra-cold gases
Obviously, if we Wigner transform this operatorial equation, we will obtain a kinetic equation that is equivalent to (25), but without the collision integral.
Large amplitude spin waves in ultra-cold gases
These have gone from the so-called “schematic interactions”, like the above mentioned pairing plus quadrupole, which give an oversimpliﬁed representation of the real potential, to more complete interactions including operatorial terms consistent with those present in the interaction between free nucleons.
Pairing and realistic shell-model interactions
They are not elementary degree in the lagrangian, so they need an operatorial deﬁnition, a ”jet-ﬁnding” algorithm.
QCD and high energy hadronic interaction: Summary talk (theory)
The connection with operatorial formulation, whenever possible, comes only afterwards and is optional.
Topological Quantum Groups, Star Products and their relations
It should be emphasized that the Coulomb gas picture obtained here differs from the standard one in that it is ”operatorial”, i.e. there are no contours which depend on the particular correlation function under consideration.
Quantum Group Structure and Local Fields in the Algebraic Approach to 2D Gravity
The Hamiltonian constraint does not admit a simple geometric interpretation and should be implemented as an operatorial equation.
An overview of canonical quantum gravity
This operatorial method is very convenient to calculate corrections in the chiral limit.
Analysis of \epsilon'/\epsilon in the 1/N_c Expansion
Moreover one has a correspondence principle in that one needs to reproduce the classical equations of motion as quantum operatorial relations that offers guidance in the intermediate steps of the process.
Uniform discretizations: a new approach for the quantization of totally constrained systems
Some years after its discovery, a systematic derivation based on an operatorial splitting approach was proposed .
Design of quasi-symplectic propagators for Langevin dynamics
The operatorial approach is very elegant and fruitful.
Design of quasi-symplectic propagators for Langevin dynamics
In this context, the operatorial route has again been applied by considering the stochastic noise as a time-dependent perturbation or by evolving the state according to a Fokker-Planck propagator [11, 12].
Design of quasi-symplectic propagators for Langevin dynamics
In general, due to the presence of both stochastic and deterministic forces, conventional operatorial calculus should be applied with some care.
Design of quasi-symplectic propagators for Langevin dynamics
As a matter of fact, a previous operatorial approach was shown to overestimate the accuracy of the numerical tra jectory [10, 14].
Design of quasi-symplectic propagators for Langevin dynamics
The tra jectory representation employed here is clearly equivalent to the operatorial one.
Design of quasi-symplectic propagators for Langevin dynamics
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