Related papers: Patterns in Wigner-Weyl approach
We present a family of methods, analytical and numerical, which can describe behaviour in (non) equilibrium ensembles, both classical and quantum, especially in the complex systems, where the standard approaches cannot be applied. We…
In this second part we present a set of methods, analytical and numerical, which can describe behaviour in (non) equilibrium ensembles, both classical and quantum, especially in the complex systems, where the standard approaches cannot be…
We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from the basic localized modes in various collective models arising from the quantum hierarchy described by Wigner-like…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
We present the application of the variational-wavelet analysis to the analysis of quantum ensembles in Wigner framework. (Naive) deformation quantization, the multiresolution representations and the variational approach are the key points.…
It is obvious that we still have not any unified framework covering a zoo of interpretations of Quantum Mechanics, as well as satisfactory understanding of main ingredients of a phenomena like entanglement. The starting point is an idea to…
Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic…
The article explores a new formalism for describing motion in quantum mechanics. The construction is based on generalized coherent states with evolving fiducial vector. Weyl-Heisenberg coherent states are utilised to split quantum systems…
For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. We present here two counterexamples - the hydrogen atom…
We present the application of the variational-wavelet analysis to the quasiclassical calculations of the solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems. (Naive)…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
Instability features associated to topological quantum domains which emerge from the Weyl-Wigner (WW) quantum phase-space description of Gaussian ensembles driven by Aubry-Andr\'e-Harper (AAH) Hamiltonians are investigated. Hyperbolic…
Time-symmetric quantum mechanics can be described in the usual Weyl--Wigner--Moyal formalism (WWM) by using the properties of the Wigner distribution, and its generalization, the cross-Wigner distribution. The use of the latter makes clear…
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…
The resource theory of coherence addresses the extent to which quantum properties are present in a given quantum system. While coherence has been extensively studied for individual quantum states, measures of coherence for ensembles of…
The nonlinear interaction, due to quantum electrodynamical (QED) effects, between photons is investigated using a wave-kinetic description. Starting from a coherent wave description, we use the Wigner transform technique to obtain a set of…
We present applications of variational -- wavelet approach to three different models of nonlinear beam motions with underlying collective behaviour: Vlasov-Maxwell-Poisson systems, envelope dynamics, beam-beam model. We have the…
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
We sketch a group-theoretical framework, based on the Heisenberg-Weyl group, encompassing both quantum and classical statistical descriptions of mechanical systems. We re-define in group-theoretical terms the kinematical arena and the…