Related papers: Pattern Formation in Quantum Ensembles
We present a family of methods, which can describe behaviour of quantum ensembles and demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent from basic localized modes in…
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)…
A fast and efficient numerical-analytical approach is proposed for modeling complex behaviour in the BBGKY hierarchy of kinetic equations. We construct the multiscale representation for hierarchy of reduced distribution functions in the…
A fast and efficient numerical-analytical approach is proposed for modeling complex behaviour in the BBGKY hierarchy of kinetic equations. Numerical modeling shows the creation of various internal structures from localized modes, which are…
A fast and efficient numerical-analytical approach is proposed for modeling complex behaviour in the BBGKY--hierarchy of kinetic equations. Our calculations are based on variational and multiresolution approaches in the basis of polynomial…
A fast and efficient numerical-analytical approach is proposed for description of complex behaviour in non-equilibrium ensembles in the BBGKY framework. We construct the multiscale representation for hierarchy of partition functions by…
A fast and efficient numerical-analytical approach is proposed for description of complex behavior in non-equilibrium ensembles in the BBGKY framework. We construct the multiscale representation for hierarchy of partition functions by means…
Fast and efficient numerical-analytical approach is proposed for modeling complex collective behaviour in accelerator/plasma physics models based on BBGKY hierarchy of kinetic equations. Our calculations are based on variational and…
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.…
We present three statistical descriptions for systems of classical particles and consider their extension to hybrid quantum-classical systems. The classical descriptions are ensembles on configuration space, ensembles on phase space, and a…
Extending the phase-space description of the Weyl-Wigner quantum mechanics to a subset of non-linear Hamiltonians in position and momentum, gaussian functions are identified as the quantum ground state. Once a Hamiltonian, $H^{W}(q,\,p)$,…
It is an open fundamental question how the classical appearance of our environment arises from the underlying quantum many-body theory. We propose that phenomena involved in the quantum-to-classical transition can be probed in collisions of…
We present a Hamiltonian method of constructing BBGKY-like hierarchies for quantum field theories. With suitable choices, our method creates a hierarchical system of evolution equations for the k-th order reduced density matrices. These…
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…
Quantum frameworks for modeling competitive ecological systems and self-organizing structures have been investigated under multiple perspectives yielded by quantum mechanics. These comprise the description of the phase-space prey-predator…
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…
We present a theoretical study of classical Wigner crystals in two- and three-dimensional isotropic parabolic traps aiming at understanding and quantifying the configurational uncertainty due to the presence of multiple stable…
Due to the exponential growth of the state space of coupled quantum systems it is not possible, in general, to numerically store the state of a very large number of quantum systems within a classical computer. We demonstrate a method for…