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The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
The quantum rotor represents, after the harmonic oscillator, the next obvious quantum system to study the complementary pair of variables: the angular momentum and the unitary shift operator in angular momentum. Proper quantification of…
The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of…
We consider quantum correlations in a spin-1/2 open chain of $N$ nodes with the XY Hamiltonian using different bases for the density matrix representation and the initial state with a single polarized node. These bases of our choice are…
The fundamental correspondence between quantum chaotic single-particle systems and random matrix theory is well-understood via periodic orbit theory. In contrast, we show that many-body systems with explicit subsystem structure possess…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…
On the example of a quantum oscillator the connection of the dynamical coherent state with the phase symmetry breaking and the existence of the nondissipative motion is considered. In multiparticle systems of interacting particles similar…
We review the properties of chaoticity and coherence in Bose-Einstein condensation and correlations, for a dense boson system in its mean-field represented approximately by a harmonic oscillator potential. The order parameter and the nature…
We study the quantum-classical correspondence of an experimentally accessible system of interacting bosons in a tilted triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the…
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)…
Although quantum correlations in a quantum system are characterized by the evolving quantities (which are entanglement and discord usually), we reveal such basis (i.e. the set of virtual particles) for the representation of the density…
We study a quantum impurity possessing both translational and internal rotational degrees of freedom interacting with a bosonic bath. Such a system corresponds to a `rotating polaron', which can be used to model, e.g., a rotating molecule…
This review article will present some recent results and methods in the study of 1-particle quantum or wave scattering systems, in the semiclassical/high frequency limit, in cases where the corresponding classical/ray dynamics is chaotic.…
The self-consistent harmonic oscillator model including the three-dimensional cranking term is extended to describe collective excitations in the random phase approximation. It is found that quadrupole collective excitations associated with…
We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…
We have investigated S-wave bound states composed of three identical bosons interacting via regulated delta function potentials in non-relativistic quantum mechanics. For low-energy systems, these short-range potentials serve as an…
$Circuit~ Complexity$, a well known computational technique has recently become the backbone of the physics community to probe the chaotic behaviour and random quantum fluctuations of quantum fields. This paper is devoted to the study of…
We present a formalism for constructing schematic diagrams to depict chaotic three-body interactions in Newtonian gravity. This is done by decomposing each interaction in to a series of discrete transformations in energy- and angular…
We consider two-dimensional harmonic oscillator in the complex Bargmann-Fock-Segal representation with $T^*{\mathbb R}^{2}={\mathbb C}^2$ as classical phase space. We show that the eigenfunctions $\psi_n$ of the quantum Hamiltonian…
The paradoxical phenomenon of the quantum Cheshire Cat (qCC) refers to situations where different properties of a particle appear to be localised in different paths of an interferometer and therefore spatially separated. This observation is…