Related papers: Quantum systems of atoms with highly singular inte…
The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
The paper intends to lay out the first steps towards constructing a unified framework to understand the symplectic and spectral theory of finite dimensional integrable Hamiltonian systems. While it is difficult to know what the best…
Discussed are quantized dynamical systems on orthogonal and affine groups. The special stress is laid on geodetic systems with affinely-invariant kinetic energy operators. The resulting formulas show that such models may be useful in…
It is shown that, in the self-consistent quantum statistical Hartree-Fock approximation, the number of electronic states localized on one nucleus is finite. This result is obtained on the basis of the general electron-nuclear model of…
Quantum states are successfully reconstructed using the maximum likelihood estimation on the subspace where the measured projectors reproduce the identity operator. Reconstruction corresponds to normalization of incompatible observations.…
An interferometer in which all of its components are treated as quantum bodies is examined with the standard interpretation and with a model in which its uncoupled spatially separated components act collectively. These models utilize…
Quantum contextuality describes situations where the statistics observed in different measurement contexts cannot be explained by a measurement independent reality of the system. The most simple case is observed in a three-dimensional…
To study the exotic odd nuclear systems, the self-consistent continuum Skyrme-Hartree-Fock-Bogoliubov theory formulated with Green's function technique is extended to include blocking effects with the equal filling approximation. Detailed…
We investigate a quantum nonrelativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally invariant and parity conserving and identify all such systems…
There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing the limiting individual behavior of particles inside a large ensemble of identical…
Some general features of the spectrum of the Hartree-Fock-Bogoliubov equations are examined. Special attention is paid to the asymptotic behavior of the single quasiparticle wave functions (s.qp.w.fs.), matter density distribution and…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work…
By applying methods already discussed in a previous series of papers by the same authors, we construct here classes of integrable quantum systems which correspond to n fully resonant oscillators with nonlinear couplings. The same methods…
We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor.…
To obtain the basis for combining various many-body techniques to QED in a consistent manner, we investigate the theory of quantum electrodynamical self-consistent fields. The reserch interest was born mainly of the electronic structure…
We propose quantization relationships which would let us describe and solution problems originated by conflicting or cooperative behaviors among the members of a system from the point of view of quantum mechanical interactions. The quantum…
For thermal systems, standard perturbation theory breaks down because of the absence of stable, observable asymptotic states. We show, how the introduction of {\it statistical} quasi-particles (stable, but not observable) gives rise to a…