This paper obtains the exact 1-soliton solution to the chiral nonlinear Schrödinger’s equation. There are three types of integration architectures that are implemented in this paper. They are the functional variable approach, first integral method as well as the ansatz method. These soliton solutions are obtained. There are constraint conditions that also fall out which must remain valid in order for the solitons and other solutions to exist.

For a system of two-oscillator, we introduce a basis labelled by the sum and the difference between the occupation quantum numbers of the oscillators. It forms a basis for the SU(2) bosonic representation. This basis could be useful in the studies of coupled oscillator systems when the total occupation quantum number of the systems is a constant of motion, for example, in the weak coupling limit. Using this basis, we are able to show that the positive partial transpose criterion is necessary and sufficient for the separability of general mixed states in the subspaces with fixed total occupation quantum number. We find that mixed states that are diagonal in this basis are the only separable states in this subspace. The result is consistent with the fact that the identification of entanglement in infinite dimensional systems can be reduced to a problem in finite dimensions. Examples of quantum states that belong to these subspaces are the so-called \(N00N\)-states and the SU(2) coherent states used in the studies of quantum optical systems, quantum information science and quantum nonlinear rotators.

In a series of recent papers it was shown that, when the attractive \(s\)-wave interaction is dominant, the spin-orbit coupled fermions form a bound state. Attributed to a convenient momentum representation, it became a common condition of agreement to express the bound state as a function of the center-of-mass momentum \(Q\). In this paper, we prove that the bound state of Rashba fermions does not depend on the chosen representation. That is, all the states characterized by nonzero \(Q\) fail to obey the translation symmetry.

A new definition of quantum entropy by a gauge constraint on a classical Boltzmann manifold is proposed. Bohm potential is derived as Fisher information, in accordance with Bohm–Hiley idea of “Active Information”, and the geometries underlying Bohm trajectories and Feynman paths are compared. Given a quantum system, it is shown how the modifications of such geometries are connected to the microstates that quantum entropy provides.

A new prescription, in the framework of condensate models for space-times, for physical stationary gravitational fields is presented. We show that the spinning cosmic string metric describes the gravitational field associated with the single vortex in a superfluid condensate model for space-time outside the vortex core. This metric differs significantly from the usual acoustic metric for the Onsager–Feynman vortex. We also consider the question of what happens when many vortices are present, and show that on large scales a Gödel-like metric emerges. In both the single and multiple vortex cases, the failure of general relativity exemplified by the presence of closed time-like curves is attributed to the breakdown of superfluid rigidity.

The coherent states for twist-deformed oscillator model provided in article by M. Daszkiewicz, C.J. Walczyk [Acta Phys. Pol. B40, 293 (2009)] are constructed. Besides, it is demonstrated that the energy spectrum of considered model is labeled by two quantum numbers — by the so-called main and azimutal quantum numbers respectively.

An isospin and spin dependent form of the equation of state for nuclear matter is presented. This form is used for the description of nucleon interaction in a new dynamical model. Preliminary calculations show that the new approach makes possible predicting the alpha-like structures appearing in the case of the even–even nuclei ground state.

In this work, we build a superlattice Ising model based on periodic trilayers consisting of spin particles \(\sigma =\frac {1}{2}\), \(S=1\) and \(q=\frac {3}{2}\) placed at square lattice sites. More precisely, we study the effect of the inter-couplings \(J_{\alpha \beta } (\alpha ,\beta = \sigma ,S,q)\) between the trilayers in the presence of an external magnetic field \(H\). We first elaborate the ground state phase diagrams in the (\(H, J_{\sigma S}\))-plane. We find that the most stable phases are associated with the triplets \((\sigma , S, q)=((-\frac {1}{2},1,\frac {3}{2})\), \((\frac {1}{2},-1,-\frac {3}{2})\) \((\frac {1}{2},1,\frac {3}{2})\)). For \(J_{ Sq}=-1\), three extra stable phases appear. In this case, seven different stable configurations arise. Then, we discuss the magnetic properties using Monte Carlo simulations. The thermal behaviors of the magnetizations and the susceptibilities are computed and discussed. For different temperatures, the magnetic field effect on the total magnetization has been investigated, leading to the hysteresis loops. Moreover, it has been found that the effect of the coupling interactions on the total magnetization controls the magnetic phase type, which can be either ferromagnetic or ferrimagnetic depending on the values of \(J_{\alpha \beta }\) couplings.

We propose that the time duration distribution of Gamma-Ray Bursts (GRBs) is due to the central engine’s environment. The observed time duration of each prompt burst is here directly attributed to the evolution of a generic collimated ultra-relativistic flow in its interaction with a hypothetical cloud which surrounds the central engine. These clouds might be imagined to be some extremely amorphous and heterogeneous envelopes surrounding the cores of collapsars just before the explosion. While, in our modeling, the ultra-relativistic flow is taken to be a standard candle, the size and density of the surrounding clouds are assumed to vary in different directions as seen from the core, and perhaps differ from one burster to another. Both the relevant size and density (in the path of the flow) are taken as random quantities which undergo the Gaussian distribution. This model, while explaining the bimodal form of GRBs’ time duration distribution, presents plausible values for the flow’s initial Lorentz factor (\(\sim 10^{3}\)) and its initial collimation angle (\(\sim 1^{\circ }\)). Furthermore, the mean mass of the assumed clouds (envelopes) is predicted to be about \(6M_{\odot }\). The model also accounts for the presence/absence of variability in long/short GRBs’ light curve, while explaining why short GRBs are less energetic and harder in comparison with long GRBs.