Related papers: Piecewise-constant potentials with practically the…
The three-dimensional potential equation, motivated by representations of quantum mechanics, is investigated in four different scenarios: (i) In the usual Euclidean space $\mathbb{E}_{3}$ where the potential is singular but invariant under…
Recent studies of the phase diagram for spherical, purely repulsive, active particles established the existence of a transition from a liquid-like to a solid-like phase analogous to the one observed in colloidal systems at thermal…
We consider cloning transformations of d-dimensional states of the form e^{i\phi_0}|0> + e^{i\phi_1}|1> +...+ e^{i\phi_{d-1}}|d-1> that are covariant with respect to rotations of the phases \phi_i's. The optimal cloning maps are easily…
A supersymmetric method for the construction of so-called conditionally exactly solvable quantum systems is reviewed and extended to classical stochastic dynamical systems characterized by a Fokker-Planck equation with drift. A class of…
We present a phase-space analysis of cosmology containing multiple scalar fields with a positive or negative cross-coupling exponential potential. We show that there exist power-law kinetic-potential-scaling solutions for a sufficiently…
An approach is presented for coupled chaotic systems, estimating an inferior bound value for the absolute phase difference, in order to say that phase synchronization is present. This approach shows that synchronicity in phase implies…
A systematic procedure to derive exact solutions of the associated Lame equation for an arbitrary value of the energy is presented. Supersymmetric transformations in which the seed solutions have factorization energies inside the gaps are…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
We investigate the possible restoration of chiral and axial symmetries across the phase transition at finite temperature and chemical potential, by analyzing the behavior of several physics quantities, such as the quark condensates and the…
It is shown that a scalar field, minimally coupled to gravity may have collapsing modes even when the energy condition is violated, that is, for $(\rho+3p)<0$. This result may be useful in the investigation of the possible clustering of…
Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding…
Arguably one can use a canonical scalar field $\varphi$, minimally coupled to gravity, with quadratic potentials $V = \Lambda \pm \frac12 m^2\varphi^2$ to explore some general features of slow-roll and hilltop thawing quintessence,…
We consider here quasiperiodic potentials on the plane, which can serve as a "transitional link" between ordered (periodic) and chaotic (random) potentials. As can be shown, in almost any family of quasiperiodic potentials depending on a…
We demonstrate that a large ensemble of noiseless globally coupled-pinned oscillators is capable of rectifying spatial disorder with spontaneous current activated through a dynamical phase transition mechanism, either of first or second…
It has long been assumed that there is an intrinsic conflict between optical vortices and partial coherence, in that deterministic phase vortices do not appear in partially coherent fields. We demonstrate, however, that it is possible to…
The power series method has been adapted to compute the spectrum of the Schrodinger equation for central potential of the form $V(r)={d_{-2}\over r^2}+{d_{-1}\over r}+\sum_{i=0}^{\infty} d_{i}r^i$. The bound-state energies are given as…
We consider ideal fluid and equivalent scalar field dark energy universes where all four known types of finite-time, future singularities occur at some parameter values. It is demonstrated that pressure/energy density of such…
We present here the canonical treatment of spherically symmetric (quantum) gravity coupled to spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the reduced phase space which is…
We determine sufficient and necessary conditions for a spherically symmetric initial data set to satisfy the dynamical horizon conditions in the spacetime development. The constraint equations reduce to a single second order linear master…
We prove the existence of equilibrium states for geometric potentials in a class of piecewise weakly convex interval maps. This class includes systems with indifferent fixed points and non-Markov partitions. Under additional hypotheses we…