Related papers: Wigner quantum oscillators. Osp(3/2) oscillators
A nonpolynomial one-dimensional quantum potential representing an oscillator, that can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (harmonic oscillator with a centripetal barrier), is…
We examine the groundstate wavefunction of the rotor model for different boundary conditions. Three conjectures are made on the appearance of numbers enumerating alternating sign matrices. In addition to those occurring in the O($n=1$)…
Oscillating shapes of the primordial bispectrum are present in many inflationary models. The Planck experiment has recently published measurements of oscillating shapes, which were however limited to the efficient frequency range of the…
Wave packets for the Quantum Non-Linear Oscillator are considered in the Generalized Coherent State framerwork. To first order in the non-linearity parameter the Coherent State behaves very similarly to its classical counterpart. The…
We investigate the quantum transition to a correlated state of coupled oscillators in the regime where they display period tripling in response to a drive at triple the eigenfrequency. Correlations are formed between the discrete…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
In this work we study symplectic unitary representations for the Galilei group. As a consequence the Schr\"odinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using…
We study "the Caged Anisotropic Harmonic Oscillator", which is a new example of a superintegrable, or accidentally degenerate Hamiltonian. The potential is that of the harmonic oscillator with rational frequency ratio (l:m:n), but…
We introduce a family of criteria to detect quantum non-Gaussian states of a harmonic oscillator, that is, quantum states that can not be expressed as a convex mixture of Gaussian states. In particular we prove that, for convex mixtures of…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
The Nijmegen Unitarized Meson Model and its application to scalar mesons is briefly revisited. It is shown that all scalar states up to 1.5 GeV can be described as triplet-P-zero quark+antiquark states coupled to the OZI-allowed open and…
The sine-Gordon model in 3+1 dimensions is known to admit two oscillons of different energy and frequency but comparable lifetime. We show that the oscillon spectrum includes more spherically symmetric ``states''. We identify new…
Geometric models of quantum relativistic rotating oscillators in arbitrary dimensions are defined on backgrounds with deformed anti-de Sitter metrics. It is shown that these models are analytically solvable, deriving the formulas of the…
We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner's ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with…
The classical limit of quantum q-oscillators suggests an interpretation of the deformation as a way to introduce non linearity. Guided by this idea, we considered q-fields, the partition fumction, and compute a consequence on specific heat…
Magnons are viewed as local deviations from the ordered state. Usually, the spin magnetic moment of magnons is considered. In a 3D-confined structure of a magnetic insulator with magnetodipolar mode (MDM) oscillations, an orbital angular…
For a quantum oscillator with the polynomial potential an explicit expression that describes the energy distribution as a coordinate (and momentum) function is obtained. The presence of the energy function poles is shown for the quantum…
The SU(2) Wigner function represents a quantum state of a spin-$J$ as a real-valued function on the surface of a 2-sphere. For an ensemble of $N$ spin-1/2 particles, this representation is useful when the dynamics is restricted to a single…
We propose novel types of parametric oscillators generating both three-photon and four-photon bright light which are accessible for an experiment. The devices are based on the cascaded down-conversion processes and consist of second-order…
There are no phase-space trajectories for anharmonic quantum systems, but Wigner's phase-space representation of quantum mechanics features Wigner current~$\bf J$. This current reveals fine details of quantum dynamics -- finer than is…