Related papers: Topological quantization of the harmonic oscillato…
Explicit methods are presented for computing the cohomology of stable, holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds. The complete particle spectrum of the low-energy, four-dimensional theory is specified by the…
Despite their simplicity, quantum harmonic oscillators are ubiquitous in the modeling of physical systems. They are able to capture universal properties that serve as reference for the more complex systems found in nature. In this spirit,…
We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. {\bf 62}, 092101 (2021)] in the classical and quantum formalisms, by introducing the effect of the mass function in both kinetic…
We consider a set of N linearly coupled harmonic oscillators and show that the diagonalization of this problem can be put in geometrical terms. The matrix techniques developed here allowed for solutions in both the classical and quantum…
Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…
We formulate the concept of dominant interaction Hamiltonians to obtain an integrable approximation to the dynamics of an electron exposed to a strong laser field and an atomic potential leading to high harmonic generation. The concept…
We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of…
Assuming that a constant potential energy function has meaning for a dissipated harmonic oscillator, then an important issue is the time dependence of the turning points. Turning point studies demonstrate that the common model of external…
The redistribution of energy levels between energy bands is studied for a family of simple effective Hamiltonians depending on one control parameter and possessing axial symmetry and energy-reflection symmetry. Further study is made on the…
Harmonic oscillator in Fock space is defined. Isospectral as well as polynomiality-of-eigenfunctions preserving, translation-invariant discretization of the harmonic oscillator is presented. Dilatation-invariant and…
We discuss the exact discretization of the classical harmonic oscillator equation (including the inhomogeneous case and multidimensional generalizations) with a special stress on the energy integral. We present and suggest some numerical…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even…
It is well known that the spectrum condition, i.e. the positivity of the energy in every inertial coordinate system, is one of the central conceptual ingredients in model-independent approaches to relativistic quantum field theory. When one…
A one-dimensional quantum harmonic oscillator perturbed by a smooth compactly supported potential is considered. For the corresponding eigenvalues $\lambda_n$, a complete asymptotic expansion for large $n$ is obtained, and the coefficients…
Topologically quantized response is one of the focal points of contemporary condensed matter physics. While it directly results in quantized response coefficients in quantum systems, there has been no notion of quantized response in…
A classical particle in a harmonic potential gives rise to a continuous energy spectra, whereas the corresponding quantum particle exhibits countably infinite quantized energy levels. In recent years, classical non-Markovian wave-particle…
We define a monodromy, directly from the spectrum of small non-selfadjoint perturbations of a selfadjoint semiclassical operator with two degrees of freedom, which is classically integrable. It is a combinatorial invariant that obstructs…
The quantization of the forced harmonic oscillator is studied with the quantum variable ($x,\hat v$), with the commutation relation $[x,\hat v]=i\hbar/m$, and using a Shr\"odinger's like equation on these variable, and associating a linear…