Related papers: Quantum harmonic oscillator with superoscillating …
Quantum resonance in the paradigmatic kicked rotor system is a purely quantum effect that ignores the state of underlying classical chaos. In this work, it is shown that quantum resonance leads to superlinear entanglement production. In…
We study the supersymmetric partners of the harmonic oscillator with an infinite potential barrier at the origin and obtain the conditions under which it is possible to add levels to the energy spectrum of these systems. It is found that…
We consider the logarithmic Schr{\"o}dinger equation in a semiclassical scaling, in the presence of a smooth, at most quadratic, external potential. For initial data under the form of a single coherent state, we identify the notion of…
We explore a thermodynamical effect of anharmonicity in quantum mechanical oscillators. We show that small quartic perturbations to the oscillator potential lead to an enhancement of performance of quantum refrigerators for both the Otto…
Consider quantum harmonic oscillator, perturbed by an even almost-periodic complex-valued potential with bounded derivative and primitive. Suppose that we know the first correction to the spectral asymptotics $\{\Delta\mu_n\}_{n=0}^\infty$…
In this paper we solve for the quantum propagator of a general time dependent system quadratic in both position and momentum, linearly coupled to an infinite bath of harmonic oscillators. We work in the regime where the quantum optical…
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…
This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation…
Superoscillations are a phenomenon in physics, where linear combinations of low-frequency plane waves interfere almost destructively in such a way that the resulting wave has a higher frequency than any of the individual waves. The…
We consider the large time behavior of solutions to defocusing nonlinear Schrodinger equation in the presence of a time dependent external potential. The main assumption on the potential is that it grows at most quadratically in space,…
In this manuscript, we investigate the analytical solution of the time-dependent Schr\"odinger equation for a harmonic oscillator with time-dependent mass and frequency, coupled with angular-dependent potential energy by utilizing the Dunkl…
We transform the time-dependent Schroedinger equation for the most general variable quadratic Hamiltonians into a standard autonomous form. As a result, the time-evolution of exact wave functions of generalized harmonic oscillators is…
We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a…
We prove unique continuation properties for solutions of the evolution Schr\"odinger equation with time dependent potentials. As an application of our method we also obtain results concerning the possible concentration profiles of blow up…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
We construct a formalism for evolving spherically symmetric black hole initial data sets within a canonical approach to quantum gravity. This problem can be formulated precisely in quantum reduced loop gravity, a framework which has been…
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,…
Driven quantum nonlinear oscillators, while essential for quantum technologies, are generally prone to complex chaotic dynamics that fall beyond the reach of perturbative analysis. By focusing on subharmonic bifurcations of a harmonically…
Different from the usual harmonic oscillator, the time-decaying harmonic oscillator accelerates particles and generates scattering states. We study one of the multidimensional inverse scatterings in this two-body quantum system perturbed by…
We discuss a new completely integrable case of the time-dependent Schroedinger equation in $R^n$ with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator…