Related papers: The transient route to resonance
The three dimensional harmonic oscillator model including a cranking term is used for an energy variational calculation. Energy minima are found under variation of the three oscillator frequencies determining the shape of the system for…
Using the Wigner-Weyl mapping of quantum mechanics to phase space we consider exactly the quantum mechanics of an harmonic oscillator driven by an external white noise force or whose frequency is time dependent, either adiabatically or…
We aim at an understanding of the dynamical properties of a periodically driven damped harmonic oscillator coupled to a Random Field Ising Model (RFIM) at zero temperature, which is capable to show complex hysteresis. The system is a…
We study the time evolution for the quantum harmonic oscillator subjected to a sudden change of frequency. It is based on an approximate analytic solution to the time dependent Ermakov equation for a step function. This approach allows for…
The manner in which probability amplitudes of paths sum up to form wave functions of a harmonic oscillator, as well as other, simple 1-dimensional problems, is described. Using known, closed-form, path-based propagators for each problem, an…
A system obeying the harmonic oscillator equation of motion can be used as a force or proper acceleration sensor. In this short review we derive analytical expressions for the sensitivity of such sensors in a range of different situations,…
Following the Caldeira-Leggett approach to describe dissipative quantum systems the structure function for a harmonic oscillator with Ohmic dissipation is evaluated by an analytic continuation from euclidean to real time. The analytic…
We develop a resonance theory to describe the evolution of open systems with time-dependent dynamics. Our approach is based on piecewise constant Hamiltonians: we represent the evolution on each constant bit using a recently developed…
Adelic quantum mechanics is formulated. The corresponding model of the harmonic oscillator is considered. The adelic harmonic oscillator exhibits many interesting features. One of them is a softening of the uncertainty relation.
We point out that harmonic oscillator coherent states, in coordinate representation, require particular phase factor, in order to represent classical time evolution properly. The presence of such a phase is clearly stated only in a minority…
How do transformers model physics? Do transformers model systems with interpretable analytical solutions, or do they create "alien physics" that are difficult for humans to decipher? We take a step in demystifying this larger puzzle by…
There is recently a surge of interest to cut down the time it takes to change the state of a quantum system adiabatically. We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes designed to…
In this paper, a new approach for constructing Lagrangians for driven and undriven linearly damped systems is proposed, by introducing a redefined time coordinate and an associated coordinate transformation to ensure that the resulting…
Coherently displaced harmonic oscillator number states of a harmonically bound ion can be coupled to two internal states of the ion by a laser-induced motional sideband interaction. The internal states can subsequently be read out in a…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
Theoretically, solutions of the damped harmonic oscillator asymptotically approach equilibrium, i.e., the zero energy state, without ever reaching it exactly, and the critically damped solution approaches equilibrium faster than the…
In this paper it is studied the influence of a minimal thermal environment on the dynamics of a quantum harmonic oscillator (labelled A), prepared in a coherent state. The environment itself consists of a second oscillator (labelled B),…
Motivated by improving the understanding of the quantum-to-classical transition we use a simple model of classical discrete interactions for studying the discrete-to-continuous transition in the classical harmonic oscillator. A parallel is…
The coherent states for twist-deformed oscillator model provided in article [1] are constructed. Besides, it is demonstrated that the energy spectrum of considered model is labeled by two quantum numbers - by so-called main and azimutal…
By definition, the Kraus representation of a harmonic oscillator suffering from the environment effect, modeled as the amplitude damping or the phase damping, is directly given by a simple operator algebra solution. As examples and…