Search results for "HARMONIC OSCILLATOR"
showing 10 items of 109 documents
Tunneling in a ?breathing? double well: Adiabatic and antiadiabatic limits and tunneling suppression
1995
Tunneling in a piecewise harmonic potential coupled to a harmonic oscillator is considered by means of the path integral technique. The reduced propagator for the tunneling particle is calculated explicitly and the tunneling splitting is found in semiclassical approximation. The result holds for arbitrary values of the parameters of the system. From this the adiabatic and antiadiabatic approximations are obtained as particular cases and compared with the results obtained differently. The limit of a strong interaction is also considered. It is found that for strong interaction or equivalently for the harmonic frequency tending to zero the preexponential factor in the tunneling splitting tend…
Partition Function for the Harmonic Oscillator
2001
We start by making the following changes from Minkowski real time t = x0 to Euclidean “time” τ = tE:
Driven harmonic oscillators in the adiabatic Magnus approximation
1993
The time evolution of driven harmonic oscillators is determined by applying the Magnus expansion in the basis set of instantaneous eigenstates of the total Hamiltonian. It is shown that the first-order approximation already provides transition probabilities close to the exact values even in the intermediate regime.
Experimental Setup with Chaotic and Periodic Excitations for Cell Growth Studies
2020
The paper presents circuits used for excitation living cells to increase their growth rate. The main novelty is the proposal of using chaotic oscillations for the electromagnetic excitation. The research is in a preliminary phase and no conclusions have been yet derived for applications in biotechnology.
�ber die Stabilit�t periodischer L�sungen bei zeitabh�ngigen Hamiltonschen Differentialgleichungen von einem Freiheitsgrad
1987
The preservation of certain stable period solutions of the harmonic oscillator under small time-dependent, non-isochronous, and Hamiltonian perturbations is proved.
Subharmonic excitation of the eigenmodes of charged particles in a Penning trap
2004
When parametrically excited, a harmonic system reveals a nonlinear dynamical behaviour which is common to non-deterministic phenomena. The ion motion in a Penning trap -- which can be regarded as a system of harmonic oscillators -- offers the possibility to study anharmonic characteristics when perturbed by an external periodical driving force. In our experiment we excited an electron cloud stored in a Penning trap by applying an additional quadrupole r.f. field to the endcaps. We observed phenomena such as individual and center-of-mass oscillations of an electron cloud and fractional frequencies, so-called subharmonics, to the axial oscillation. The latter show a characteristic threshold b…
Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: a new v…
2012
We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic-oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (E…
Finite-dimensional pseudo-bosons: a non-Hermitian version of the truncated harmonic oscillator
2018
We propose a deformed version of the commutation rule introduced in 1967 by Buchdahl to describe a particular model of the truncated harmonic oscillator. The rule we consider is defined on a $N$-dimensional Hilbert space $\Hil_N$, and produces two biorhogonal bases of $\Hil_N$ which are eigenstates of the Hamiltonians $h=\frac{1}{2}(q^2+p^2)$, and of its adjoint $h^\dagger$. Here $q$ and $p$ are non-Hermitian operators obeying $[q,p]=i(\1-Nk)$, where $k$ is a suitable orthogonal projection operator. These eigenstates are connected by ladder operators constructed out of $q$, $p$, $q^\dagger$ and $p^\dagger$. Some examples are discussed.
A no-go result for the quantum damped harmonic oscillator
2019
Abstract In this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman Lagrangian. In particular, we prove that no square integrable vacuum exists for the natural ladder operators of the system, and that the only vacua can be found as distributions. This implies that the procedure proposed by some authors is only formally correct, and requires a much deeper analysis to be made rigorous.
Motion of the wave-function zeros in spin-boson systems.
1995
In the analytic Bargmann representation associated with the harmonic oscillator and spin coherent states, the wave functions considered as consisting of entire complex functions can be factorized in terms of their zeros in a unique way. The Schr\"odinger equation of motion for the wave function is turned to a system of equations for the zeros of the wave function. The motion of these zeros as a nonlinear flow of points is studied and interpreted for linear and nonlinear bosonic and spin Hamiltonians. Attention is given to the study of the zeros of the Jaynes-Cummings model and to its finite analog. Numerical solutions are derived and dicussed.