Search results for "harmonic oscillator"
showing 10 items of 109 documents
Geometric-phase backaction in a mesoscopic qubit-oscillator system
2012
We illustrate a reverse Von Neumann measurement scheme in which a geometric phase induced on a quantum harmonic oscillator is measured using a microscopic qubit as a probe. We show how such a phase, generated by a cyclic evolution in the phase space of the harmonic oscillator, can be kicked back on the qubit, which plays the role of a quantum interferometer. We also extend our study to finite-temperature dissipative Markovian dynamics and discuss potential implementations in micro- and nanomechanical devices coupled to an effective two-level system. © 2012 American Physical Society.
Mathematical models on the way from superstring to photon
2002
Molecular modeling and experimental studies on structure and NMR parameters of 9-benzyl-3,6-diiodo-9H-carbazole
2015
A combined experimental and theoretical study has been performed on 9-benzyl-3,6-diiodo-9H-carbazole. Experimental X-ray (100.0 K) and room-temperature 13C NMR studies were supported by advanced density functional theory (DFT) calculations. The non relativistic structure optimization was performed and the 13C nuclear magnetic shieldings were predicted at the relativistic level of theory using the Zeroth Order Regular Approximation (ZORA). The changes in the benzene and pyrrole rings compared to the unsubstituted carbazole or the parent molecules were discussed in terms of aromaticity changes using the harmonic oscillator model of aromaticity (HOMA) and the nucleus independent chemical shift…
The “Maslov Anomaly” for the Harmonic Oscillator
2001
Specializing the discussion of the previous section to the harmonic oscillator we have for \(N = 1,\ \eta ^{a} = (p,x),\ a = 1,2,\ \eta ^{1} \equiv p,\ \eta ^{2} \equiv x\) $$\displaystyle{ H(p,x) = \frac{1} {2}\eta ^{a}\eta ^{a} = \frac{1} {2}{\bigl (p^{2} + x^{2}\bigr )}\;. }$$ (30.1) The only conserved quantity is J = H. In the action we need the combination $$\displaystyle{ \frac{1} {2}\eta ^{a}\omega _{ ab}\dot{\eta }^{b} -\mathcal{H}(\eta ) = \frac{1} {2}\eta ^{a}\left [\omega _{ ab} \frac{d} {dt} -{\bigl ( 1 + A(t)\bigr )}\mathrm{1l}_{ab}\right ]\eta ^{b} }$$ (30.2) and $$\displaystyle{ \tilde{M}_{\phantom{a}b}^{a} =\omega ^{ac}\partial _{ c}\partial _{b}(H + AJ\,) ={\bigl ( 1 + A(t)…
Berry Phase and Parametric Harmonic Oscillator
2001
Our concern in this section is once more with the time-dependent harmonic oscillator with Lagrangian $$\displaystyle{ L = \frac{1} {2}\dot{x}^{2} -\frac{1} {2}\omega ^{2}(t)x^{2}\;. }$$ To present a coherent picture of the whole problem, let us briefly review some of the results of Chap. 21. There we found the propagation function
Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons
2010
In a series of recent papers one of us has analyzed in some details a class of elementary excitations called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. Here, after a two-dimensional extension of the general framework, we apply the theory to a generalized version of the two-dimensional Hamiltonian describing Landau levels. Moreover, for this system, we discuss coherent states and we deduce a resolution of the identity. We also consider a different class of examples arising from a classical system, i.e. a damped harmonic oscillator.
Weak pseudo-bosons
2020
We show how the notion of {\em pseudo-bosons}, originally introduced as operators acting on some Hilbert space, can be extended to a distributional settings. In doing so, we are able to construct a rather general framework to deal with generalized eigenvectors of the multiplication and of the derivation operators. Connections with the quantum damped harmonic oscillator are also briefly considered.
Modular Structures on Trace Class Operators and Applications to Landau Levels
2009
The energy levels, generally known as the Landau levels, which characterize the motion of an electron in a constant magnetic field, are those of the one-dimensional harmonic oscillator, with each level being infinitely degenerate. We show in this paper how the associated von Neumann algebra of observables displays a modular structure in the sense of the Tomita–Takesaki theory, with the algebra and its commutant referring to the two orientations of the magnetic field. A Kubo–Martin–Schwinger state can be built which, in fact, is the Gibbs state for an ensemble of harmonic oscillators. Mathematically, the modular structure is shown to arise as the natural modular structure associated with the…
Some results on the rotated infinitely deep potential and its coherent states
2021
The Swanson model is an exactly solvable model in quantum mechanics with a manifestly non self-adjoint Hamiltonian whose eigenvalues are all real. Its eigenvectors can be deduced easily, by means of suitable ladder operators. This is because the Swanson Hamiltonian is deeply connected with that of a standard quantum Harmonic oscillator, after a suitable rotation in configuration space is performed. In this paper we consider a rotated version of a different quantum system, the infinitely deep potential, and we consider some of the consequences of this rotation. In particular, we show that differences arise with respect to the Swanson model, mainly because of the technical need of working, he…
Time-dependent perturbation treatment of independent Raman schemes
2007
The problem of a trapped ion subjected to the action of two or more independent Raman schemes is analysed through a suitable time-dependent perturbative approach based on the factorization of the evolution operator in terms of other unitary operators. We show that the dynamics of the system may be traced back to an effective Hamiltonian up to a suitable dressing. Moreover, we give the method to write the master equation corresponding to the case wherein spontaneous decays occur.