We analyze the distribution of eigenvalues quantum-mechanical rotating harmonic oscillator by means Frobenius method. A suitable ansatz leads to a three-term recurrence relation for expansion coefficients. Truncation series yields some particular and eigenfunctions in exact analytical form. The former can be organized such way that one obtains information about whole spectrum model.

We derive and analyze the Born-Markov master equation for a quantum harmonic oscillator interacting with a bath of independent two-level systems. This hitherto virtually unexplored model plays a fundamental role as one of the four “canonical” system-environment models for decoherence and dissipation. To investigate the influence of further couplings of the environmental spins to a dissipative b...

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, ...

Factors influencing the rates of quantum mechanical particle transfer reactions in many-body systems are discussed. The investigations are carried out on a simple model for a proton transfer reaction that captures generic features seen in more realistic models of condensed phase systems. The model involves a bistable quantum oscillator coupled to a one-dimensional double-well reaction coordinat...

The quantum properties of electromagnetic, mechanical or other harmonic oscillators can be revealed by investigating their strong coherent coupling to a single quantum two level system in an approach known as cavity quantum electrodynamics (QED). At temperatures much lower than the characteristic energy level spacing the observation of vacuum Rabi oscillations or mode splittings with one or a f...

We present a class of waveguide arrays that is the classical analog of a quantum harmonic oscillator, where the mass and frequency depend on the propagation distance. In these photonic lattices, refractive indices and second-neighbor couplings define the mass and frequency of the analog quantum oscillator, while first-neighbor couplings are a free parameter to adjust the model. The quantum mode...

In this diploma work we discuss a soliton in the context of quantum field theory. The model considered is the O(3) nonlinear σ-model in 3 dimensions with a symmetry breaking mass term. The stability properties of the circularly symmetric “hedgehog” soliton with topological number 1 is analyzed both classically and quantum mechanically. As far as classical field mechanics is concerned, a numeric...

We perform an analytical study of the correspondence between a classical oscillator with frequency perturbed by a coloured noise and the one-dimensional Anderson-type model with correlated diagonal disorder. It is rigorously shown that localisation of electronic states in the quantum model corresponds to exponential divergence of nearby trajectories of the classical random oscillator. We discus...

Considering a multi-dimensional q-oscillator invariant under the (non quantum) group U(n), we construct a q-deformed Levi-Civita epsilon tensor from the inner product states. The invariance of this q-epsilon tensor is shown to yield the quantum group SLq(n) and establishes the relationship of the U(n) invariant q-oscillator to quantum groups and quantum group related oscillators. Furthermore th...

We derive a microscopic bound on the maximal field variation of the inflaton during warped Dbrane inflation. By a result of Lyth, this implies an upper limit on the amount of gravitational waves produced during inflation. We show that a detection at the level r > 0.01 would falsify slow roll D-brane inflation. In DBI inflation, detectable tensors may be possible in special compactifications, pr...