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Actions for an Hierarchy of Attractive Nonlinear Oscillators Including the Quartic Oscillator in 1+1 Dimensions
Actions Hierarchy of Attractive Nonlinear Oscillators the Quartic Oscillator 1+1 Dimensions Mathematical Physics
2012/4/23
In this paper, we present an explicit form in terms of end-point data for the classical action $S_{2n}$ evaluated on extremals satisfying the Hamilton-Jacobi equation for each member of a hierarchy of...
An Invertible Linearization Map for the Quartic Oscillator
Invertible Linearization Map the Quartic Oscillator Mathematical Physics
2012/4/23
The set of world lines for the non-relativistic quartic oscillator satisfying Newton's equation of motion for all space and time in 1-1 dimensions with no constraints other than the "spring" restoring...
Lie-algebraic structure of 2D harmonic oscillator with non-separable complex coupling
Lie-algebra Non-Hermitian quantum mechanics PT-symmetry Multidimensional models Harmonic oscillator Exactly solvable
2011/10/8
Abstract: Using SU(2)X SU(2) Lie-group structure we obtain the algebraization of 2D harmonic oscillator model with complex quadratic coupling. It is shown that the original time-independent Schr\"odin...
A semiclassical heat trace expansion for the perturbed harmonic oscillator
semiclassical heat trace expansion the perturbed harmonic oscillator Spectral Theory
2011/9/9
Abstract: In this paper we study a semiclassical heat trace expansion for perturbations of the harmonic oscillator, by adapting to the semiclassical setting techniques developed by Hitrik and Polterov...
Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials
multiple Charlier polynomials non-Hermitian Hamiltonians algebraic model
2011/7/26
Abstract: A set of r non-Hermitian oscillator Hamiltonians in r dimensions is shown to be simultaneously diagonalizable. Their spectra is real and the common eigenstates are expressed in terms of mult...
Dissipation evidence for the quantum damped harmonic oscillator via pseudo-bosons
the quantum damped harmonic oscillator pseudo-bosons
2011/7/26
Abstract: It is known that a self-adjoint, time-independent hamiltonian can be defined for the quantum damped harmonic oscillator. We show here that the two vacua naturally associated to this operator...
The su(2)_α Hahn oscillator and a discrete Hahn-Fourier transform
su(2)_α Hahn oscillator discrete Hahn-Fourier High Energy Physics
2011/7/25
Abstract: We define the quadratic algebra su(2)_{\alpha} which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with...
Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state
quantum ground optomechanical micromechanical oscillator
2010/11/8
Cooling a mesoscopic mechanical oscillator to its quantum ground state is elementary for the preparation and control of low entropy quantum states of large scale objects. Here, we pre-cool a 70-MHz mi...
Decoherence in a quantum harmonic oscillator monitored by a Bose-Einstein condensate
Decoherence quantum harmonic oscillator monitored Bose-Einstein condensate
2010/11/9
We investigate the dynamics of a quantum oscillator, whose evolution is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double well potential. It is demonstrated that the oscillat...
Dynamics of a qubit coupled to a dissipative nonlinear quantum oscillator: an effective bath approach
Dynamics qubit coupled dissipative nonlinear quantum oscillator effective bath approach
2010/11/8
We consider a qubit coupled to a nonlinear quantum oscillator, the latter coupled to an Ohmic bath, and investigate the qubit dynamics. This composed system can be mapped onto that of a qubit coupled...
Generalized quantum isotonic nonlinear oscillator in d dimensions
Generalized quantum isotonic nonlinear oscillator d dimensions
2010/11/9
We present a supersymmetric analysis for the d-dimensional Schroedinger equation with the generalized isotonic nonlinear-oscillator potential V(r)={B^2}/{r^{2}}+\omega^{2} r^{2}+2g{(r^{2}-a^{2})}/{(r^...
Functional renormalization group for quantized anharmonic oscillator
Functional renormalization group quantized anharmonic oscillator
2010/10/27
Functional renormalization group methods formulated in the real-time formalism are applied to
the O(N) symmetric quantum anharmonic oscillator, considered as a 0 + 1 dimensional quantum
field-theori...
Analysis of a continuous-variable quadripartite cluster state from a single optical parametric oscillator
continuous-variable quadripartite cluster state single optical parametric oscillator
2010/10/20
We examine the feasibility of generating continuous-variable multipartite entanglement in an
intra-cavity quadruply concurrent downconversion scheme that has been proposed for the generation of clust...
Semiclassical theory of energy diffusive escape in a Duffing oscillator
Semiclassical theory energy diffusive escape Duffing oscillator
2010/10/27
Motivated by recent experimental progress to read out quantum bits implemented in superconducting circuits via the phenomenon of dynamical bifurcation, transitions between steady orbits in a driven an...
Ultimate quantum bounds on mass measurements with a nano-mechanical oscillator
Ultimate quantum bounds mass measurements nano-mechanical oscillator
2010/10/21
Nano-mechanical resonators have a large potential as sensors of very small adsorbed masses,
down to the atomic level and beyond. Here I establish the fundamental lower bound on the mass
that can be ...