Related papers: Linearly coupled quantum harmonic oscillators and …
Classical integrable Hamiltonian systems generated by elements of the Poisson commuting ring of spectral invariants on rational coadjoint orbits of the loop algebra $\wt{\gr{gl}}^{+*}(2,{\bf R})$ are integrated by separation of variables in…
We analyze the quantum entanglement between two interacting atoms trapped in a spherical harmonic potential. At ultra-cold temperature, ground state entanglement is generated by the dominated s-wave interaction. Based on a regularized…
The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the oscillator. Harmonic oscillators with different…
We study the quantum mechanical harmonic oscillator in two and three dimensions, with particular attention to the solutions as represents of their respective symmetry groups: O(2), O(3), and O(2,1). Solving the Schrodinger equation by…
The quantum quartic anharmonic oscillator with the Hamiltonian $H=\frac{1}{2}\left( p^{2}+x^{2}\right) +\lambda x^{4}$ is a classical and fundamental model that plays a key role in various branches of physics, including quantum mechanics,…
We map the Hilbert space of the quantum Harmonic oscillator to the space of Glauber's $n$th-order intensity correlators, in effect showing "the correlations between the correlators" for a random sampling of the quantum states. In…
We study the non-equilibrium dynamics of two coupled oscillators interacting with their own heat baths of quantum scalar fields at different temperature $T_1$ and $T_2$ with bilinear couplings between them. We particularly focus on the…
Application of the path-integral approach to continuous measurements leads to effective Lagrangians or Hamiltonians in which the effect of the measurement is taken into account through an imaginary term. We apply these considerations to…
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0< q < 1, these normalized states form an overcomplete set that resolves the unity with respect to an explicit…
We summarize recent work showing that the $1/r^2$ model of interacting particles in 1-dimension is a universal Hamiltonian for quantum chaotic systems. The problem is analyzed in terms of random matrices and of the evolution of their…
It is shown that in a quantized space determined by the $B_2\quad (O(5)=Sp(4))$ algebra with three dimensional parameters of the length $L^2$, momentum $(Mc)^2$, and action $S$, the spectrum of the Coulomb problem with conserving Runge-Lenz…
We present a proposal for heralded entanglement between two quantum dots via Hong--Ou--Mandel effect. Each of the quantum dots, drived off-resonance by two lasers, can be entangled with the coherent cavity mode. The output photons from the…
The ability to coherently couple arbitrary harmonic oscillators in a fully-controlled way is an important tool to process quantum information. Coupling between quantum harmonic oscillators has previously been demonstrated in several…
In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be…
A set of coupled complex Ginzburg-landau type amplitude equations which operates near a Hopf-Turing instability boundary is analytically investigated to show localized oscillatory patterns. The spatial structure of those patterns are the…
We consider the Dirac equation with a generalized uncertainty principle in the presence of the Harmonic interaction and an external magnetic field. By doing the study in the momentum space, the problem solved in an exact analytical manner…
The quantum harmonic oscillator with parity-time ($\mathcal{PT}$) symmetry, obtained from the ordinary (Hermitian) quantum harmonic oscillator by an imaginary displacement of the spatial coordinate, provides an important and…
The entanglement Hamiltonian (EH) provides the most comprehensive characterization of bipartite entanglement in many-body quantum systems. Ground states of local Hamiltonians inherit this locality, resulting in EHs that are dominated by…
We introduce a method of quantum tomography for a continuous variable system in position and momentum space. We consider a single two-level probe interacting with a quantum harmonic oscillator by means of a class of Hamiltonians, linear in…
Quantum entanglement is considered, by and large, to be a very delicate and non-robust phenomenon that is very hard to maintain in the presence of noise, or non-zero temperatures. In recent years however, and motivated, in part, by a quest…