相关论文: Algebraic treatment of $\mathcal{PT}$-symmetric co…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
We consider a set of N linearly coupled harmonic oscillators and show that the diagonalization of this problem can be put in geometrical terms. The matrix techniques developed here allowed for solutions in both the classical and quantum…
This paper examines chains of $N$ coupled harmonic oscillators. In isolation, the $j$th oscillator ($1\leq j\leq N$) has the natural frequency $\omega_j$ and is described by the Hamiltonian $\frac{1}{2}p_j^2+\frac{1}{2}\omega_j^2x_j^2$. The…
We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the…
The inspiration for this theoretical paper comes from recent experiments on a PT-symmetric system of two coupled optical whispering galleries (optical resonators). The optical system can be modeled as a pair of coupled linear oscillators,…
The harmonic oscillator is one of the most studied systems in Physics with a myriad of applications. One of the first problems solved in a Quantum Mechanics course is calculating the energy spectrum of the simple harmonic oscillator with…
The Hermiticity axiom of quantum mechanics guarantees that the energy spectrum is real and the time evolution is unitary (probability-preserving). Nevertheless, non-Hermitian but $\mathcal{PT}$-symmetric Hamiltonians may also have real…
The symmetry algebra of the two-dimensional quantum harmonic oscillator with rational ratio of frequencies is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are…
We perform a perturbative calculation of the physical observables, in particular pseudo-Hermitian position and momentum operators, the equivalent Hermitian Hamiltonian operator, and the classical Hamiltonian for the PT-symmetric cubic…
Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the delta-kicked harmonic oscillator, and present a theoretical discussion of the quantum…
We take a qualitative comparative look at quantum and classical quartic anharmonic oscillators. It has been shown that the behavior of the quantum anharmonic oscillator mimics that of the classical anharmonic oscillators with the…
The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat…
We consider a class of one-dimensional nonhermitian oscillators and discuss the relationship between the real eigenvalues of PT-symmetric oscillators and the resonances obtained by different authors. We also show the relationship between…
The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic…
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of…
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
The system of two $Q$-deformed oscillators coupled so that the total Hamiltonian has the su$_Q$(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the…
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 standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…