相关论文: Classical and quantum coupled oscillators: symplec…

A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the…

Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…

We investigate the quantum algorithm of Babbush et al. (arXiv:2303.13012v3) for simulating coupled harmonic oscillators, which promises exponential speedups over classical methods. Focusing on linearly connected oscillator chains, we bridge…

Coherent states of the two dimensional harmonic oscillator are constructed as superpositions of energy and angular momentum eigenstates. It is shown that these states are Gaussian wave-packets moving along a classical trajectory, with a…

We describe a quantum system consisting of a one-dimensional linear chain of n identical harmonic oscillators coupled by a nearest neighbor interaction. Two boundary conditions are taken into account: periodic boundary conditions (where the…

We develop an approach in solving exactly the problem of three-body oscillators including general quadratic interactions in the coordinates for arbitrary masses and couplings. We introduce a unitary transformation of three independent…

Courses on undergraduate quantum mechanics usually focus on solutions of the Schr\"odinger equation for several simple one-dimensional examples. When the notion of a Hilbert space is introduced only academic examples are used, such as the…

We develop a general theoretical framework of semiclassical phase reduction for analyzing synchronization of quantum limit-cycle oscillators. The dynamics of quantum dissipative systems exhibiting limit-cycle oscillations are reduced to a…

A prepotential approach to constructing the quantum systems with dynamical symmetry is proposed. As applications, we derive generalizations of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with…

We consider the coupling of quantum fields to classical gravity in the formalism of ensembles on configuration space, a model that allows a consistent formulation of interacting classical and quantum systems. Explicit calculations show that…

The system of two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem already addressed by many authors that we present here in some fresh points of view and carry on smoothly a whole…

The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the $N$-fold application of the transformation is also established, and…

In this work, we perform a careful study of an special arrangement of coupled systems that consists of two external harmonic oscillators weakly coupled to an arbitrary network (data bus) of strongly interacting oscillators. Our aim is to…

Constrained Hamiltonian dynamics of a quantum system of nonlinear oscillators is used to provide the mathematical formulation of a coarse-grained description of the quantum system. It is seen that the evolution of the coarse-grained system…

We consider a system of N phase oscillators having randomly distributed natural frequencies and diagonalizable interactions among the oscillators. We show that in the limit of N going to infinity, all solutions of such a system are…

We propose a simple model of classical open system consisting of two subsystems all stationary states of which correspond to phase synchronization between the subsystems. The model is generalized to quantum systems in a finite-dimensional…

Classical coupled harmonic oscillator models are capable of describing the optical and infrared response of nanophotonic systems where a cavity photon couples to dipolar matter excitations. The distinct forms of coupling adopted in these…

The one-dimensional quantum harmonic oscillator problem is examined via the Laplace transform method. The stationary states are determined by requiring definite parity and good behaviour of the eigenfunction at the origin and at infinity.

The synchronization properties of two self-sustained quantum oscillators are studied in the Wigner representation. Instead of considering the quantum limit of the quantum van-der-Pol master equation we derive the quantum master equation…

For $N$-coupled generalized time-dependent oscillators, primary invariants and a generalized invariant are found in terms of classical solutions. Exact quantum motions satisfying the Heisenberg equation of motion are also found. For number…