相关论文: Quantum-Classical System: Simple Harmonic Oscillat…

Motivated by improving the understanding of the quantum-to-classical transition we use a simple model of classical discrete interactions for studying the discrete-to-continuous transition in the classical harmonic oscillator. A parallel is…

We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of…

In this paper, we consider an anharmonic perturbation to the harmonic oscillator in the classical and the quantum regimes. We analyse a relativistic particle subjected to such a potential and then proceed to study a gas of such particles.…

Canonical quantization has taught us great things. A common example is that of the harmonic oscillator, which is like swinging a ball on a string back and forth. However, the half-harmonic oscillator blocks the ball at the bottom and then…

A consistent description of interactions between classical and quantum systems is relevant to quantum measurement theory, and to calculations in quantum chemistry and quantum gravity. A solution is offered here to this longstanding problem,…

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…

The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…

We report that upon excitation by a single pulse, the classical harmonic oscillator immersed in classical electromagnetic zero-point radiation, as described by random electrodynamics, exhibits a quantized excitation spectrum in agreement to…

In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.

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…

The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a…

We discuss the exact discretization of the classical harmonic oscillator equation (including the inhomogeneous case and multidimensional generalizations) with a special stress on the energy integral. We present and suggest some numerical…

A quantum particle on a circle in a quadratic potential exhibits a spectrum that is not harmonic, despite having all algebraic properties of the quantum harmonic oscillator. This raises the question where the usual algebraic argument --…

Harmonic inversion techniques have been shown to be a powerful tool for the semiclassical quantization and analysis of quantum spectra of both classically integrable and chaotic dynamical systems. Various computational procedures have been…

The so-called classical limit of quantum mechanics is generally studied in terms of the decoherence of the state operator that characterizes a system. This is not the only possible approach to decoherence. In previous works we have…

Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…

In (quant-ph/0701141) Rajeev studied quantization of the damped simple harmonic oscillator and introduced a complex-valued Hamiltonian (which is normal). In this note we point out that the quantization is interpreted as a quantum mechanics…

The frequency of a classical periodic system and the energy levels of the corresponding quantum system can both be obtained using action variables. We demonstrate the construction of two forms of the action variable for a one dimensional…

There are several regimes in chaotic inflationary cosmology where some part of the system is classical and some other quantum. I describe how to deal with such systems and how to disentangle their dynamics into classical behaviour and…

Precise measurements of tiny forces and displacements play an important role in science and technology. The precision of recent experiments, while beginning to reach the limits imposed by quantum mechanics, is necessarily spoiled by the…