相关论文: ABC-formula and R-operation for decay processes

We give an explicit prescription for experimentally determining the evolution operators which completely describe the dynamics of a quantum mechanical black box -- an arbitrary open quantum system. We show necessary and sufficient…

We consider an open quantum system which contains unstable states. The time evolution of the system can be described by an effective non-hermitian Hamiltonian H_{eff}, in accord with the Wigner--Weisskopf approximation, and an additional…

One of the axioms of quantum field theory is the property of unitarity of the evolution operator. However, if one considers the quantum electrodynamics in the external field in the leading order of perturbation theory, one will find that…

We develop a Lie algebraic approach to systematically calculate the evolution operator of the generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach…

We obtain a time-evolution operator for a forced optomechanical quantum system using Lie algebraic methods when the normalized coupling between the electromagnetic field and a mechanical oscillator, $G/\omega_m$, is not negligible compared…

The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…

In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…

When we quantize a system consisting of a single particle, the proper time $\tau $ and the rest mass $m$ are usually dealt with as parameters. In the present article, however, we introduce a new quantization rule by which these quantities…

Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and…

Time-dependent terms in Hamiltonians and equations of motion are rather important for a quantum-mechanical description of particles with arbitrary spins in nonstationary fields. We use the Foldy-Wouthuysen representation which allows one to…

For relativistic closed systems, an operator is explained which has as stationary eigenvalues the squares of the total cms energies, while the wave function has only half as many components as the corresponding Dirac wave function. The…

Operators play a substantial role in mathematical formalism of quantum mechanics. However, explicit forms of the operators are usually postulated, based on the intuitive assumptions. In this study, variational principle was applied to the…

We present a general framework for finding the time-optimal evolution and the optimal Hamiltonian for a quantum system with a given set of initial and final states. Our formulation is based on the variational principle and is analogous to…

The convolution formula is derived within the framework of the decay-chain method for decay channels with three and four particles in a final state. To get this formula exactly for unstable particle of any type one must modify the…

The role of response operators is well established in quantum mechanics. We investigate their use for universal quantum machine learning models of response properties in molecules. After introducing a theoretical basis, we present and…

We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…

Given a Hamiltonian $H$ on a Hilbert space $\mathcal H$ it is shown that, under the assumption that $\sigma(H)=\sigma_{ac}(H)=R^+$, there exist unique positive operators $T_F$ and $T_B$ registering the Schr\"odinger time evolution generated…

This is an attempt to create a consistent and non-trivial extension of quantum theory, describing in detail the quantum measurement process. A tentative but concrete model is presented, based on the concept of multiple…

It is shown that if the decoherence matrix corresponding to a qubit master equation has a block-diagonal real part, then the evolution is determined by a one-dimensional oscillator equation. Further, when the full decoherence matrix is…

An explicit construction is given of field operators satisfying the free Dirac equation. The quantum expectation of these field operators forms a spinor which satisfies the original Dirac equation. The current operators are defined as pair…