Related papers: Propagator of Quantum Systems in the Probability R…
In quantum experiments the acquisition and representation of basic experimental information is governed by the multinomial probability distribution. There exist unique random variables, whose standard deviation becomes asymptotically…
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…
The quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta are considered. It is found that an appropriate ordering procedure exists which allows to convert the classical integrals into their…
We investigate dispersive and Strichartz estimates for the Schr\"{o}dinger time evolution propagator $\mathrm{e}^{-\mathrm{i}tH}$ on a star-shaped metric graph. The linear operator, $H$, taken into consideration is the self-adjoint…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
In this article we propose a generalization of the theory of diffusion approximation for random ODE to a nonlinear system of random Schr\"{o}dinger equations. This system arises in the study of pulse propagation in randomly birefringent…
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…
We derive a nonlinear envelope equation to describe the propagation of broadband optical pulses in second order nonlinear materials. The equation is first order in the propagation coordinate and is valid for arbitrarily wide pulse…
In this paper we suggest a simple mathematical procedure to derive the classical probability density of quantum systems via Bohr's correspondence principle. Using Fourier expansions for the classical and quantum distributions, we assume…
We study the tomography of propagators for spin systems in the context of finite-dimensional Wigner representations, which completely characterize and visualize operators using shapes assembled from linear combinations of spherical…
The method of separation of variables is shown to apply to both the classical and quantum Neumann model. In the classical case this nicely yields the linearization of the flow on the Jacobian of the spectral curve. In the quantum case the…
The macro-objectivation problem derives from the fact that the Schrodinger equation is linear and thus requires that a macroscopic system interacting with an entangled state must be entangled as well. However, such a requirement entails…
The Schrodinger and Heisenberg pictures are equivalent formulations of quantum mechanics. Here we use the Schrodinger picture to calculate the decoherence that occurs when an optical Schrodinger cat state is passed through a beam splitter.…
Explicit expressions for most interesting quantum operators in optical tomography representation are found. General formalism of symbols of operators is presented in optical tomographic representation. The symbols of the operators are found…
In a generalized Heisenberg/Schroedinger picture we use an invariant space-time transformation to describe the motion of a relativistic particle. We discuss the relation with the relativistic mechanics and find that the propagation of the…
In the probability representation of quantum mechanics, quantum states are represented by a classical probability distribution, the marginal distribution function (MDF), whose time dependence is governed by a classical evolution equation.…
One of the most important mathematical tools necessary for Quantum Field Theory calculations is the field propagator. Applications are always done in terms of plane waves and although this has furnished many magnificent results, one may…
In this work, we make use of Lie algebraic methods to obtain the time evolution operator for an optomechanical system with linear and quadratic couplings between the field and the mechanical oscillator. Firstly, we consider the case of a…
The Lindblad master equation for an open quantum system with a Hamiltonian containing an arbitrary potential is written as an equation for the Wigner distribution function in the phase space representation. The time derivative of this…
A new approach to multi-dimensional quantum scattering by the infinite order discrete variable representation is presented. Determining the expansion coefficients of the wave function at the asymptotic regions by the solution of the…