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Some inequalities for probability vector are discussed. The probability representation of quantum mechanics where the states are mapped onto probability vectors (either finite or infinite dimensional) called the state tomograms is used.…
We consider a one dimensional evolution problem modeling the dynamics of an acoustic field coupled with a set of mechanical oscillators. We analyze solutions of the system of ordinary and partial differential equations with time-dependent…
We show how to construct general probabilistic theories that contain an energy observable dependent on position and momentum. The construction is in accordance with classical and quantum theory and allows for physical predictions, such as…
The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation. It is found that pairs of nonclassical trajectories contribute to the path-integral representation of the Wigner…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
We propose a gate-based quantum algorithm for the prediction step of Bayesian state estimation based on the Fokker-Planck equation on a discretized position-velocity state space. The probability density is encoded in the amplitudes of a…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…
The quadrature distribution for the quantum damped oscillator is introduced in the framework of the formulation of quantum mechanics based on the tomography scheme. The probability distribution for the coherent and Fock states of the damped…
We study a class of dynamical systems for which the motions can be described in terms of geodesics on a manifold (ordinary potential models can be cast into this form by means of a conformal map). It is rigorously proven that the geodesic…
The phenomenology of quantum systems in curved space-times is among the most fascinating fields of physics, allowing --often at the gedankenexperiment level-- constraints on tentative theories of quantum gravity. Determining the dynamics of…
We calculate transition amplitudes and probabilities between the coherent and Fock states of a quantum harmonic oscillator with a moving center for an arbitrary law of motion. These quantities are determined by the Fourier transform of the…
Modifications of quantum mechanics are considered, in which the state vector of any system, large or small, undergoes a stochastic evolution. The general class of theories is described, in which the probability distribution of the state…
The question of the representation of quantum stationary partially polarized waves as random superpositions of different polarization ellipses is addressed. To this end, the Bohmian formulation of quantum mechanics is considered and…
The problem of defining time (or phase) operator for three-dimensional harmonic oscillator has been analyzed. A new formula for this operator has been derived. The results have been used to demonstrate a possibility of representing…
We consider a driven quantum harmonic oscillator strongly coupled to a heat bath. Starting from the exact quantum Langevin equation, we use a Green's function approach to determine the corresponding semiclassical equation for the Wigner…
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…
Usual approach to investigate the statistical properties of deterministically thermostated systems is to analyze the regime of the system motion. In this work the cumulant analysis is used to study the properties of the stationary…
The linear canonical transforms of position and momentum are used to construct the tomographic probability representation of quantum states where the fair probability distribution determines the quantum state instead of the wave function or…
For a time-dependent $\tau$-periodic harmonic oscillator of two linearly independent homogeneous solutions of classical equation of motion which are bounded all over the time (stable), it is shown, there is a representation of states cyclic…
This paper develops further the semi-classical theory of an harmonic oscillator acted on by a Gaussian white noise force discussed in (arXiv:1508.02379). Here I add to that theory the effects of Brownian damping (friction). Albeit…