arXiv subjects

B. A. Nikolov

Publications and source records attributed to B. A. Nikolov.

5 recordsLinked to original sources

arXiv2009

On the Uncertainty Relations in Stochastic Mechanics

It is shown that the Bohm equations for the phase $S$ and squared modulus $ρ$ of the quantum mechanical wave function can be derived from the classical ensemble equations admiting an aditional momentum $p_s$ of the form proportional to the osmotic velocity in the Nelson stochastic mechanics and using the variational principle with appropriate change of variables. The possibility to treat grad$S$ and $p_s$ as two parts of the momentum of quantum ensemble particles is considered from the view point of uncertainty relations of Robertson - Schroedinger type on the examples of the stochastic image of quantum mechanical canonical coherent and squeezed states.

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arXiv2004

Geometric Quantization, Coherent States and Stochastic Measurements

The geometric quantization problem is considered from the point of view of the Davies and Lewis approach to quantum mechanics. The influence of the measuring device is accounted in the classical and quantum case and it is shown that the conditions of the measurement define the type of quantization (Weyl, normal, antinormal, etc.). The quantum states and quantum operators are obtained by means of the projection, defined from the system of generalized coherent states.

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arXiv2004

On the Dynamics of Generalized Coherent States. I. Exact and Stable Evolution

The exact and stable evolutions of generalized coherent states (GCS) for quantum systems are considered by making use of the time-dependent integrals of motion method and of the Klauder approach to the relationship between quantum and classical mechanics. It is shown that one can construct for any quantum system overcomplete family of states (OFS), related to the unitary representations of the Lie group G by means of integral of motion generators, and the possibility of using this group as a dynamical symmetry group is pointed out. The relation of the OFS with quantum measurement theory is also established.

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arXiv2004

On the Dynamics of Generalized Coherent States. II. Classical Equations of Motions

Using the Klauder approach the stable evolution of generalized coherent states (GCS) for some groups (SU(2), SU(1,1) and SU(N)) is considered and it is shown that one and the same classical solution z(t) can correctly characterize the quantum evolution of many different (in general nonequivalent) systems. As examples some concrete systems are treated in greater detail: it is obtained that the nonstationary systems of the singular oscillator, of the particle motion in a magnetic field, and of the oscillator with friction all have stable SU(1,1) GCS whose quantum evolution is determined by one and the same classical function z(t). The physical properties of the constructed SU(1,1) GCS are discussed and it is shown particularly that in the case of discrete series D_k^+ they are those states for which the quantum mean values coincide with the statistical ones for an oscillator in a thermostat.

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arXiv2003

Quantum Information as Reduced Classical Information

It is shown on a simple classical model of a quantum particle at rest that information contained into the quantum state (quantum information) can be obtained by integrating the corresponding probability distribution on phase space, i.e. by reduction of the information contained into the classical state.

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