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Author

Vladimir I. Man’ko

Bio: Vladimir I. Man’ko is an academic researcher from Moscow Institute of Physics and Technology. The author has contributed to research in topics: Quantum state & Probability distribution. The author has an hindex of 53, co-authored 665 publications receiving 13825 citations. Previous affiliations of Vladimir I. Man’ko include Lebedev Physical Institute & Tomsk State University.


Papers
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Journal ArticleDOI
TL;DR: In this paper, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy.
Abstract: The notion of f-oscillators generalizing q-oscillators is introduced. For classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy. The f-coherent states (nonlinear coherent states) generalizing q-coherent states are constructed. Applied to quantum optics, photon distribution function, photon number means, and dispersions are calculated for the f-coherent states as well as the Wigner function and Q-function. As an example, it is shown how this nonlinearity may affect the Planck distribution formula.

571 citations

Journal ArticleDOI
TL;DR: In this article, the authors introduce even and odd coherent states, where the transition amplitudes between the energy levels of a singular nonstationary oscillator in the case of constant frequency in the remote past and future and generating functions for these amplitudes are obtained, by a method similar to the usual coherent-state method.

513 citations

Journal ArticleDOI
TL;DR: By using a generalization of the optical tomography technique, the authors describe the dynamics of a quantum system in terms of equations for a purely classical probability distribution which contains complete information about the system.

484 citations

Journal ArticleDOI
TL;DR: In this paper, the authors reviewed the theory of fair probability distributions (i.e. tomographic probabilities) in a pedagogical style, and the relation between the quantum state description and the classical state description is elucidated.
Abstract: Starting from the famous Pauli problem on the possibility of associating quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e. tomographic probabilities) is reviewed in a pedagogical style. The relation between the quantum state description and the classical state description is elucidated. The difference between those sets of tomograms is described by inequalities equivalent to a complete set of uncertainty relations for the quantum domain and to non-negativity of probability density on phase space in the classical domain. The intersection of such sets is studied. The mathematical mechanism that allows us to construct different kinds of tomographic probabilities like symplectic tomograms, spin tomograms, photon number tomograms, etc is clarified and a connection with abstract Hilbert space properties is established. The superposition rule and uncertainty relations in terms of probabilities as well as quantum basic equations like quantum evolution and energy spectra equations are given in an explicit form. A method to check experimentally the uncertainty relations is suggested using optical tomograms. Entanglement phenomena and the connection with semigroups acting on simplexes are studied in detail for spin states in the case of two-qubits. The star-product formalism is associated with the tomographic probability formulation of quantum mechanics.

313 citations

Journal ArticleDOI
TL;DR: A spin state reconstruction procedure similar to the symplectic tomography is considered in this paper, where a quantum evolution equation for the classical-like positive distribution function is found, and generalization to arbitrary values of angular momentum is discussed.

294 citations


Cited by
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08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

01 Jan 2016
TL;DR: The table of integrals series and products is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
Abstract: Thank you very much for downloading table of integrals series and products. Maybe you have knowledge that, people have look hundreds times for their chosen books like this table of integrals series and products, but end up in harmful downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they cope with some harmful virus inside their laptop. table of integrals series and products is available in our book collection an online access to it is set as public so you can get it instantly. Our book servers saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the table of integrals series and products is universally compatible with any devices to read.

4,085 citations

Journal ArticleDOI
TL;DR: The field of cavity optomechanics explores the interaction between electromagnetic radiation and nano-or micromechanical motion as mentioned in this paper, which explores the interactions between optical cavities and mechanical resonators.
Abstract: We review the field of cavity optomechanics, which explores the interaction between electromagnetic radiation and nano- or micromechanical motion This review covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation pressure force, the large variety of experimental systems which exhibit this interaction, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and proposals for future cavity quantum optomechanics experiments In addition, we describe the perspectives for fundamental quantum physics and for possible applications of optomechanical devices

4,031 citations

Proceedings Article
14 Jul 1996
TL;DR: The striking signature of Bose condensation was the sudden appearance of a bimodal velocity distribution below the critical temperature of ~2µK.
Abstract: Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

3,530 citations

Journal ArticleDOI
TL;DR: In this article, the authors review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications, including shape invariance and operator transformations, and show that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials.

2,688 citations