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 …

I and i

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Table Of Integrals Series And Products

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

Cavity Optomechanics

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.

Bose-Einstein condensation in a gas of sodium atoms

http://cds.cern.ch/record/262851/files/9405029.pdf

Supersymmetry and quantum mechanics

We consider information characteristics of a single qudit (spin j = 9/2), such as the von Neumann entropy, and define the von Neumann mutual information for this system, which does not contain any subsystems. In addition, we consider the von Neumann information of a qudit toy model as a function of real parameters. The inequalities obtained describe the quantum hidden correlations in the single-qudit system.

New Entropic Inequalities for Qudit (Spin j = 9/2)

We consider optical tomography of photon Fock state superpositions in connection with recent experimental achievements. The emphasis is put on the fact that it suffices to represent the measured tomogram as a main result of the experiment. We suggest a test for checking the correctness of experimental data. Explicit expressions for optical tomograms of Fock state superpositions are given in terms of Hermite polynomials. Particular cases of vacuum and low photon-number state superposition are considered as well as influence of thermal noise on state purity is studied.

Optical tomography of Fock state superpositions

Physical Mechanisms of Activation of Radical Reactions in Aqueous Solutions under Mechanical and Magnetic Effect: Problem of Singlet Oxygen

Using the entropic inequalities for Shannon and Tsallis entropies new inequalities for some classical polynomials are obtained. To this end, an invertible mapping for the irreducible unitary representation of groups $SU(2)$ and $SU(1,1)$ like Jacoby polynomials and Gauss' hypergeometric functions, respectively, are used.

Entropic inequalities for matrix elements of rotation group irreducible representations

The symmetry properties under permutation of tomograms representing the states of a system of identical particles are studied. Starting from the action of the permutation group on the density matrix we define its action on the tomographic probability distribution. Explicit calculations are performed in the case of the two-dimensional harmonic oscillator.

Vladimir I. Man’ko

Papers

New Entropic Inequalities for Qudit (Spin j = 9/2)

Optical tomography of Fock state superpositions

Physical Mechanisms of Activation of Radical Reactions in Aqueous Solutions under Mechanical and Magnetic Effect: Problem of Singlet Oxygen

Entropic inequalities for matrix elements of rotation group irreducible representations

Permutation symmetry for the tomographic probability distribution of a system of identical particles