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 classical and quantum propagators for two different time intervals. If these propagators follow one another in a Fibonacci sequence we get a discrete quasiperiodic system. A theorem due to Nielsen provides a novel conserved quantity for this system. The Nielsen quantity controls the transition between commutative and non-commutative propagation in time. The quasiperiodically kicked oscillator moreover is dominated by quasiperiodic analogues of the Floquet theorem.

Propagation in time of some classical/quantum systems and Nielsen's conserved quantity

The symplectic quantum tomography for the general linear quantization is introduced. Using the approach based upon the Wigner function techniques the evolution equation of quantum tomograms is derived for a parametric driven oscillator.

http://iopscience.iop.org/article/10.1088/0031-8949/79/01/015004/pdf

Evolution equation of quantum tomograms for a driven oscillator in the case of the general linear quantization

We study the properties of marginal distributions-projections of the phase space representation of a physical system-under relativistic transforms. We consider the Galileo case as well as the Lorentz transforms exploiting the relativistic oscillator model used for describing the mass spectrum of elementary particles.

Relativistic properties of marginal distributions

SU(2) and SU(1,1) group parametrizations via qubit induced correlated probabilities

/pdf/neravenstvo-bella-dlia-dvuchastichnykh-smeshannykh-spinovykh-1ogmdv3x82.pdf

Vladimir I. Man’ko

Papers

Propagation in time of some classical/quantum systems and Nielsen's conserved quantity

Evolution equation of quantum tomograms for a driven oscillator in the case of the general linear quantization

Relativistic properties of marginal distributions

SU(2) and SU(1,1) group parametrizations via qubit induced correlated probabilities

Неравенство Белла для двучастичных смешанных спиновых состояний@@@Bell's Inequality for Two-Particle Mixed Spin States