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

/pdf/novye-neravenstva-dlia-tomogramm-v-veroiatnostnom-1x5gt7rgn2.pdf

Новые неравенства для томограмм в вероятностном представлении квантовых состояний@@@New inequalities for tomograms in the probability representation of quantum states

We develop a Radon like transformation, in which $P$ quasiprobability distribution for spin 1/2 states is written in terms the tomographic probability distribution $w$.

https://arxiv.org/pdf/quant-ph/0102038.pdf

Quasiprobability and Probability Distributions for Spin 1/2 States

We define the separability and entanglement notion for particle with spin $s=1$. We consider two cases. In the first the particle is composed of two fermions with $s_1=1/2$ and $s_2=1/2$. In the second case the state is the qutrit state which is not composed system. The notion of negativity and concurrence is defined for the qutrit state. The concurrence and negativity of entangled and separable qutrit states determined by the parameters of the density matrix are explicitly calculated. The maximum entanglement of the qutrit state is observed for maximum values of non diagonal matrix elements of the density matrix. New entropic inequalities for the density matrix of the qutrit state are obtained.

Separability and entanglement of spin $1$ particle

The q-deformation of a single quantized radiation mode interacting with a collection of two level atoms is introduced, analysing its effects on the cooperative behavior of the system.

Collective spontaneous emission in a q-deformed Dicke model

A method for filtering and controlling soliton states of the Bose-Einstein condensate is presented. The analysis is carried out by considering the 3D Gross-Pitaevskii (GP) equation with appropriate confining potential wells. Suitable matching conditions, which are relevant for filtering and mantaining localized states in experiments, are established and exact controlled analytical solutions of the 3D GP equation are found and compared with the approximate ones obtained with variational approches.

http://iopscience.iop.org/article/10.1238/Physica.Topical.116a00010/pdf

Vladimir I. Man’ko

Papers

Новые неравенства для томограмм в вероятностном представлении квантовых состояний@@@New inequalities for tomograms in the probability representation of quantum states

Quasiprobability and Probability Distributions for Spin 1/2 States

Separability and entanglement of spin $1$ particle

Collective spontaneous emission in a q-deformed Dicke model

A Method for Filtering and Controlling Soliton States of Bose-Einstein Condensates