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

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

http://ieeexplore.ieee.org/iel5/3/22993/01069961.pdf

Quantum electrodynamics

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Gravitation And Cosmology

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Plasma Physics and Controlled Fusion Conference: Focussing on Tokamak Research

The fundamental equations of the microscopic quantum hydrodynamics of fermions in an external electromagnetic field (i.e., the particle balance equation, the momentum balance equation, the energy balance equation, and the magnetic moment balance equation) are derived using the Schrodinger equation. The form of the spin–spin interaction Hamiltonian is specified. To close the system of the balance equations for a multiparticle fermion system, the effective one-particle Schrodinger equation must be introduced.

Microscopic Quantum Hydrodynamics of Systems of Fermions: Part I

The problem with the construction of the Gross-Pitaevskii (GP) equation and related wave functions in a medium is associated with the necessity to begin with a description of the configuration space and proceed to a description of the physical space. We show that the balance equations of the number of particles and momentum immediately follow from the multiparticle Schr\"odinger equation. From the obtained set of balance equations, the equation for the wave function in the medium coincides in form with the GP equation, where we can restrict ourselves only by the first-order terms of the interaction radius of the stress tensor of bosons, for dilute gases. As a generalization of the GP equation, we made allowance for the contribution of the third-order terms of the interaction radius to the stress tensor of bosons. For a system of particles that comprises an ultracold mixture of bosons and fermions, a two-kind quantum hydrodynamics is constructed for the third-order terms of the interaction radius. The spectrum of eigenmodes involves additional information on the interparticle interaction as a correction to the Bogoliubov spectrum.

Problem with the single-particle description and the spectra of intrinsic modes of degenerate boson-fermion systems

In this paper, we explicate a method of quantum hydrodynamics (QHD) for the study of the quantum evolution of a system of polarized particles. Although we focused primarily on the two-dimensional (2D) physical systems, the method is valid for three-dimensional (3D) and one-dimensional (1D) systems too. The presented method is based upon the Schr\"odinger equation. Fundamental QHD equations for charged and neutral particles were derived from the many-particle microscopic Schr\"odinger equation. The fact that particles possess the electric dipole moment (EDM) was taken into account. The explicated QHD approach was used to study dispersion characteristics of various physical systems. We analyzed dispersion of waves in a two-dimensional ion and hole gas placed into an external electric field, which is orthogonal to the gas plane. Elementary excitations in a system of neutral polarized particles were studied for 1D, 2D, and 3D cases. The polarization dynamics in systems of both neutral and charged particles is shown to cause formation of a new type of waves as well as changes in the dispersion characteristics of already known waves. We also analyzed wave dispersion in 2D exciton systems, in 2D electron-ion plasma, and in 2D electron-hole plasma. Generation of waves in 3D-system neutral particles with EDM by means of the beam of electrons and neutral polarized particles is investigated.

Quantum hydrodynamics approach to the formation of waves in polarized two-dimensional systems of charged and neutral particles

Oblique propagation of longitudinal waves in magnetized spin-1/2 plasmas: Independent evolution of spin-up and spin-down electrons

Degenerate plasmas with motionless ions show existence of three surface waves: the Langmuir wave, the electromagnetic wave, and the zeroth sound. Applying the separated spin evolution quantum hydrodynamics to half-space plasma, we demonstrate the existence of the surface spin-electron acoustic wave (SSEAW). We study dispersion of the SSEAW. We show that there is hybridization between the surfaceLangmuir wave and the SSEAW at rather small spin polarization. In the hybridization area, the dispersion branches are located close to each other. In this area, there is a strong interaction between these waves leading to the energy exchange. Consequently, generating the Langmuir waves with the frequencies close to hybridization area we can generate the SSEAWs. Thus, we report a method of creation of the spin-electron acoustic waves.

L. S. Kuz'menkov

Papers

Microscopic Quantum Hydrodynamics of Systems of Fermions: Part I

Problem with the single-particle description and the spectra of intrinsic modes of degenerate boson-fermion systems

Quantum hydrodynamics approach to the formation of waves in polarized two-dimensional systems of charged and neutral particles

Oblique propagation of longitudinal waves in magnetized spin-1/2 plasmas: Independent evolution of spin-up and spin-down electrons

Surface spin-electron acoustic waves in magnetically ordered metals