Collective Effects in Quantum Statistics of Radiation and Matter

ISBN-13: 9789401078405 / Angielski / Miękka / 2011 / 215 str.

V. N. Popov; V. S. Yarunin

Opis

Material particles, electrons, atoms, molecules, interact with one another by means of electromagnetic forces. That is, these forces are the cause of their being combined into condensed (liquid or solid) states. In these condensed states, the motion of the particles relative to one another proceeds in orderly fashion; their individual properties as well as the electric and magnetic dipole moments and the radiation and absorption spectra, ordinarily vary little by comparison with their properties in the free state. Exceptiotls are the special so-called collective states of condensed media that are formed under phase transitions of the second kind. The collective states of matter are characterized to a high degree by the micro-ordering that arises as a result of the interaction between the particles and which is broken down by chaotic thermal motion under heating. Examples of such pheonomena are the superfluidity of liquid helium, and the superconductivity and ferromagnetism of metals, which exist only at temperatures below the critical temperature. At low temperature states the particles do not exhibit their individual characteristics and conduct themselves as a single whole in many respects. They flow along capillaries in ordered fashion and create an undamped current in a conductor or a macroscopic magnetic moment. In this regard the material acquires special properties that are not usually inherent to it.

Spis treści

1. Functional integrals In quantum theory.- §1. Gaussian functional integrals for systems of non-interacting particles.- Coherent states of harmonic oscillators. Partition functions.- Finite multiplicity approximations for partition functions. Functional- integral passage to the limit.- Functional methods of calculation.- Matrix elements of the statistical operator and the evolution operator.- The ideal Bose gas.- Green’s functions.- §2. Methods of functional integration for interacting particles.- The stationary phase method. Extremals.- The harmonic Bose oscillator under the action of external forces.- The second variation and excitation spectrum.- Perturbation theory for a non-ideal Bose gas.- Fermi statistics.- Partial summation of diagrams.- Formulae for average values.- 2. Superfluid Bose systems.- §1. Perturbation theory for superfluid Bose systems.- Zero-temperature theory. Breakdown of symmetry.- Separation of the condensate.- Low-density Bose gas. Phonon character of the spectrum.- Higher diagrams of perturbation theory.- Superfluidity.- §2. The effective action functional for superfluid systems.- The method of integrating with respect to the rapid and slow variables.- The modified perturbation theory. Removal of infra-red divergences.- Two-dimensional and one-dimensional Bose systems. Superfluidity without a Bose condensate.- §3. Quantum vortices in superfluid systems.- The description of vortices by the method functional integration.- The electrodynamical analogue.- The role of the vortices in the phase transition.- 3. Superfluid Fermi systems.- §1. Perturbation theory for superfluid Fermi systems.- Superfluidity and long-range correlations in Fermi systems.- The diagram technique for superfluid Fermi systems.- The low-density Fermi gas.- One-particle excitations and the energy gap.- §2. Collective excitations in superfluid Fermi systems.- The method of integration with respect to rapid and slow fields forFermi systems.- Conversion to the effective action functional.- The Fermi gas.- Taking into account the Coulomb interaction.- The effective action functional for the 3He model.- Collective excitations.- The Fermi gas with attraction.- The Bose spectrum of the Fermi gas in the critical region.- The Bose spectrum of the Fermi gas at low temperatures.- The Bose spectrum with Coulomb interaction.- The 3He model.- The possibility of several superfluid phases in 3He.- The Bose spectrum of the 3He model in the critical region.- The low-temperature Bose spectrum of the B-phase of 3He.- The Bose spectrum of the A-phase.- 4. Interaction of radiation with matter. The linear theory.- § 1. Coherent and thermal radiation.- Equations of the electromagnetic field in Hamiltonian form. Approximation of the given currents.- Single-mode radiation. The canonical distribution for the field of asignal with noise.- The Planck and Poisson distributions for the number of photons.- §2. The two-level system in an external field.- Dipole interaction.- The two-level system.- The resonance approximation.- The trilinear model of the interaction of light with matter.- The evolution of atoms in a given field.- Quasi-energy.- The adiabatic approximation.- 5. Superradiant phase transitions.- §1. The static field in the single-centre model of the interaction of matterwith single-mode radiation.- Three classical operators with constraints.- Quantum oscillators. Accounting for the constraint in the Canonical Gibbs ensemble.- Static ordering.- Non-resonance interaction. Accounting for the constraint in thegrand canonical ensemble.- The excitation spectrum.- §2. The static field in the multi-centre model of the interaction of matter withsingle-mode radiation.- The grand canonical ensemble.- The average over the lattice variables. The effective action functional.- The equations for stationariness. Static solutions.- The superradiant phase transition and the statistics of the medium.- The excitation spectrum.- Non-resonance interaction of radiation with matter.- §3. Other models and a discussion of the results.- Spontaneous breakdown of symmetry.- The Dicke model with fluctuations of the parameters.- The influence of the interaction of the lattice with the field on the phase transition.- Superradiant ordering and seignetto-electricity.- 6. Superradiant coherent impulses.- § 1. Non-linear interaction of light with matter.- Dicke superradiation.- The Maxwell-Bloch equations. Accounting for the damping.- The Lamb theory.- Solitons.- The threshold condition, randomization, and synergetics.- Irreversibility and the projection operator.- Integration over a closed time contour.- §2. The dynamics of the single-centre model of the interaction of lightwith matter.- The coherent dynamics of three Bose oscillators. Periodic solutionsand 2?-impulses.- The ?-impulses.- The two-mode single-centre model. The equations for the field andthe population-density levels.- The approximation of close frequencies. The dependence of the absorption coefficients on the initial conditions and parameters of the problem.- The influence of the detuning on the frequency of vibration of the field.- §3. The dynamics of the single-mode multi-centre model of the interaction oflight with matter.- The effective action for the field.- The approximation of weak non-linearity.- The approximation of strong non-linearity.- The vibrational and rotational states of the field oscillator.- Concluding Remarks.