Theory Of Collective Modes Research Articles

Kinetic Theory of Collective Modes in Atomic Clouds Above the Bose–Einstein Transition Temperature

We calculate frequencies and damping rates of the lowest collective modes of a dilute Bose gas confined in an anisotropic trapping potential above the Bose–Einstein transition temperature. From the Boltzmann equation with a simplified collision integral we derive a general dispersion relation that interpolates between the collisionless and hydrodynamic regimes. In the case of axially symmetric traps we obtain explicit expressions for the frequencies and damping rates of the lowest modes in terms of a phenomenological collision time. Our results are compared with microscopic calculations and with experiment.

Excitonic modes in a Bose-condensed electron-hole gas in the pairing approximation.

In studying the low-temperature state of an electron-hole gas in an optically pumped semiconductor there has been increasing realization that the pair approximation (similar to the Gor'kov approximation for BCS superfluids) can deal with both the low-density phase of excitons in a Bose-condensed state as well as the high-density excitonic insulator phase. Using functional differentiation techniques, we use this pair approximation to give a systematic derivation of the two-particle Green's function and the associated collective modes. Our equations of motion give what is often called the generalized random-phase approximation (GRPA). The collective modes are shown to correspond to the solution of the standard electron-hole ladder and bubble diagram sum, but with 2\ifmmode\times\else\texttimes\fi{}2 matrix propagators. Our model calculations are for a simple two-band direct-band-gap semiconductor with parabolic bands and a positive band gap (the semiconductor limit as opposed to the semimetal limit) and thus might be appropriate for optically pumped ${\mathrm{Cu}}_{2}$O. In the appropriate limits, our formalism leads to the phonon modes discussed (in the late 1960s) by Maksimov and Kozlov in the excitonic insulator and by Keldysh and Kozlov in the Bose-condensed state of excitons. In the low-density limit, the excitation of these collective modes is crucial in understanding how the Bose condensate is depleted at higher temperatures. Besides the excitonic modes, our equations of motion allow a systematic study of the complete spectrum of collective modes in the GRPA, including plasmons. Throughout, we emphasize the formal similarity with the theory of collective modes and excited Cooper-pair states in BCS superfluids.

Remarks on the Derivation of Langevin Equations for Nonequilibrium States

In this article we propose a new theory for collective modes of a many-body system which contains linear response theory and supplies us with systematic methods for the analysis of Brownian motion. The essential idea is to develop a method to find the possible justification for Zubarev's nonequilibrium ensemble from the new standpoint which is to draw attention to the usage of the dynamical invariance. The present theory has many interesting features which are relevant to irreversible processes. In this article we are more interested in problems of principle than in problems of applicability.

Phenomenological theory of collective modes and relaxation effects in type II superconductors

The general phenomenological dispersion law for type II superconductors is presented. In addition to thermal conduction, charge fluctuation decay, and contact potential modes, it is shown that there in general exists a high-frequency propagating mode determined by the low-frequency resistance at super-normal junctions. This may be the mode observed by Carlson and Goldman.

Kinetic Theory of Collective Modes in Classical Liquids

Kinetic Theory of Collective Modes in Classical Liquids