Electrostatic interaction in plasma with charged bose condensate
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ELEMENTARY PARTICLES AND FIELDS Theory
Electrostatic Interaction in Plasma with Charged Bose Condensate* A. Lepidi** Universita` degli Studi di Ferrara, and Istituto Nazionale di Fisica Nucleare Sezione di Ferrara, Italy Received November 15, 2011
Abstract—Screening in plasma with Bose–Einstein condensate is studied. Finite temperature effects are taken into account. It is shown that, due to condensate effects, the potential has several unusual features. It contains two oscillating terms, one of which is analogous to the fermionic Friedel oscillations in standard QED, and a power law decreasing term. In the T → 0 limit, only one of the oscillating terms survives. On the whole, any charge impurity is screened more efficiently than in ordinary plasma. DOI: 10.1134/S1063778812090098
e2 nF /T , where
1. INTRODUCTION
It is a well known fact that any interaction may be affected by medium effects. As an example, let us consider the electrostatic potential generated by some charge impurity Q that is described in vacuum by the standard Coulomb potential: U (r) =
Q . 4πr
(1)
If the same interaction takes place in a medium, the resulting potential, called Yukawa potential, is exponentially damped, a phenomenon called screening: U (r) =
Q −mD x e . 4πr
(2)
In the last equation mD is the Debye mass that depends on the medium features, such as its temperature, the mass and the chemical potential of the composing particles and so on. It has been calculated for several media, such as a massive charged fermion gas (e.g., e− e+ ) and the corresponding boson system (φ− φ+ ), both at finite temperature T and chemical potential μ [1]. Some examples that can be found in the literature are plasma consisting of: relativistic fermions with mF T, μF : m2D = e2 T 2 /3 + μ2F /π 2 ; nonrelativistic fermions: m2D = ∗ **
The text was submitted by the author in English. E-mail: [email protected]
nF = exp(μ/T )/π 2
dqq 2 exp(−q 2 /(2mF T ));
massless scalars without chemical potential: m2D = e2 T 2 /3. Screening can be intuitively understood in terms of polarization: the charge impurity polarizes the medium and hence the resulting effective interaction is weaker. Surprisingly, till a few years ago, no one has considered what happens when the interaction takes place in a medium with a Bose–Einstein condensate (BEC) component. The BEC is a collection of particles which reside all in the same quantum state. Its existence was predicted in 1925 by S. N. Bose and A. Einstein, although it took 70 years to observe it experimentally. The first observation was performed in 1995 at the University of Colorado using a gas of rubidium atoms cooled to 170 nK [2]. It was awarded the 2001 Nobel Prize in Physics. To deal with BEC in quantum field theory (QFT) it is convenient to adopt a statistical approach. It is well known that the equilibrium distribution function of a collection of bosons is, up to spin counting factor: fB = (exp[(E − μB )/T ] − 1)−1 , where μB is the boson chemical potential assumed to be smaller than the boson mass mB . The chemica
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