Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pair Excitations, Collective Modes and Gauge Invariance in the BCS --
  Bose-Einstein Crossover Scenario   In this paper we study the BCS Bose Einstein condensation (BEC) crossover
scenario within the superconducting state, using a T-matrix approach which
yields the ground state proposed by Leggett. Here we extend this ground state
analysis to finite temperatures T and interpret the resulting physics. We find
two types of bosonic-like excitations of the system: long lived, incoherent
pair excitations and collective modes of the superconducting order parameter,
which have different dynamics. Using a gauge invariant formalism, this paper
addresses their contrasting behavior as a function of T and superconducting
coupling constant g. At a more physical level, our paper emphasizes how, at
finite T, BCS-BEC approaches introduce an important parameter \Delta^2_{pg} =
\Delta^2 - \Delta_{sc}^2 into the description of superconductivity. This
parameter is governed by the pair excitations and is associated with
particle-hole asymmetry effects which are important for sufficiently large g.
In the fermionic regime, \Delta_{pg}^2 represents the difference between the
square of the excitation gap \Delta^2 and that of the superconducting order
parameter \Delta_{sc}^2. The parameter \Delta_{pg}^2, which is necessarily zero
in the BCS (mean field) limit increases monotonically with the strength of the
attractive interaction g. It follows that there is a significant physical
distinction between this BCS-BEC crossover approach (in which g is the
essential variable which determines \Delta_{pg}) and the widely discussed
(Coulomb-modulated) phase fluctuation scenario in which the plasma frequency is
the tuning parameter.

1
The categories of this paper are: cs
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys