3,619 research outputs found
Relaxation and persistent oscillations of the order parameter in the non-stationary BCS theory
We determine the limiting dynamics of a fermionic condensate following a
sudden perturbation for various initial conditions. We demonstrate that
possible initial states of the condensate fall into two classes. In the first
case, the order parameter asymptotes to a constant value. The approach to a
constant is oscillatory with an inverse square root decay. This happens, e.g.,
when the strength of pairing is abruptly changed while the system is in the
paired ground state and more generally for any nonequilibrium state that is in
the same class as the ground state. In the second case, the order parameter
exhibits persistent oscillations with several frequencies. This is realized for
nonequilibrium states that belong to the same class as excited stationary
states. Our classification of initial states extends the concept of excitation
spectrum to nonequilibrium regime and allows one to predict the evolution
without solving equations of motion.Comment: 8 pages, 4 figure
Large System Analysis of the Energy Consumption Distribution in Multi-User MIMO Systems with Mobility
In this work, we consider the downlink of a single-cell multi-user MIMO
system in which the base station (BS) makes use of antennas to communicate
with single-antenna user equipments (UEs). The UEs move around in the cell
according to a random walk mobility model. We aim at determining the energy
consumption distribution when different linear precoding techniques are used at
the BS to guarantee target rates within a finite time interval . The
analysis is conducted in the asymptotic regime where and grow large
with fixed ratio under the assumption of perfect channel state information
(CSI). Both recent and standard results from large system analysis are used to
provide concise formulae for the asymptotic transmit powers and beamforming
vectors for all considered schemes. These results are eventually used to
provide a deterministic approximation of the energy consumption and to study
its fluctuations around this value in the form of a central limit theorem.
Closed-form expressions for the asymptotic means and variances are given.
Numerical results are used to validate the accuracy of the theoretical analysis
and to make comparisons. We show how the results can be used to approximate the
probability that a battery-powered BS runs out of energy and also to design the
cell radius for minimizing the energy consumption per unit area. The imperfect
CSI case is also briefly considered.Comment: 8 figures, 2 tables, to appear on IEEE Transactions on Wireless
Communication
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