In one-dimensional disordered wires electronic states are localized at any energy. Correlations of the states at close positive energies and the AC conductivity \sigma(\omega) in the limit of small frequency are described by the Mott-Berezinskii theory. We revisit the instanton approach to the statistics of wave functions and AC transport valid in the tails of the spectrum (large negative energies). Applying our recent results on functional determinants, we calculate exactly the integral over Gaussian fluctuations around the exact two-instanton saddle point. We derive correlators of wave functions at different energies beyond the leading order in the energy difference. This allows us to calculate corrections to the Mott-Berezinskii law (the leading small-frequency asymptotic behavior of \sigma(\omega)) which approximate the exact result in a broad range of \omega. We compare our results with the ones obtained for positive energies.
Context: Only 55% of the athletes return to competitive sports after an anterior cruciate ligament (ACL) injury. Athletes younger than 25 years who return to sports have a second injury rate of 23%. There may be a mismatch between rehabilitation contents and the demands an athlete faces after returning to sports. Current return-to-sports (RTS) tests utilize closed and predictable motor skills; however, demands on the field are different. Neurocognitive functions are essential to manage dynamic sport situations and may fluctuate after peripheral injuries. Most RTS and rehabilitation paradigms appear to lack this aspect, which might be linked to increased risk of second injury.Objective: This systematic and scoping review aims to map existing evidence about neurocognitive and neurophysiological functions in athletes, which could be linked to ACL injury in an integrated fashion and bring an extensive perspective to assessment and rehabilitation approaches.Data Sources: PubMed and Cochrane databases were searched to identify relevant studies published between 2005 and 2020 using the keywords ACL, brain, cortical, neuroplasticity, cognitive, cognition, neurocognition, and athletes.Study Selection: Studies investigating either neurocognitive or neurophysiological functions in athletes and linking these to ACL injury regardless of their design and technique were included.Study Design: Systematic review. Level of Evidence: Level 3.Data Extraction: The demographic, temporal, neurological, and behavioral data revealing possible injury-related aspects were extracted and summarized.Results: A total of 16 studies were included in this review. Deficits in different neurocognitive domains and changes in neurophysiological functions could be a predisposing risk factor for, or a consequence caused by, ACL injuries.Conclusion: Clinicians should view ACL injuries not only as a musculoskeletal but also as a neural lesion with neurocognitive and neurophysiological aspects. Rehabilitation and RTS paradigms should consider these changes for assessment and interventions after injury.
