Brain signals such as electroencephalogram (EEG) often show oscillations at various frequencies, which are represented as distinct ″bumps″ in the power spectral density (PSD) of these signals. In addition, the PSD also shows a distinct reduction in power with increasing frequency, which pertains to aperiodic activity and is often termed as the ″1/f″ component. While a change in periodic activity in brain signals with healthy aging and mental disorders has been reported, recent studies have shown a reduction in the slope of the aperiodic activity with these factors as well. However, these studies only analysed PSD slopes over a limited frequency range (<100 Hz). To test whether the PSD slope is affected over a wider frequency range with aging and mental disorder, we collected EEG data with high sampling rate (2500 Hz) from a large population of elderly subjects (>49 years) who were healthy (N=217) or had mild cognitive impairment (MCI; N=11) or Alzheimer′s Disease (AD; N=5), and analysed the PSD slope till 800 Hz. Consistent with previous studies, the 1/f slope up to ~150 Hz reduced with healthy aging. Surprisingly, we found the opposite at higher frequencies (>200 Hz): the slope increased with age. This result was observed in all electrodes, for both eyes open and eyes closed conditions, and for different reference schemes. Slopes were not significantly different in MCI/AD subjects compared to age and gender matched healthy controls. Overall, our results constrain the biophysical mechanisms that are reflected in the PSD slopes in healthy and pathological aging.

The power spectral density (PSD) of the brain signals is characterized by two distinct features: oscillations, that are represented as distinct “bumps,” and broadband aperiodic activity, that reduces in power with increasing frequency and is characterized by the slope of the power falloff. Recent studies have shown a change in the slope of the aperiodic activity with healthy aging and mental disorders. However, these studies analyzed slopes over a limited frequency range (&lt;100 Hz). To test whether the PSD slope is affected over a wider frequency range with aging and mental disorder, we analyzed the slope till 800 Hz in electroencephalogram data recorded from elderly subjects (&gt;49 years) who were healthy (n = 217) or had mild cognitive impairment (MCI; n = 11) or Alzheimer’s Disease (AD; n = 5). While the slope reduced up to ~ 150 Hz with healthy aging (as shown previously), surprisingly, at higher frequencies (&gt;200 Hz), it increased with age. These results were observed in all electrodes, for both eyes open and eyes closed conditions, and for different reference schemes. However, slopes were not significantly different in MCI/AD subjects compared to healthy controls. Overall, our results constrain the biophysical mechanisms that are reflected in the PSD slopes in healthy and pathological aging.

We investigate the two-dimensional motion of relativistic cold electrons in the presence of `strictly’ spatially varying magnetic fields satisfying, however, no magnetic monopole condition. We find that the degeneracy of Landau levels, which arises in the case of the constant magnetic field, lifts out when the field is variable and the energy levels of spin-up and spin-down electrons align in an interesting way depending on the nature of change of field. Also, the varying magnetic field splits Landau levels of electrons with zero angular momentum from positive angular momentum, unlike the constant field which only can split the levels between positive and negative angular momenta. Exploring Landau quantization in non-uniform magnetic fields is a unique venture on its own and has interdisciplinary implications in the fields ranging from condensed matter to astrophysics to quantum information. As examples, we show magnetized white dwarfs, with varying magnetic fields, involved simultaneously with Lorentz force and Landau quantization affecting the underlying degenerate electron gas, exhibiting a significant violation of the Chandrasekhar mass-limit; and an increase in quantum speed of electrons in the presence of a spatially growing magnetic field.

We probe the quantum speed limit (QSL) of an electron when it is trapped in a non-uniform magnetic field. We show that the QSL increases to a large value, but within the regime of causality, by choosing a proper variation in magnetic fields. We also probe the dependence of quantum speed (QS) on spin of electron and find that it is higher for spin-down electron for ground level based transition in the relativistic regime. This can be useful in achieving a faster speed of transmission of quantum information. Further, we use the Bremermann--Bekenstein bound to find a critical magnetic field that bridges the gap between non-relativistic and relativistic treatments and relates to the stability of matter. An analytical framework is developed. We also provide a plausible experimental design to supplement our theory.

We investigate the two-dimensional motion of relativistic cold electrons in the presence of 'strictly' spatially varying magnetic fields satisfying, however, no magnetic monopole condition. We find that the degeneracy of Landau levels, which arises in the case of the constant magnetic field, lifts out when the field is variable and the energy levels of spin-up and spin-down electrons align in an interesting way depending on the nature of change of field. Also the varying magnetic field splits Landau levels of electrons with zero angular momentum from positive angular momentum, unlike the constant field which only can split the levels between positive and negative angular momenta. Exploring Landau quantization in nonuniform magnetic fields is a unique venture on its own and has interdisciplinary implications in the fields ranging from condensed matter to astrophysics to quantum information. As examples, we show magnetized white dwarfs, with varying magnetic fields, involved simultaneously with Lorentz force and Landau quantization affecting the underlying degenerate electron gas, exhibiting a significant violation of the Chandrasekhar mass-limit; and an increase in quantum speed of electrons in the presence of a spatially growing magnetic field.