arXiv subjects

Aniekan Magnus Ukpong

Publications and source records attributed to Aniekan Magnus Ukpong.

3 recordsLinked to original sources

arXiv2024

Cellular Griffiths-like phase

Protein compartmentalization in the frame of a liquid-liquid phase separation is a key mechanism to optimize spatiotemporal control of biological systems. Such a compartmentalization process reduces the intrinsic noise in protein concentration due to stochasticity in gene expression. Employing Flory-Huggins solution theory, Avramov/Casalini's model, and the Grüneisen parameter, we unprecedentedly propose a cellular Griffiths-like phase (CGLP), which can impact its functionality and self-organization. The here-proposed CGLP is key ranging from the understanding of primary organisms' evolution to the treatment of diseases. Our findings pave the way for an alternative Biophysics approach to investigate coacervation processes.

physics.bio-ph↗

arXiv2024

Grüneisen parameter as an entanglement compass and the breakdown of the Hellmann-Feynman theorem

The Grüneisen ratio $Γ$, i.e., the singular part of the ratio of thermal expansion to the specific heat, has been broadly employed to explore both finite-$T$ and quantum critical points (QCPs). For a genuine quantum phase transition (QPT), thermal fluctuations are absent and thus the thermodynamic $Γ$ cannot be employed. We propose a quantum analogue to $Γ$ that computes entanglement as a function of a tuning parameter $λ$ and show that QPTs take place only for systems in which the ground-state energy depends on $λ$ non-linearly. Furthermore, we demonstrate the breakdown of the Hellmann-Feynman theorem in the thermodynamic limit at any QCP. We showcase our approach using the quantum 1D Ising model with transverse field and Kane's quantum computer. The slowing down of the dynamics and thus the "creation of mass" close to any QCP/QPT is also discussed.

quant-ph↗

arXiv2023

Higher order first integrals of autonomous non-Riemannian dynamical systems

We consider autonomous holonomic dynamical systems defined by equations of the form $\ddot{q}^{a}=-Γ_{bc}^{a}(q) \dot{q}^{b}\dot{q}^{c}$ $-Q^{a}(q)$, where $Γ^{a}_{bc}(q)$ are the coefficients of a symmetric (possibly non-metrical) connection and $-Q^{a}(q)$ are the generalized forces. We prove a theorem which for these systems determines autonomous and time-dependent first integrals (FIs) of any order in a systematic way, using the `symmetries' of the geometry defined by the dynamical equations. We demonstrate the application of the theorem to compute linear, quadratic, and cubic FIs of various Riemannian and non-Riemannian dynamical systems.

math-ph↗