Life Sciences & Biotechnology
Title : | Unusual fluctuations around non-equilibrium states |
Area of research : | Life Sciences & Biotechnology |
Focus area : | Stochastic processes |
Principal Investigator : | Prof. Pradeep Kumar Mohanty, Indian Institute Of Science Education And Research (IISER) Kolkata, West Bengal |
Timeline Start Year : | 2024 |
Timeline End Year : | 2027 |
Contact info : | pkmohanty@iiserkol.ac.in |
Details
Executive Summary : | Randomness appears in many areas in natural sciences.An important property of of randomly distributed objects in a given volume is that, if their density is ρ, then the number of such objects N in any sub-volume V is a stochastic variable having both the mean and standard deviation proportional to V; this is a mere consequence of the widely applicable statistical principle called central limit theorem (or law of large numbers). Recently we observed (PRL 2012) that the law of large numbers is violated in critical absorbing states ( PRE 2016, 2023) where the variance of number fluctuation is sub-linear in volume. This state, formally known as a Hyperuniformity, is a new state of matter; its property is opposite to that of liquids - it is disordered in small scales and ordered in thermodynamic scale. In a way it is bizarre, but it is very useful: (i) birds can focus at different length scales as the photoreceptors are placed in their retina hyperuniformly (Jiao et. al., PRE 2014) (ii) a hyper uniform solar cell can utilize a larger range of solar spectrum (Tavakoli, Photonics 2022). Diffusion is a natural process that homogenizes ( uniformity, obeying law of large numbers) any initial distribution of matter. Is there a universal mechanism similar to diffusion that can create a hyperuniform state? We are planning to construct different mathematical models that lead to hyperuniform states and study them numerically (and analytically, whenever possible). The commonality among these models may give us a hint on why certain stochastic processes lead to super-homogeneity. One of the candidates is a distribution process which locally conserves momentum - primary investigations already tell us that number or mass fluctuations in these states are sub-linear in volume, though it is not clear what determines the exponent that characterizes the sublinearity. The law of large numbers is also violated when number fluctuations are superlinear in volume - some systems (like condensating or phase separating states) do exhibit the behaviour, namely 'giant fluctuations'. We are planning to rope both hyperuniformity and giant fluctuations in one frame - where, by changing some tuning parameter one can go from a hyperuniform state to giant fluctuations, exhibiting ordinary uniformity (Normal distribution of matter) in between. The task in hand can be summarised in three steps: (1) Construct and investigate mathematical models that exhibit unusual fluctuations (Hyperuniformity and/or Giant fluctuations). (2) Try to write an effective field theoretic or hydrodynamic model or a simple Langevin type dynamics that captures these phenomena. (3) Apply these concepts to understand hyperuniformity observed in critical absorbing states, self organised systems etc. |
Total Budget (INR): | 6,60,000 |
Organizations involved