Research

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 :

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