Thermodynamics and Phase Transition in Shapere-Wilczek {\it fgh} model: Cosmological Time Crystal in Quadratic Gravity

The Shapere-Wilczek model \cite{wil}, or so called $fgh$ model, enjoys the remarkable features of a Time Crystal (TC) that has a non-trivial time dependence in its lowest energy state (or the classical ground state). We construct a particular form of $fgh$ model (with specified $f,g,h$ functions) that is derived from a Mini-superspace version of a quadratic $f(R,R_{\mu\nu})$ gravity theory. Main part of the investigation deals with thermodynamic properties of such systems from classical statistical mechanics perspective. Our analysis reveals the possibility of a {\it phase transition}. Because of the higher (time) derivative nature of the model computation of the partial function is non-trivial and requires newly discovered techniques. We speculate about possible connection between our model and the Multiverse scenario.Comment: 9 pages including supplements, 6 captioned figures; title has been changed, some references are added; version accepted for publication in Physics Letters

Chiral Induced Spin Selectivity Effect: Fundamental Studies and Applications

Since the discovery, chiral induced spin selectivity effect or CISS effect, which refers to the preferential transmission of electron of one spin over another through a chiral molecule/material, has generated significant interest due to its versatile application in different branches of science. Over the years, a large number of theoretical and experimental studies are done to understand the mechanism of CISS effect and also to utilize the effect in different field of science; such as memory devices, electrocatalytic experiments, chiral separation etc. In this dissertation, fundamental studies of the chiral molecule at the ferromagnetic interface are investigated through surface potential and magnetic measurements. Experiments are also done to study the spin filtering properties of chiral thin film and explore their electrocatalytic activity In the first study chiral molecule induced magnetization of the superparamagnetic particles was shown. This experiment shows a novel method to create ferromagnetic particle of 10 nm size from superparamagnetic particle using CISS. In the second study, spin dependent charge penetration to chiral molecule from the ferromagnetic substrate is presented by measuring surface potential using Kelvin probe method. In the third study, spin dependent electron transmission through chiral cobalt oxide thin film was performed by using magnetic conductive AFM and magnetoresistance measurements. In the forth study the electrocatalytic efficiency for water splitting was studied using chiral and magnetic thin cobalt oxide film. The finding of these studies serve to progress the CISS field and may help developing new CISS based spintronics device and electrocatalysts

Cosmology in a Time-Crystal Background

We investigate the effects of a Time Crystal-like Condensate on cosmological dynamics. It is well known that quadratic gravity reduces to Einstein gravity along with a decoupled higher derivative dynamical scalar \cite{Alvarez-Gaume:2015rwa}. According to \cite{Chakraborty:2020ktp}, the above scalar sector can sustain a Time Crystal-like minimum energy state, with non-trivial time dependence. In the present work we treat the Time Crystal-like state as the background (that replaces the classical Minkowski vacuum) and study cosmic evolution on this ``dynamic'' ground state. In the first part we re-derive \cite{Chakraborty:2020ktp}, in a covariant and more systematic way, the frequencies that characterize the oscillator like Time crystalline condensate and interpret it as a background energy-momentum tensor simulating a matter-like effect. Importantly, no external matter is introduced here and the condensate, consists of a combination of the metric field $g_{\mu\nu}$ and is generated due to the $R^2$-term ($R$ is the Ricci scalar) in quadratic gravity \cite{Alvarez-Gaume:2015rwa}. In a way the spurious degrees of freedom of $R^2$-gravity turns into a useful component. The second part comprises of new effects where the cosmology in Friedmann-Lem\^{i}atre-Robertson-Walker (FLRW) universe is studied in presence of the energy-momentum tensor characterizing the Time Crystal Condensate. Under certain approximations, the scale factor of the FLRW universe is analytically obtained for any spatial geometry. We also find that the Time Crystal Condensate contributes as a new matter candidate having radiation-like behavior in the universe. Additionally, irrespective of the spatial geometry of the universe, the Time Crystal condensate generates a decelerating phase before the early acceleration starts. This is an indication of a contracting phase of the universe before its accelerated expansion.Comment: 11 pages, 4 compound figures. Comments are welcom

Thermodynamics of micelle formation of some cationic surfactants as a function of temperature and solvent

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Substituent effects in the micellar hydrolysis of N-phenylbenzohydroxamic acid under acidic conditions

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