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Research Areas
 
Statistical physics
Biological physics
Quantum Gravity
Quantum Measurements and Quantum - Entanglement
 
General Relativity
Theorist’s Laboratory
 
 
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Statistical physics
 
A theoretical and experimental understanding of heat and electron transport processes in systems of mesoscopic (a few microns to the size of a single atom) scale are fundamentally important to improve the performance of nano-devices and their applications. To this end research is carried out by the TP group on the transport of heat and electricity using the Langevin equation and scattering approaches. The role of disorder, nonlinearity and dissipation on the transport properties of such systems are also under investigation. Analytical work starting from first principles, on understanding the mechanical response of amorphous and crystalline solids (elastic media) to large deformations, nucleation dynamics and dynamics of solid-solid transformations is also being pursued at RRI at the moment. The equilibrium and dynamical properties of polymers is another area of soft condensed matter research that the TP group is currently engaged in. In this area, there are several experimental groups, which can bend and twist DNA molecules to study their elastic properties. The packaging of DNA in the cell nucleus is one of the motivations for the study. The work from the TP group addresses elastic properties of semiflexible polymers over a range of stiffness. Using the concept of geometric phase, a simple theoretical model has been arrived at that captures a range of molecular elastic properties in polymers, from DNA to actin. Similarly the role of thermal fluctuations on the elastic response of bent and twisted ribbons is expected to shed light on DNA looping “J Factor” and on the bending elasticity of twisted graphene ribbons. The above studies can be viewed as an application of the methods of theoretical physics to biology.

Non-equilibrium statistical mechanics is another field of interest for the TP group. Large deviations, probability and statistics of rare and extreme events or driven systems are some of the problems being explored currently within this realm. Examples of such problems being explored in the past one year include universal large deviations for a tagged particle in single-file motion, tagged particle diffusion in one-dimensional systems of interacting point particles evolving under Hamiltonian dynamics and fluctuations of the work done by an external correlated random force on a Brownian particle in a given time interval in the steady state. Driven inelastic Maxwell gases, which consist of a collection of particles characterised only by their velocities, and evolving through binary collisions and external driving, have also been investigated by the TP group during the period 2014-2015. The system is found to reach a steady state under specific conditions such as the type of driving and the value of the coefficient of restitution for collision between the driven gaseous particles.

A stochastic process, when subject to resetting to its initial condition at a constant rate, generically reaches a non-equilibrium steady state. The TP group is analytically studying various stochastic processes under resetting conditions. Specific questions being addressed include studies on how the steady state is approached in time by a resetting stochastic system and Levy flights with optimal search times that show a remarkable first order transition in the optimal parameters allowing for a successful search. In the former case, researchers find a dynamical transition occurring in the relaxation mechanism of these systems. These apart, issues pertaining to jamming of granular matter and onset of shear waves in a bacterial bath are also being addressed using techniques typical to non-equilibrium statistical physics.
 
 
Biological Physics
 
Members from the Soft Condensed Matter and Theoretical Physics groups are together involved in the work being done on various topics in the field of biophysics but which concentrate primarily on understanding the mechanics of living systems (cells, tissues etc.) at different scales and how that helps in organizing molecules and arranging cells etc. with broader implications for homeostatic control. These problems include studies of vesicle formation and their transport in cells, mitochondrial distribution dynamics, DNA stretching and twisting, molecular transport through the secretory pathway in cells, the active composite cell surface, active tissue mechanics, biogenesis of organelles using non-equilibrium physics models and active mechanics of membranes, polymers, fluids, solids, semisolids etc. Cell mechanics from the point of view of information processing and computation, embodies another very interesting biological problem with the potential to overthrow many established ideas behind the whys and hows of cell mechanics. Research in biophysics at RRI involves active collaborations not only within the Institute but also with the National Centre for Biological Sciences, Bangalore, TCIS-TIFR, Hyderabad, IIT Madras, and several institutes abroad.
 
 
Quantum Gravity
 
The TP group at RRI carries out research on quantum gravity from two distinct viewpoints, Loop Quantum Gravity (LQG) and Causal Set Theory (CST).

LQG is a method where standard Hamiltonian ways of quantization are applied to the classical gravitational field without resorting to perturbation theory. The consequent absence of a spatial geometry in LQG has been addressed through some new ideas and tools by the TP group, while the absence of a background time and an overall recovery of the space-time continuum in the classical limit are the two issues being looked into currently. Also applications of LQG ideas to solve a truncated space of homogeneous and isotropic (cosmological) gravitational fields are being actively pursued through studying simpler covariant toy models. Recently the Koslowski-Sahlmann (KS) representation has been studied extensively by the TP group. KS representation is a generalization of the representation underlying the discrete spatial geometry of LQG particularly to accommodate states labelled by smooth spatial geometries. The KS representation has been shown by the TP group to support not only the holonomy and flux operators but also those that are the quantum counterparts of connection dependent “SU(2)” electric fields called “background exponential operators”. The latest contribution to this field by RRI has been an explanation of the quantum kinematics for asymptotically flat space-times using the above representation.

In the CST approach to quantum gravity, on the other hand, one replaces continuum spacetime by a discrete substructure, which is a locally finite, partially ordered set, the Causal Set. While the partial order represents the underlying causal structure of a causal Lorentzian spacetime, the local finiteness encodes the hypothesis of a covariant discrete cut-off. In the CST approach the continuum arises as an approximation, rather than as a limit since the cut-off is a physical input rather than a mathematical convenience as in other discrete approaches. At RRI, a broad range of directions in causal set theory has been pursued. These include a close examination of causal set kinematics in which continuum quantities like topology, dimension, curvature and geometry are reconstructed from purely order theoretic considerations. There has also been active work on quantum dynamics, both using numerical MCMC methods as well as the quantum measure approach. In both cases, the construction of quantum observables rests on previous work on causal set kinematics. An important result in numerical simulations for full 2D causal set quantum gravity using the RRI cluster is that the spacetime continuum is emergent. Most recently, research at RRI on these topics has led to some key insights like spatial homogeneity of the Hartle-Hawking no-boundary wave function for CST over the discrete analogues of space-like hyper-surfaces at low temperature – indicating a possible role of quantum gravity in shaping the observable universe.

Another line of investigation motivated by causal sets and quantum cosmology considerations is the quantum measure approach to quantum foundations. Here, one places quantum theory in parallel with stochastic physics with its attendant interpretational generalisations. Work is on at RRI to understand how this framework can be used to obtain covariant observables in quantum gravity.

As an example of the multi-faceted research being carried out by the TP group we have a research problem that explores in detail the analogy between quantum gravity effects that cost too high an energy and are thus unfeasible to test out in a standard laboratory, with the fluctuating surface tension of micron sized fluid membranes. The background to the problem involves the smallness of the cosmological constant, or the dark energy that drives the expanding universe. It has been suggested that quantum gravity fluctuations could lead to this smallness and thus the need to probe more closely quantum gravity effects experimentally. This makes the aforementioned analogous study of surface tension a topic of fundamental importance in the field.
 
 
Quantum Measurements and Quantum Entanglement
 
During the period 2014-2015, the TP group at RRI has arrived at an extremely important result with far-reaching consequences in the measurement of time and the degree of accuracy that can be achieved in its measurement. It turns out that there is a fundamental limit to the measurement of time, set by a combination of three basic physical principles – uncertainty relation, gravitational redshift and relativistic time dilation effects. This result is expected to find large-scale applications in the designing of better clocks that are important in astronomy, metrology and global positioning systems.

In an analytical study treating the spin of a silver atom as a quantum system in the context of the Stern-Gerlach experiment, the TP group at RRI has proposed the concept of a coarse quantum measurement. It appears that quantum measurements are limited in their resolution by bounded resources, which results in a non-unitary evolution of the system in question, not governable by the Schrodinger equation. It is proposed that the coarseness of the detection process is what renders a quantum system non-unitary.
 
 
General Relativity
 
Laser interferometer gravitational wave detectors like LIGO and VIRGO with their remarkable sensitivity to wave signals from distant astrophysical sources have sparked off dedicated research in the calculation of gravitational waveforms from inspiralling super massive black hole binaries. The wave signals received by LIGO and VIRGO are, however, weak and heavily noise-ridden, which in turn intensifies the need for accurate templates to compare and cross-correlate with the data. The TP group at RRI examines this signal detection using future space based gravity-wave detectors like LISA and performs a complete and detailed study of the entire waveform. Taking into account the entire waveform ensures improved angular resolution for super massive black hole binaries and the data obtained is able to achieve a consistency with the dark energy equation of state to within a few percent.
 
 
Theorist’s Laboratory
 
This is a forum for theorists to dirty their hands with simple table-top experiments and have better clarity in understanding certain fundamental aspects of theoretical physics through designing and performing such experiments. There have been experiments to study the mechanics of vibrated grains, the Marangoni effect between two interacting fluids and Brownian motion in milk globules. Several demonstrations using simple materials such as a rotating cube, an Archimedian screw pump, soap films and soap bubbles and concepts such as the effect of low Reynold's number, surface tension etc. on fluid motion have also been made at the Theorist’s Laboratory. Recently, there have also been some polymer stretching experiments with theraband strips, using a setup put together with the help of the RRI workshop, with a view to understanding similarities between such experiments and molecular scale biopolymer stretching experiments. The overall aim of the Theorist’s Laboratory at RRI is to build a solid ground in understanding key theoretical concepts.
 
 
 
 
 
 
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