Chintalpati Umashankar Shastry

Here I am undertaking the project, in the continuation of a project formulated during my internship, where I am working under the supervision of Dr Andrea Rocco to apply the renormalisation group approach to open quantum systems and obtain an exact renormalisation group equation in the Non-Markovian limit. In this project we are trying to use Wilson’s renormalization group techniques to get the correction terms due to the quantum fluctuations at large frequency cut-off in the Fourier modes of the effective action of the system, this can be calculated by the shell mode integration of the Wilsonian effective action. we are trying to derive the two point Wegner-Houghton equation for the Super-propagator and then translate this finding to know the change in the dynamics of the system's reduced density matrix. Since the theory becomes scale invariant at quantum-classical phase transition point, we are trying to study QC interface by demanding the scale invariance in the two point Wegner-Houghton Equation. By doing so we can characterize the masters equation at this QC interface. Also, we are trying to get the critical damping constant at QC interface.

In this project I am working under the supervision of Dr Andrea Rocco and Dr Marian Florescu, in the department of physics at the University of Surrey. Here we are trying to understand how the different definitions of entropy can be incorporated and derived in open quantum system. We also aim to understand what are the criteria to decide which definition of entropy should be adopted in any given case. Later in the project we aim to explore the origin of entropy and how can we incorporate the entropy in the equation of  motion, such as Schrödinger’s equation or Master equation for reduced density matrix, in the case of open quantum system.

In this project, I am working with Dr Andrea Rocco and Dr Marian Florescu to understand how the systems achieve equilibrium in the presence of Non-Markovian Bath

In this project I am working under the supervision of Dr Andrea Rocco and Dr Marian Florescu, in the department of physics at the University of Surrey. In this project we aim to investigate how life maintains its highly ordered, low-entropy, far-from-equilibrium dynamical state. We will adopt open quantum systems theory and quantum thermodynamics to make predictions that may be used to assess the underlying classical and quantum dynamics of physical and biological systems. We will focus on systems with memory effects and identify deviations from standard thermodynamics, which may require reformulations of entropy functions and fluctuation-dissipation relations. Analysis of these deviations is expected to shed light on the fundamental differences between living and non-living systems.

I did my MSc dissertation on solving the Dirac equation for hydrogen atom in finite basis expansion. This project was supervised by Dr Paul Stevenson.

In this work, matrix representation of Dirac Hamiltonian was obtained in a finite set basis spinors. In principle any infinite basis set can be used to obtain a matrix representation of the Hamiltonian of the system, however, if the basis set are not kinetically balanced, then the so called spurious energy states fill the energy spectrum. Two methods were developed, namely basis expansion method and Variational method. In basis expansion method the inner product of kinetically balanced Dirac basis spinors were taken with Dirac Hamiltonian to get the matrix elements, while in the Variational method large component was expanded in terms of orthonormal basis functions while the small component was expanded in kinetically balanced basis functions.

Both methods give rise to the spurious energy states, however, variational method shows less spurious states than basis expansion method for the given number of basis functions (or spinors in the case of basis expansion method). Variational method is slower and the convergence of largest positive energy eigenvalue to the theoretical ground state energy is slower than basis expansion method.