etd@IISc Collection:http://hdl.handle.net/2005/422015-11-28T08:14:41Z2015-11-28T08:14:41ZStudies Of Electronic, Magnetic And Entanglement Properties Of Correlated Models In Low-Dimensional SystemsSahoo, Shaonhttp://hdl.handle.net/2005/24802015-09-04T09:41:54Z2015-09-03T18:30:00ZTitle: Studies Of Electronic, Magnetic And Entanglement Properties Of Correlated Models In Low-Dimensional Systems
Authors: Sahoo, Shaon
Abstract: This thesis consists of six chapters. The first chapter gives an introduction to the field of low-dimensional magnetic and electronic systems and relevant numerical techniques. The recent developments in molecular magnets are highlighted. The numerical techniques are reviewed along with their advantages and disadvantages from the present perspective. Study of entanglement of a system can give a great insight into the system. At the last part of this chapter a general overview is given regarding entanglement, its measures and its significance in studying many-body systems.
Chapter 2 deals with the technique that has been developed by us for the full symmetry adaptation of non-relativistic Hamiltonians. It is advantageous both computationally and physically/chemically to exploit both spin and spatial symmetries of a system. It has been a long-standing problem to target a state which has definite total spin and also belongs to a definite irreducible representation of a point group, particularly for non-Abelian point groups. A very general technique is discussed in this chapter which is a hybrid method based on valence-bond basis and the basis of the z-component of the total spin. This technique is not only applicable to a system with arbitrary site spins and belonging to any point group symmetry, it is also quite easy to implement computationally. To demonstrate the power of the method, it is applied to the molecular magnetic system, Cu6Fe8, with cubic symmetry.
In chapter 3, the extension of the previous hybrid technique to electronic systems is discussed. The power of the method is illustrated by applying it to a model icosahedral half-filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and is in the largest non-Abelian point group. All the eigenstates of the model are obtained using our technique.
Chapter 4 deals with the thermodynamic properties of an important class of single-chain magnets (SCMs). This class of SCMs has alternate isotropic spin-1/2 units and anisotropic high spin units with the anisotropy axes being non-collinear. Here anisotropy is assumed to be large and negative, as a result, anisotropic units behave like canted spins at low temperatures; but even then simple Ising-type model does not capture the essential physics of the system due to quantum mechanical nature of the isotropic units. A transfer matrix (TM) method is developed to study statistical behavior of this class of SCMs. For the first time, it is also discussed in detail that how weak inter-chain interactions can be treated by a TM method. The finite size effect is also discussed which becomes important for low temperature dynamics. This technique is applied to a real helical chain magnet, which has been studied experimentally.
In the fifth chapter a bipartite entanglement entropy of finite systems is studied using exact diagonalization techniques to examine how the entanglement changes in the presence of long-range interactions. The PariserParrPople model with long-range interactions is used for this purpose and corresponding results are com-pared with those for the Hubbard and Heisenberg models with short-range interactions. This study helps understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions in the PPP model. It is also investigated if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, an interesting observation is made on the entanglement profiles of different states, across the full energy spectrum, in comparison with the corresponding profile of the density of states.
The entanglement can be localized between two noncomplementary parts of a many-body system by performing local measurements on the rest of the system. This localized entanglement (LE) depends on the chosen basis set of measurement (BSM). In this chapter six, an optimality condition for the LE is derived, which would be helpful in finding optimal values of the LE, besides, can also be of use in studying mixed states of a general bipartite system. A canonical way of localizing entanglement is further discussed, where the BSM is not chosen arbitrarily, rather, is fully determined by the properties of a system. The LE obtained in this way, called the localized entanglement by canonical measurement (LECM), is not only easy to calculate practically, it provides a nice way to define the entanglement length. For spin-1/2 systems, the LECM is shown to be optimal in some important cases. At the end of this chapter, some numerical results are presented for j1 −j2 spin model to demonstrate how the LECM behaves.2015-09-03T18:30:00ZSlow Dynamics In Complex Fluids : Confined Polymers And Soft ColloidsKandar, Ajoy Kumarhttp://hdl.handle.net/2005/24592015-08-05T12:02:20Z2015-08-04T18:30:00ZTitle: Slow Dynamics In Complex Fluids : Confined Polymers And Soft Colloids
Authors: Kandar, Ajoy Kumar
Abstract: The thesis describes the study of slow dynamics of confined polymers and
soft colloids. We study the finite size effect on the dynamics of glassy polymers
using newly developed interfacial microrheology technique. Systematic
measurement have been performed to address the issue of reduction of glass
transition under confinements. Slow and heterogeneous dynamics are the underlined observed behavior for dynamics in confined glassy polymers. The slow relaxation dynamics and dynamical heterogeneity in polymer grafted nanoparticles (PGNPs) systems were studied using advanced X - ray photon correlation spectroscopy (XPCS) techniques. Our studies presented in this thesis on dynamics of polymer grafted nanoparticle systems in melts and solution are the first attempt to study them experimentally. Thus our work shed the light about new technique to study confined system more accurately and explore new soft colloidal system to study fascinating dynamics and interesting phase behavior.
In Chapter 1, we provide the theoretical background along with brief review of the literature for understanding the results presented in this thesis. The details of the experimental set up and their operating principle along with the details of the experimental conditions are provided in Chapter 2. In Chapter 3 we present our newly developed technique (interfacial microrhelogy) and its consequences to study the complex fluids at interface. Chapter 4 discusses the concentration and temperature dependent glassy dynamics in confined glassy
polymers. In Chapter 5 we provide the structural and dynamical study of polymer
grafted nanoparticles in melts and solutions. We provide the summary of
our result and the future prospective of the work in Chapter 6.
Chapter-1 provides the ground work and theoretical aspects for understanding
the results presented in this thesis. It starts with the discussion about
the slow dynamics of complex fluids and transit to dynamic behavior of polymer
in confinement, glassy dynamics in confinements . This also discusses
the basic aspects of studying viscoelastic properties using rheology, interface
rheology, microrheology, interface microrheology techinques. In continuation it
discusses structure and dynamics of different soft colloids investigated for last decade and then theoretical aspects of XPCS is discussed. Towards the end
of this Chapter, we discuss the procedure to explain and understand systems
dynamical heterogeneity near glass like phase transition.
Chapter-2 contains the details of the experimental techniques which has been used for the study of confined polymers and soft colloids. Brief introduction to basic principles of the measurements followed by details of the material and
methods have been provided.
Chapter-3 we discuss the interafacial microrheology of different complex fluids and advantages of the techniques is discussed in Chapter 3. This includes
discussion about the technique sensitivity at the surface using quantum dots
(QDs) as a probe and about the configuration of the QDs at/on monolayer. Later
on establishment of the technique has been demonstrated through easurements on arachidic acid, poly(methylmethacrylate) (PMMA), poly(vinylacetate) (PVAc), poly(methylacrylate) (PMA) monolayers. The extracted subdiffusive nature of QDs in on monolayers through mean square displacement has been explained using fractional Brownian motion model. Towards the end of the chapter we discuss about the extraction of real and imaginary elastic modulus from mean square displacement data using generalized Stokes-Einstein relation for the quasi two dimensional systems and explains about the possible viscoelastic transition in the different monolayers.
The concentration and temperature dependent glassy dynamics of confined polymers (PMMA) are discussed in Chapter-4. We demonstrate the microscopic nature of spatio-temporal variation of dynamics of glassy polymers confined to a monolayer of 2 3 nm thickness as a function of surface density and temperature. It illustrates the systems dynamical heterogeneity and explain the observed large reduction of glass transition temperature in confined system through finite size effect.
In Chapter 5 we discuss the result based on systematic studies of dynamics of PGNPs in melts and solutions. In addition it also illustrates the structural anisotropy and anomalous dynamical transitions in binary mixture of PGNPs and homopolymers in good solvent condition. It provides temperature
and wave vector dependent XPCS measurements on polymer grafted nanoparticles with the variation of functionality. The functionality ( f ) dependent nonmonotonic relaxation in melts of PGNPs and solvent quality dependent non monotonic relaxation of PGNPs system have been elaborated in the continuation.
We present possible phase behavior of PGNPs system in good solvent with addition of homopolymer of two different molecular weight.
Chapter 6 contains the summary and the future perspective of the work presented.2015-08-04T18:30:00ZExperimental Studies Of Electron Spin Dynamics In Semiconductors Using A Novel Radio Frequency Detection TechniqueGuite, Chinkhanlunhttp://hdl.handle.net/2005/24582015-08-05T11:41:02Z2015-08-04T18:30:00ZTitle: Experimental Studies Of Electron Spin Dynamics In Semiconductors Using A Novel Radio Frequency Detection Technique
Authors: Guite, Chinkhanlun
Abstract: A novel experimental setup has been realized to measure weak magnetic moments which can be modulated at radio frequencies (~1–5 MHz). Using an optimized radio-frequency (RF) pickup coil and lock-in amplifier, an experimental sensitivity of 10 -15 Am2 corresponding to 10 -18 emu has been demonstrated with a one second time constant. The detection limit at room temperature is 9.3 10 -16 Am2/√Hz limited by Johnson noise of the coil. In order to demonstrate the sensitivity of this technique it was used to electrically detect the polarized spins in semiconductors in zero applied magnetic fields. For example in GaAs, the magnetic moment due to a small number (~ 7 x 108) of spin polarized electrons generated by polarization modulated optical radiation was detected.
Spin polarization was generated by optical injection using circularly polarized light which is modulated rapidly using an electro-optic cell. The modulated spin polarization generates a weak time-varying magnetic field which is detected by the sensitive radio-frequency coil. Using a radio-frequency lock-in amplifier, clear signals were obtained for bulk GaAs and Ge samples from which an optical spin orientation efficiency of ~ 10–20% could be determined for Ge at 1342 nm excitation wavelength at 127 K. In the presence of a small external magnetic field, the signal decayed according to the Hanle Effect, from which a spin lifetime of 4.6 ± 1.0 ns for electrons in bulk Ge at 127 K was extracted. The spin dynamics in n-Ge was further explored and the temperature dependence of the spin lifetime was plotted for a temperature range of about 90 K to 180 K. The temperature dependence of the optical pumping efficiency was also measured though no quantitative conclusions could be derived.
The signals observed for semi-insulating GaAs, n-GaAs, GaSb and CdTe which are direct gap semiconductors are much larger than expected (almost two orders of magnitude). An attempt was made to explain this unexpected behavior of these direct gap semiconductors using the spin hall effect.2015-08-04T18:30:00ZWarped Galaxies : Recovery Of Pattern Speed, Velocity Field And The Warp EquationMaji, Moupiyahttp://hdl.handle.net/2005/24562015-08-04T07:53:10Z2015-08-03T18:30:00ZTitle: Warped Galaxies : Recovery Of Pattern Speed, Velocity Field And The Warp Equation
Authors: Maji, Moupiya
Abstract: Pattern speed is an important parameter of the density wave theory for spiral galaxies. In this thesis we have determined the pattern speed for warped galaxies (flat galaxies being a special case of this generalization) using the observable data of the surface brightness and line-of-sight velocity distribution of the galaxy. We have also extracted the transverse velocity field for the warped galaxy using the same data. Here we have simulated the data and applied our method to it and we found that our method works well in warped galaxy. We assume a parameterized model of the warp and by the method of minimizing χ2 error we can determine the parameters of the model also and thus we can construct the warp equation. We have also discussed the implications and the limitations of this method.2015-08-03T18:30:00Z