etd@IISc Collection:http://etd.iisc.ernet.in/2005/372018-08-17T03:32:20Z2018-08-17T03:32:20ZTransport In Quasi-One-Dimensional Quantum SystemsAgarwal, Amit Kumarhttp://etd.iisc.ernet.in/2005/11072011-04-01T20:30:30Z2011-03-31T18:30:00ZTitle: Transport In Quasi-One-Dimensional Quantum Systems
Authors: Agarwal, Amit Kumar
Abstract: This thesis reports our work on transport related problems in mesoscopic physics using analytical as well as numerical techniques. Some of the problems we studied are: effect of interactions and static impurities on the conductance of a ballistic quantum wire[1], aspects of quantum charge pumping [2, 3, 4], DC and AC conductivity of a (dissipative) quantum Hall (edge) line junctions[5, 6], and junctions of three or more Luttinger liquid (LL)quantum wires[7].
This thesis begins with an introductory chapter which gives a brief glimpse of the underlying physical systems and the ideas and techniques used in our studies. In most of the problems we will look at the physical effects caused by e-e interactions and static scattering processes.
In the second chapter we study the effects of a static impurity and interactions on the conductance of a 1D-quantum wire numerically. We use the non-equilibrium Green’s function (NEGF) formalism along with a self-consistent Hartree-Fock approximation to numerically study the effects of a single impurity and interactions between the electrons (with and without spin) on the conductance of a quantum wire [1]. We study the variation of the conductance with the wire length, temperature and the strength of the impurity and electron-electron interactions. We find our numerical results to be in agreement with the results obtained from the weak interaction RG analysis. We also discover that bound states produce large density deviations at short distances and have an appreciable effect on the conductance which is not captured by the renormalization group analysis.
In the third chapter we use the equations of motion (EOM) for the density matrix and Floquet scattering theory to study different aspects of charge pumping of non-interacting electrons in a one-dimensional system. We study the effects of the pumping frequency, amplitude, band filling and finite bias on the charge pumped per cycle, and the spectra of the charge and energy currents in the leads[2]. The EOM method works for all values of parameters, and gives the complete time-dependences of the current and charge at any site of the system. In particular we study a system with oscillating impurities at several sites and our results agree with Floquet and adiabatic theory where these are applicable, and provides support for a mechanism proposed elsewhere for charge pumping by a traveling potential wave in such systems. For non-adiabatic and strong pumping, the charge and energy currents are found to have a marked asymmetry between the two leads, and pumping can work even against a substantial bias. We also study one-parameter charge pumping in a system where an oscillating potential is applied at one site while a static potential is applied in a different region [3]. Using Floquet scattering theory, we calculate the current up to second order in the oscillation amplitude and exactly in the oscillation frequency. For low frequency, the charge pumped per cycle is proportional to the frequency and therefore vanishes in the adiabatic limit. If the static potential has a bound state, we find that such a state has a significant effect on the pumped charge if the oscillating potential can excite the bound state into the continuum states or vice versa.
In the fourth chapter we study the current produced in a Tomonaga-Luttinger liquid (TLL) by an applied bias and by weak, point-like impurity potentials which are oscillating in time[4]. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the DC and AC components of the current have power law dependences on the bias and pumping frequencies with an exponent 2K−1 for spinless electrons, where Kis the interaction parameter. For K<1/2, the current grows large for special values of the bias. For non-interacting electrons with K= 1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1/2 electrons.
In chapter five, we present a microscopic model for a line junction formed by counter or co-propagating single mode quantum Halledges corresponding to different filling factors and calculate the DC [5] and AC[6] conductivity of the system in the diffusive transport regime. The ends of the line junction can be described by two possible current splitting matrices which are dictated by the conditions of both lack of dissipation and the existence of chiral commutation relations between the outgoing bosonic fields. Tunneling between the two edges of the line junction then leads to a microscopic understanding of a phenomenological description of line junctions introduced by Wen. The effect of density-density interactions between the two edges is considered exactly, and renormalization group (RG) ideas are used to study how the tunneling parameter changes with the length scale. The RG analysis leads to a power law variation of the conductance of the line junction with the temperature (or other energy scales) and the line junction may exhibit metallic or insulating phase depending on the strength of the interactions. Our results can be tested in bent quantum Hall systems fabricated recently.
In chapter six, we study a junction of several Luttinger Liquid (LL) wires. We use bosonization with delayed evaluation of boundary conditions for our study. We first study the fixed points of the system and discuss RG flow of various fixed points under switching of different ‘tunneling’ operators at the junction. Then We study the DC conductivity, AC conductivity and noise due to tunneling operators at the junction (perturbative).We also study the tunneling density of states of a junction of three Tomonaga-Luttinger liquid quantum wires[7]. and find an anomalous enhancement in the TDOS for certain fixed points even with repulsive e-e interactions.2011-03-31T18:30:00ZTopics in the Exploration of New Physics at the International Linear Collider with the inclusion of Beam PolarizationPatra, Monalisahttp://etd.iisc.ernet.in/2005/33262018-04-03T15:51:27Z2018-04-02T18:30:00ZTitle: Topics in the Exploration of New Physics at the International Linear Collider with the inclusion of Beam Polarization
Authors: Patra, Monalisa
Abstract: The Standard Model of particle physics which attempts to describe all matter and all forces in the universe (except gravity),has been in agreement with most of the experiments till date. However theoretically and phenomenologically many questions remain unanswered in the SM. The present and future colliders will help the physicists learn more about the nature of matter and all forces in the universe. In this thesis work we have mainly focused on the physics case of the future linear collider which will be a succession of the presently running Large Hadron Collider in CERN Geneva.
As an introduction to the thesis work in Chapter 1 we have discussed in detail about the most planned future collider the International Linear Collider. This collider apart from being a high luminosity machine will have the advantage of beam polarization. Chapter 2 discusses about the basis structure of the Standard Model, along with its many unanswered questions. Some of the theories proposed to take care of these deficiencies are also discussed. These theories apart from explaining the shortcomings of the SM, also predicts many new particles and are thus phenomenologically rich. Exploration of these new physics scenarios can be done many ways. A detailed investigation of the direct production of particles which are not present in the SM spectrum, is one of the techniques provided the particles are within the collider reach. The other is an indirect way, where deviations from SM is studied by a through scrutinization of the SM processes. Provided new physics is observed in either of the way, in the present or future colliders it becomes necessary to pin point them. The main objective of this thesis work has been to look for various scenarios, both in a direct and indirect way and identify them. The different cases of beam polarization is also explored. Overall we ﬁnd that the full potential of the linear collider can be realized only with the availability of the electron and positron beam polarization, both transverse and longitudinal. We give an overview of the importance of beam polarization and its inclusion in the calculation of e+e- collisions in Chapter 3.
In Chapter 4 we have considered the possibility of finger printing the presence of heavy additional Z′bosons that arise naturally in extensions of the Standard Model such as E6 models and left-right symmetric models, through their mixing with the standard model Z boson. They are probed using W pair production and leptonic decay of one of the W’s. The Littlest Higgs Model which addresses the hierarchy problem and where the Z′arises naturally is also considered. By considering a class of observables including total cross sections, energy distributions and angular distributions of decay leptons we find significant deviation from the Standard Model predictions for these quantities with right-handed electrons and left-handed positrons at √s=800 GeV. This process complements the study of fermion pair production processes that have been considered before for discrimination between these models.
We have then studied the possibility of identifying a strongly interacting Wboson sector inChapter5 which is consistent with present day Large Hadron Collider searches, at the International Linear Collider with longitudinal as well as transversely polarized electron and positron beams. We account for the final state interaction using a suitable Omnes formalism in terms of a plausible resonance description, and carry out thorough analyses of cross sections, asymmetries and angular distributions of the Ws. In order to have a fully comprehensive study we also carry out a comparison with other extensions of the Standard Model, where an s channel resonance like heavy additional Z′bosons arise naturally. We also consider the effect of the strong final state interaction on a correlation that depends on(φ- - φ+), where the φ∓are the azimuthal angles of decay leptons, and find that it is a useful discriminant.
The importance of top polarization in the process e+e−→ tt with transverse beam polarization to probe interactions of the scalar and tensor type beyond the Standard Model and the way to disentangle their individual contributions is discussed in Chapter 6. 90% confidence level limits on the interactions with realistic integrated luminosity are presented and are found to improve by an order of magnitude compared to the case when the spin of the top quark is not measured. Sensitivities of the order of a few times 10−3 TeV−2 for real and imaginary parts of both scalar and tensor couplings at √s=500 and 800 GeV with an integrated luminosity of 500 fb−1 and completely polarized beams is shown to be possible.
We next consider the process e+e- → γ Z with transverse beam polarization in the
presence of anomalous CP-violating γZZ coupling λ1 and γγZ coupling λ2 in Chapter
7. We point out that similar to the approach in Chapter 6 if the final-state spins are resolved, then it becomes possible to fingerprint the anomalous coupling Reλ1. 90% confidence level limit on Reλ1 achievable with center-of-mass energy of 500 GeV or 800 GeV with realistic initial beam polarization and integrated luminosity is of the order of few times of 10−2 when the helicity of Zis used and 10−3 when the helicity of γis used. The resulting corrections at quadratic order to the cross section and its influence on these limits are also evaluated and are shown to be small.
In Chapter 8 the production of the lightest neutralinos in the radiative process
e+e−→ χ˜10χ˜10γ in supersymmetric models with grand unification is considered. We
consider models wherein the standard model gauge group SU(3)c x SU(2)L x U(1)Y is unified in to the grand unified gauge groups SU(5),or SO(10). We compare and contrast the dependence of the signal cross section on the grand unified gauge group, and different representations of the grand unified gauge group, into which the standard model gauge group is unified. We carry out a comprehensive study of the radiative production process which includes higher order QED corrections in our calculations. In addition we carry out a detailed study of the background to the signal process coming from the Standard Model radiative neutrino production e+e−→ νv*γ, as well as from the radiative production of the scalar partners of the neutrinos (sneutrinos) e+e ν˜ν˜γ. The latter can be a major supersymmetric background to the radiative production of neutralinos when the sneutrinos decay invisibly.
Finally in Chapter 9, we conclude and present the summary of the thesis.2018-04-02T18:30:00ZTopics In Noncommutative Gauge Theories And Deformed Relativistic TheoriesChandra, Nitinhttp://etd.iisc.ernet.in/2005/24682018-01-09T06:43:46Z2015-08-11T18:30:00ZTitle: Topics In Noncommutative Gauge Theories And Deformed Relativistic Theories
Authors: Chandra, Nitin
Abstract: There is a growing consensus among physicists that the classical notion of spacetime has to be drastically revised in order to nd a consistent formulation of quantum mechanics and gravity. One such nontrivial attempt comprises of replacing functions of continuous spacetime coordinates with functions over noncommutative algebra. Dynamics on such noncommutative spacetimes (noncommutative theories) are of great interest for a variety of reasons among the physicists. Additionally arguments combining quantum uncertain-ties with classical gravity provide an alternative motivation for their study, and it is hoped that these theories can provide a self-consistent deformation of ordinary quantum field theories at small distances, yielding non-locality, or create a framework for finite truncation of quantum field theories while preserving symmetries.
In this thesis we study the gauge theories on noncommutative Moyal space. We nd new static solitons and instantons in terms of the so-called generalized Bose operators (GBO). GBOs are constructed to describe reducible representation of the oscillator algebra. They create/annihilate k-quanta, k being a positive integer. We start with giving an alternative description to the already found static magnetic flux tube solutions of the noncommutative gauge theories in terms of GBOs. The Nielsen-Olesen vortex solutions found in terms of these operators also reduce to the ones known in the literature. On the other hand, we nd a class of new instanton solutions which are unitarily inequivalent to the ones found from ADHM construction on noncommutative space. The charge of the instanton has a description in terms of the index representing the reducibility of the Fock space representation, i.e., k. After studying the static soliton solutions in noncommutative Minkowski space and the instanton solutions in noncommutative Euclidean space we go on to study the implications of the time-space noncommutativity in Minkowski space. To understand it properly we study the time-dependent transitions of a forced harmonic oscillator in noncommutative 1+1 dimensional spacetime. We also provide an interpretation of our results in the context of non-linear quantum optics. We then shift to the so-called DSR theories which are related to a different kind of noncommutative ( -Minkowski) space. DSR (Doubly/Deformed Special Relativity) aims to search for an alternate relativistic theory which keeps a length/energy scale (the Planck scale) and a velocity scale (the speed of light scale) invariant. We study thermodynamics of an ideal gas in such a scenario.
In first chapter we introduce the subjects of the noncommutative quantum theories and the DSR. Chapter 2 starts with describing the GBOs. They correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the GBO. When used in conjunction with the noncommutative ADHM construction, we nd that these new instantons are in general not unitarily equivalent to the ones currently known in literature.
Chapter 3 studies the time dependent transitions of quantum forced harmonic oscillator (QFHO) in noncommutative R1;1 perturbatively to linear order in the noncommutativity . We show that the Poisson distribution gets modified, and that the vacuum state evolves into a \squeezed" state rather than a coherent state. The time evolutions of un-certainties in position and momentum in vacuum are also studied and imply interesting consequences for modelling nonlinear phenomena in quantum optics.
In chapter 4 we study thermodynamics of an ideal gas in Doubly Special Relativity. We obtain a series solution for the partition function and derive thermodynamic quantities. We observe that DSR thermodynamics is non-perturbative in the SR and massless limits. A stiffer equation of state is found. We conclude our results in the last chapter.2015-08-11T18:30:00ZStudy Of CP-Violation And Determination Of Higgs Boson Properties At Future CollidersSingh, Ritesh Khttp://etd.iisc.ernet.in/2005/13662018-01-09T06:07:03Z2011-08-17T18:30:00ZTitle: Study Of CP-Violation And Determination Of Higgs Boson Properties At Future Colliders
Authors: Singh, Ritesh K2011-08-17T18:30:00Z