Necessity for quantum mechanical simulation for the future technology nodes

In this paper we present and compare the results obtained from semi-classical and quantum mechanical simulation for a Double Gate MOSFET structure to analyze the electrostatics and carrier dynamics of this device. The geometries like gate length, body, thickness of this device have been chosen according to the ITRS specification for the different technology nodes. We have shown the extent of deviation between the semi-classical and quantum mechanical results and hence the need of quantum simulations for the promising nanoscale devices in the future technology nodes predicted in ITRS.

Quantum spin nematics, dimerization, and deconfined criticality in Quasi-1D spin-one magnets

We study theoretically the destruction of spin nematic order due to quantum fluctuations in quasi-one-dimensional spin-1 magnets. If the nematic ordering is disordered by condensing disclinations, then quantum Berry phase effects induce dimerization in the resulting paramagnet. We develop a theory for a Landau-forbidden second order transition between the spin nematic and dimerized states found in recent numerical calculations. Numerical tests of the theory are suggested.

Influence of quantum confinement on the photoemission from superlattices of optoelectronic materials

We study the photoemission from quantum wire and quantum dot superlattices with graded interfaces of optoelectronic materials on the basis of newly formulated electron dispersion relations in the presence of external photo-excitation. Besides, the influence of a magnetic field on the photoemission from the aforementioned superlattices together with quantum well superlattices in the presence of a quantizing magnetic field has also been studied in this context. It has been observed taking into account HgTe/Hg1-xCdxTe and InxGa1-xAs/InP that the photoemission from these nanostructures increases with increasing photon energy in quantized steps and exhibits oscillatory dependences with the increase in carrier concentration. Besides, the photoemission decreases with increasing light intensity and wavelength, together with the fact that said emission decreases with increasing thickness exhibiting oscillatory spikes. The strong dependences of the photoemission on the light intensity reflects the direct signature of light waves on the carrier energy spectra. The content of this paper finds six applications in the fields of low dimensional systems in general. (C) 2010 Elsevier Ltd. All rights reserved.

The Photoemission from Quantum Wells, Wires and Carbon Nanotubes:Simplified Theory and Relative Comparison

We investigate the photoemission from quantum wells (QWs) in ultrathin films (UFs) and quantum well wires (QWWs) of non-linear optical materials on the basis of a newly formulated electron dispersion law considering the anisotropies of the effective electron masses, the spin-orbit splitting constants and the presence of the crystal field splitting within the framework of k.p formalism. The results of quantum confined Ill-V compounds form the special cases of our generalized analysis. The photoemission has also been studied for quantum confined II-VI, n-GaP, n-Ge, PtSb2, stressed materials and Bismuth on the basis of respective dispersion relations. It has been found taking quantum confined CdGeAS(2), InAs, InSb, CdS, GaP, Ge, PtSb2, stressed n-InSb and B1 that the photoemission exhibits quantized variations with the incident photon energy, changing electron concentration and film thickness, respectively, for all types of quantum confinement. The photoemission from CNs exhibits oscillatory dependence with increasing normalized electron degeneracy and the signature of the entirely different types of quantum systems are evident from the plots. Besides, under certain special conditions, all the results for all the materials gets simplified to the well-known expression of photoemission from non-degenerate semiconductors and parabolic energy bands, leading to the compatibility test.

Quench dynamics and defect production in the Kitaev and extended Kitaev models

We study quench dynamics and defect production in the Kitaev and the extended Kitaev models. For the Kitaev model in one dimension, we show that in the limit of slow quench rate, the defect density n∼1/√τ, where 1/τ is the quench rate. We also compute the defect correlation function by providing an exact calculation of all independent nonzero spin correlation functions of the model. In two dimensions, where the quench dynamics takes the system across a critical line, we elaborate on the results of earlier work [K. Sengupta, D. Sen, and S. Mondal, Phys. Rev. Lett. 100, 077204 (2008)] to discuss the unconventional scaling of the defect density with the quench rate. In this context, we outline a general proof that for a d-dimensional quantum model, where the quench takes the system through a d−m dimensional gapless (critical) surface characterized by correlation length exponent ν and dynamical critical exponent z, the defect density n∼1/τmν/(zν+1). We also discuss the variation of the shape and spatial extent of the defect correlation function with both the rate of quench and the model parameters and compute the entropy generated during such a quenching process. Finally, we study the defect scaling law, entropy generation and defect correlation function of the two-dimensional extended Kitaev model.

A quantum stochastic Lie-Trotter product formula

A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.

Quantum Space-Time and Noncommutative Gauge Field Theories

Arguments arising from quantum mechanics and gravitation theory as well as from string theory, indicate that the description of space-time as a continuous manifold is not adequate at very short distances. An important candidate for the description of space-time at such scales is provided by noncommutative space-time where the coordinates are promoted to noncommuting operators. Thus, the study of quantum field theory in noncommutative space-time provides an interesting interface where ordinary field theoretic tools can be used to study the properties of quantum spacetime. The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative space-time is the apparent loss of Lorentz invariance that has been addressed in different ways in the literature. One recently developed approach is to eliminate the Lorentz violating effects by integrating over the parameter of noncommutativity. Fundamental properties of such theories are investigated in this thesis. Another issue addressed is model building, which is difficult in the noncommutative setting due to severe restrictions on the possible gauge symmetries imposed by the noncommutativity of the space-time. Possible ways to relieve these restrictions are investigated and applied and a noncommutative version of the Minimal Supersymmetric Standard Model is presented. While putting the results obtained in the three original publications into their proper context, the introductory part of this thesis aims to provide an overview of the present situation in the field.

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Quantum Chemical Studies on Tropospheric Nucleation Mechanisms Involving Sulfuric Acid

Nucleation is the first step of the process by which gas molecules in the atmosphere condense to form liquid or solid particles. Despite the importance of atmospheric new-particle formation for both climate and health-related issues, little information exists on its precise molecular-level mechanisms. In this thesis, potential nucleation mechanisms involving sulfuric acid together with either water and ammonia or reactive biogenic molecules are studied using quantum chemical methods. Quantum chemistry calculations are based on the numerical solution of Schrödinger's equation for a system of atoms and electrons subject to various sets of approximations, the precise details of which give rise to a large number of model chemistries. A comparison of several different model chemistries indicates that the computational method must be chosen with care if accurate results for sulfuric acid - water - ammonia clusters are desired. Specifically, binding energies are incorrectly predicted by some popular density functionals, and vibrational anharmonicity must be accounted for if quantitatively reliable formation free energies are desired. The calculations reported in this thesis show that a combination of different high-level energy corrections and advanced thermochemical analysis can quantitatively replicate experimental results concerning the hydration of sulfuric acid. The role of ammonia in sulfuric acid - water nucleation was revealed by a series of calculations on molecular clusters of increasing size with respect to all three co-ordinates; sulfuric acid, water and ammonia. As indicated by experimental measurements, ammonia significantly assists the growth of clusters in the sulfuric acid - co-ordinate. The calculations presented in this thesis predict that in atmospheric conditions, this effect becomes important as the number of acid molecules increases from two to three. On the other hand, small molecular clusters are unlikely to contain more than one ammonia molecule per sulfuric acid. This implies that the average NH3:H2SO4 mole ratio of small molecular clusters in atmospheric conditions is likely to be between 1:3 and 1:1. Calculations on charged clusters confirm the experimental result that the HSO4- ion is much more strongly hydrated than neutral sulfuric acid. Preliminary calculations on HSO4- NH3 clusters indicate that ammonia is likely to play at most a minor role in ion-induced nucleation in the sulfuric acid - water system. Calculations of thermodynamic and kinetic parameters for the reaction of stabilized Criegee Intermediates with sulfuric acid demonstrate that quantum chemistry is a powerful tool for investigating chemically complicated nucleation mechanisms. The calculations indicate that if the biogenic Criegee Intermediates have sufficiently long lifetimes in atmospheric conditions, the studied reaction may be an important source of nucleation precursors.