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Includes bibliographical references.
In this thesis, I study several problems in the following areas: collective excitations in condensed matter physics, noise in gene network and stochastic control in biophysics. In the first area, I construct an effective field theory to describe Bose-Einstein Condensate (BEC) realized in an external potential. This theory explicitly explores the idea of spontaneous symmetry breaking and its application in the description of phase transitions of confined systems. Based on the effective lagrangian, I calculate the excitation spectrum and Matsubara Green's functions using the method of functional integrals. The theory also shows that in one dimension the collective excitation of a bosonic system can be unified with that of a fermionic system, which is described by Luttinger liquid theory. The unified theory of collective excitations of lo...
(cont.) These dynamics occur on a relatively local (i.e. molecular) length scale. At times greater than ~300 fs the experiments observe signatures of a kinetic regime. No longer can the spectral relaxation be ascribed to a clear molecular motion. Instead, the decay originates from the collective reorganization of many molecules. Two dimensional infrared spectroscopy (2D IR) is applied to further investigate the mechanism of hydrogen bond rearrangement. 2D IR is an optical analogue of multidimensional NMR. As a correlation spectroscopy, time dependent changes in 2D IR line shapes track how vibrational oscillators relax from one frequency to another. I describe two methods of acquiring high fidelity 2D line shapes at wavelengths of 3 gtm. Both methods utilize a HeNe laser as a frequency standard and balanced detection of the signal field...
Includes bibliographical references (leaves 103-104).
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