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Path Integral Approach to Levy Flights and Hindered Rotations

Electronic Theses of Indian Institute of Science

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Title Path Integral Approach to Levy Flights and Hindered Rotations
 
Creator Janakiraman, Deepika
 
Subject Path Integrals
Levy Noise
Levy Flight
Anomalous Diffusion
Hamiltonian Path Integral
Harmonic Oscillators - Path Integrals
Barrier Crossing - Path Integrals
Statistical Mechanics
Hindered Rotors
Friction (Levy Flights)
Levy Flights - Path Integrals
Hindered Rotations
Quantum Mechanics
 
Description Path integral approaches have been widely used for long in both quantum mechanics as well as statistical mechanics. In addition to being a tool for obtaining the probability distributions of interest(wave functions in the case of quantum mechanics),these methods are very instructive and offer great insights into the problem. In this thesis, path integrals are extensively employed to study some very interesting problems in both equilibrium and non-equilibrium statistical mechanics. In the non-equilibrium regime, we have studied, using a path integral approach, a very interesting class of anomalous diffusion, viz. the L´evy flights. In equilibrium statistical mechanics, we have evaluated the partition function for a class of molecules referred to as the hindered rotors which have a barrier for internal rotation. Also, we have evaluated the exact quantum statistical mechanical propagator for a harmonic potential with a time-dependent force constant, valid under certain conditions.
Diffusion processes have attracted a great amount of scientific attention because of their presence in a wide range of phenomena. Brownian motion is the most widely known class of diffusion which is usually driven by thermal noise. However ,there are other classes of diffusion which cannot be classified as Brownian motion and therefore, fall under the category of Anomalous diffusion. As the name suggests, the properties of this class of diffusion are very different from those for usual Brownian motion. We are interested in a particular class of anomalous diffusion referred to as L´evy flights in which the step sizes taken by the particle during the random walk are obtained from what is known as a L´evy distribution. The diverging mean square displacement is a very typical feature for L´evy flights as opposed to a finite mean square displacement with a linear dependence on time in the case of Brownian motion. L´evy distributions are characterized by an index α where 0
 
Contributor Sebastian, K L
 
Date 2018-04-12T15:31:45Z
2018-04-12T15:31:45Z
2018-04-12
2013
 
Type Thesis
 
Identifier http://etd.iisc.ernet.in/2005/3396
http://etd.iisc.ernet.in/abstracts/4262/G25859-Abs.pdf
 
Language en_US
 
Relation G25859