Sharif Digital Repository

Kardar-Parisi-Zhang (KPZ) equation was first proposed as a model to explain surface growth. This equation is very similar to Edwards-Wilkinson (EW) equation that is used to study scaling phenomena in non-equilibrium systems and phase transition. Although EW’s universality classes have been known well, it still remains a problem for KPZ. In the present thesis, in addition to a general review on surface growth models and a study on properties of rough surfaces, we study the physics of the KPZ model and the other related physical models. Also, using numerical results (like SLE method), renormalization group results and simulation, we study the dynamic and roughness exponents (α, z), and the... 

Brown and Henneaux showed that asymptotic symmetries of asymptotically form a conformal group in two dimensions [1]. Also they could derive classical central charge of theory. Fourteen years later, Maldacena, conjectured that this Holographic correspondence could be true for a specific theory a simplified chromodynamics in the boundary of ), this holographic theory attracted physicist communitee's attention. Many physicists tried to make this conjecture more precise. It is worth to say that, no example of holographic correspondence has been completely proven, till now, Because of the difficulty of the calculation. However these days we consider Madacena conjectrure in any arbitrary... 

Recently, a new tool in the study of two-dimensional continuous phase transition was provided by Schramm-Loewner evolution. The main part of SLE is a conformal map which relates growth process of a two-dimensional simple curve to one-dimensional motion on the real axis (so-called Loewner driving function). Time evolution of this map and Loewner driving function is connected via the Loewner differential equation. It turns out that for a certain class of stochastic and conformally invariant curves in two dimensions, the driving function shows Brownian motion in one dimension. Strength point of SLE comes from this fact that all the geometrical properties of such curves is described through a... 

Schramm Loewner evolution (SLE) is a one-parameter family of random simple curves in the complex plane introduced by Schramm in 1999 which is believed to describe the scaling limit of a variety of domain interfaces at criticality. This thesis is concerned with statistical properties of watersheds dividing drainage basins. The fractal dimension of this model is 1.22 which is consistent with the known fractal dimension for several important models such as Invasion percolation and minimum spanning trees (MST). We present numerical evidences that in the scaling limit this model are SLE curves with =1.73, being the only known physical example of an
SLE with <2. This lies outside the... 

XY Model due to topological defects (or vortex) has topological phase transition. According Kosterlitz-Thouless (KT) theory, phase transition is from low-temperature bounded vortices to high-temperature free vortices. XY model is appropriate choice for description of superfluidity in 2d thin films of . KT theory predicts universal jump in mass density of 2d superfluid in phase transition point. It is confirmed experimentally by Bishop and Reppy. All critical behavior of XY model is described with 2d coulomb gas, vortices are topological charges of the gas. KT predict variance of topological charge should obey of the “surface law vs perimeter law”, similar to behavior of Wilson loop in ... 

We propose a model for friction between two rough surfaces based on extreme value statistics (EVS). Different models for single-asperity contact, including adhesive and elasto-plastic contacts, were combined with EVS. The Hertzian model for contacts and Gumbel distribution for summit heights show the closest conformity with Amonton’s law. The range over which Gumbel distribution mimics Amonton’s law is wider than that of the Greenwood–Williamson (GW) model. In comparison with other EVS distribution, Gumbel distribution seems the proper choice for summit‘ s height. Interestingly, here again, elasto-plastic contact and Gumbel distribution for summits achieve the best conformity with Amontons... 

In the last two decades, Convolutional Neural Networks (CNN) have shown significant capabilities in artificial intelligence. These networks are able to provide comprehensive conclusions about the overall behavior a system by analyzing the relationship between the components of that system; Clearly, these networks have been successful in performing categorization tasks. However, there are no coherent theories as to why they work, and how to optimize them. On the other hand, according to recent research on the relationship between deep networks (in computer science) and Renormalization Group (in physics), convolutional networks seem to use a method similar to the Density Matrix Renormalization... 

Statistical mechanics offers an important outlook for studying rough surfaces. Loop model is one of the effective statistical methods for study of surfaces. We present and analyze this method for characterization of the morphology of rough surfaces. By statistics of contour loops which could be obtained from an ensemble of a surface such as the SOS model, one can calculate fractal dimension, loops’ length and the probability of connection of two points by a certain loop, etc. Armed with these results, critical exponents in two dimensions are exactly obtainable. In this thesis, after reviewing the properties of different rough surfaces, we shall pursue some results on statistical analysis of... 

Classical quench is the act of sudden change in the temperature of a system. This process is not new and has been used in some branches of science, like the smithing industry to produce a hard and stiff metal objects. Quantum Quench is the deformation of system's Hamiltonian in short time interval. This quantum version of quench is around for a few years and has attracted a lot of attention after its experimental realization in Ultracold Atoms setup. Suppose we have hamiltonian which depends on the constant g_0 which is the dynamical parameter of the system. It could be interaction strength between elements in the system or the external electric field amplitude on the system. At an arbitrary... 

The dimer model studies random dimer covers of a graph. A dimer cover is a subset of the edges of the graph such that each vertex is the endpoint of exactly one edge.The double-dimer model is a natural generalization of the dimer model, whose configuration is a union of two dimer covers, which ends up a set of even-length simple loops and doubled edges.The goal of this thesis is the study of statistical properties of very long doubledimer loops in very large lattices. To this end, we use the Grassmannian representation of the dimer model to compute some loop-related observables in rectangular domains of the square lattice, i.e. 1) the probability distribution of the number of nontrivial... 

We study different aspects of non-relativistic conformal symmetries. Schrodinger and Galilean Conformal Algebra (GCA) are reviewed extensively. We as well study possible extensions of non-relativistic conformal symmetries. We find a new class of infinite dimensional non-relativistic conformal symmetries in 2+1. We study logarithmic representation of Schrodinger symmetry. As well we utilize contraction approach and obtain both ordinary and logarithmic representations of GCA. Finally we investigate some aspects of logarithmic GCA in the context of holography principle  

Discretely holomorphic observables have recently been proposed for two dimensional lattice models at criticality, whose correlation functions satisfy a discrete version of Cauchy-Riemann relations. Existence of these observables appears to have a deep relation with integrability of the model. On the other hand at critical points of these models, there exist entities known as discrete parafermions whose Boltzmann weights satisfy the Yang-Baxter Equations. For this reason, finding parafermionic observables in any lattice model is equivalent to proof of solvability. This thesis is a step towards understanding the relation between Parafermions and Solvability. For instance, the Boltzmann weights... 

Phenomena such as will and volition, the emergence of qualities, internal and external feelings are the main problems related to consciousness. Consciousness is one of the oldest and, of course, most complex problems in science, and scientists are striving to provide a suitable explanation for this problem, but a complete answer has not yet been presented. Quantum consciousness is also an attempt to provide a suitable answer using the theory of quantum mechanics as the most fundamental scientific theory regarding the behavior of matter. In this area, the Orch OR theory by Penrose-Hameroff, the Henry P. Stap’s theory of quantum consciousness, and the Eccles-Beck’s theory of quantum... 

This dissertation on the Schrodinger-Virasoro algebra will begin by a brief historical review on the development of the symmetry arguments and its final overwhelming success in the 20th century physics. Testifying many successes of symmetry arguments and group theoretic methods in physics such as the theory of relativity, many physicists began to ask whether covariance under a larger group of symmetry transformation would explain a broader era of physical phenomena? As will be reviewed in the beginning of the second chapter, invariance under conformal group - which includes Poincaré group as a subgroup and thus underlies Lorentzian geometry as its natural background geometry – has been... 

In normal diffusion, the mean-square displacement (MSD) of a Brownian particle is proportional to time. However, diffusion in disordered systems, i.e. transport on fractal geometries, does not follow the classical laws of BM, and this leads to many anomalous physical properties. In the anomalous regime, the most famous definition of anomaly is the deviation of MSD, from the ‘normal’ linear dependence on time ⟨r2(t)⟩ ta. Specifically, we study the anomalous diffusion on the self-similar curves in two dimensions. The scaling properties of the mean-square displacement and mean first passage time (MFPT) of two sided and subordinated diffusion on the different fractal curves (loop-erased random... 

In this thesis, we investigate the effect of disorder on Majorana fermions at the boundary of one-dimensional topological superconductor. Starting from one-dimensional spin model nXY and then applying the Jordan-Wigner transformation result in one-dimensional topological superconductor. The Majorana fermions are found in the topological superconductor boundaries, protected by particle-hole and time-reversal symmetries. On the other hand, these fermions are highly localized at the boundary. Owing to non-trivial topology, the Majorana fermions are not affected by weak disorder. Increasing the disorder strength, the localization length of the Majorana fermions increases. Upon further increase in... 

We calculate NJL-Model free energy throughthe finite- temperature methods.Then according to the energy-gap equation, we determine symmetric and anti-symmetric phases under Chiral Transformation, in different regions of the phase diagram,with chemical potential() and temperature(T)as control parameter. We conclude with comparing the result of the finite temperature expansion to nonzero chemical potential to the result of,T=0 and finite ,andT=μregime.
 

Percolation is a simple probabilistic model which exhibits a phase transition. Here, we study this critical model from properties of random curves which in the scaling limit, appear as features seen on the macroscopic scale, in situations where the microscopic scale is taken to zero. Among the principal questions are the construction of the scaling limit, and the discription of some of the emergent properties, in particular the behavior under conformal maps Over the past few years, SLE has been developed as a valuable new tool to study the random paths of the scaling limit of two-dimensional critical models, and it is believed that SLE is the conformally invariant scaling limit of these... 

Schramm – Loewner Evolution (SLE) is a framework which helps to classify interfaces in critical models. At criticality two or more phases of the model are separated by an interface. In two dimensions this interface is a simple random curve, which can be addressed by SLE theory. This classification has crucial rule in our understanding of statistical models. In spite of our understanding of2 dimensional statistical models and 1+1dimensional quantum field theories, little workhas been done on these models out of criticality. In this thesis we focus on the Schramm-Loewner Evolutions and conformal field theoriesin vicinity of critical points. To this end we state the theories which the... 

Understanding of how fluid flow through porous media has many application in industry like Water filters technology and Gravel dams. also it’s very important in oil industry in areas like oil tank engineering. For doing this important thing many peoples tried to find out how fluid flows through the porous media they already invented the various kind of models, .the model used in this thesise is called pipe flow model which people use this model before but what I did have a little difference I used random lattice which people did not paid attention to it so the result of this model will be more trustable and close to what happens in nature. The result of this simulation showed us that the...