Sharif Digital Repository

With the current demands in alternative methods of energy production and increased utilization of existing energy sources, microbial fuel cells have become an important field of research. In a microbial fuel cell, organic and inorganic compounds can be oxidized by microbial catabolism at the anode to generate direct electricity. A kind of microbial fuel cell (MFC) is sediment microbial fuel cell (SMFC) consists of an anode electrode embedded in the anaerobic sediment and a cathode electrode suspended in the overlying aerobic water. microorganisms produce electrons by oxidation of organic or inorganic compounds in the sediment at anode electrode, while oxygen is reduced in the water by... 

The heavy ion collision experiments are in progress in order to investigate how the Universe has evolved after the Big Bang. The recent observations show that a nearly perfect fluid is produced after heavy ion collisions. An appropriate incorporation of the relativistic hydrodynamics and the field theory would help us to describe the dynamics of QCD (Quantum Chromodynamics) matter under extreme conditions, and to survey the expected phase transitions. The majority of efforts to investigate the characteristics of the QCD plasma are devoted to an ideal, non-dissipative one. To get the results which are highly in accordance with the experiment, it is necessary to bring also in mind the role of... 

One of the long-lived problems in the theory of quantum chromo dynamics is the violation of parity (P) and charge-parity (CP) symmetries in strong interactions. The existence of gluon configurations sourcing from topology leads to degeneracy in the vacuum structure of the theory. This phenomenon is realized by the addition of an extra term proportional to the parameter to QCD Lagrangian. Experimental estimates of neutron electric dipole, predicts a very small value for this parameter. There is no verified justification for this discrepancy. Recently at the relativistic heavy ion collider laboratory (RHIC) some experimental evidence has been found which indicates local CP violation in... 

Relativistic hydrodynamics and kinetic theory are often used to analyze the experimental data from heavy ion collisions. One of the most important observations is the anisotropy in the number density of the detected particles after the collision in the longitudinal and perpendicular directions with respect to the reaction plane. On the other hand, very strong magnetic fields are created during the early stages of non-central heavy ion collisions. The presence of constant background magnetic fields, aligned in the perpendicular direction to the reaction plane, can be one of reasons for the aforementioned anisotropy in the number density of detected particles. In this thesis, we study the... 

In particle physics, spontaneous chiral symmetry breaking generates new phases of quark matter, and leads to significant changes od quark masses. The Nambu-Jona–Lasinio (NJL) model is a useful fermionic model which describes the spontaneous chiral symmetry breaking through the creation of a condensate. This model can be for instance used to determine various phases of Quantum Chromodynamics (QCD) in finite electromagnetic fields. This work consists of several parts. First, we describe the spontaneous chiral symmetry breaking in detail. Second, we extract the NJL model from the Lagrangian density of QCD. Third, we derive a covariant form of the partition function of a fermionic system.... 

In heavy ion collisions, extremely large electromagnetic fields are produced by fast-moving charged nucleons. They are sufficiently large to affect the low energy QCD processes and thus produce observable effects, whose occurrence is, however, directly related to the lifetime of these fields. In the present dissertation, the evolution of electromagnetic fields is studied in a plasma of quarks and gluons, by analytically solving the equations of relativistic magnetohydrodynamics (RMHD). The onideal Bjorken RMHD is solved by introducing the method of nonconserved charges. Assuming an electromagnetic force-free condition, the electric and magnetic fields are found to be either parallel or... 

Relativistic collisions of heavy ions lead to the formation of a new phase of matter called Quark-Gluon Plasma (QGP). In addition, strong magnetic fields generates in these collisions that its direction is perpendicular to the collision axis. This strong magnetic field affects the dynamics of particles in the QGP, and causes the appearance of the Landau levels in the particle’s energy spectrum. In this master thesis, we investigate the impact of the magnetic field on dilepton production and synchrotron radiation. We calculate the scattering probability of quark and anti-quark annihilation and dilepton creation by taking all Landau Levels into account. Then, by assuming that the magnetic... 

In the present thesis, the effect of external magnetic fields on two-flavor Color Superconductive (2SC) phase, as one of the phases in the QCD phase diagram, is studied. To do this, an effective two-flavor Nambu-Jona Lasinio Lagrangian is used, which consists of two mass gaps, s = ?¯qq and ? = ? . The nonzero values of chiral and color mass these gaps induce spontaneous chiral and color symmetry breaking, and consequently two different phases. There is also a third phase, the normal phase, where s = ? = 0. We calculate the transition curves and the critical points in terms of three intensive quantities, the temperature, the chemical potential and the external magnetic field. We study, in... 

After the review of formation of Landau levels (LL) in non-relativistic quantum mechanics, we have obtained LL in a certain gauge A_μ=(0,-B_0/2 y,B_0/2 x) at 2+1 &3+1 dimension. then give a summary of Quantum Field Theory at non-zero temperature . obtaining LL and two-point Green function in non-uniform magnetic field which determined with A_μ=(0,0,√qB ξe^(-(t+x) ),0).Next we calculate magnetic susceptibility of in such a field with finite chemical potential and temperature. Finally we compare the obtained results with uniform magnetic field one  

The main focus of this dissertation is to investigate the effects of the created background magnetic field on some of the observables that are relevant in heavy ions experiments. Based on the phase diagram of Quantum Chromodynamics, it is expected that in extreme conditions such as high temperature or in dense medium, a new phase of matter arises, which is known as Quark-Gluon Plasma (QGP). Due to the vital role of collective behaviors, this phase behaves similar to a perfect fluid rather than a gas. In addition, the colliding nucleons have potential of creating very strong magnetic fields because of their electric charges and relativistic speeds. Therefore the investigation of the effects... 

In this thesis NJL and quark-meson models, as effective models for quantum chro-modynamics in low energies, are studied mainly. After reviewing models and phe-nomena related to the strong interaction in zero and non-zero temperature, firstly the critical coupling of NJL model for non-zero temperature and chemical potential is calculated. Then, the contribution of ring diagrams in the effective potential of quark-meson model is presented. Finaly, the effect of ring diagrams of quark-meson model on chiral phase transition is investigated. For NJL model, it is shown that the chemical potential lowers the critical coupling for chiral phase transition. Also for quark-meson model, it is shown that... 

In this study, the effect of rigid rotation on the dynamical and thermodynamic properties of Dirac fermions in a chiral environment is investigated. Using the framework of quantum field theory, the Dirac equation is solved in the presence of rigid rotation, and the corresponding propagator is derived using the Fock-Schwinger method. The results demonstrate that the angular velocity Ω acts as an effective chemical potential and plays a significant role in the dynamical behavior of fermions. Using the fermion propagator arising in the first part of this work, the chiral current phenomena, including the Chiral Vortical and the Chiral Vortical Separation Effect is also examined in the presence... 

One of the most essential concepts for describing neutron stars is investigating their radial mass distribution or mass-radius relation. The aim of this thesis is to evaluate radial mass distribution of neutron stars in the presence of magnetic fields. To achieve this objective we use the Tolman- Oppenheimer-Volkoff equation of hydrostatic equilibrium for non-rotating cases and the Hartle- Thorne equations for rotating cases. olving these equations depends on determination of equation of state of neutron star in the presence of magnetic fields. For determining the corresponding equation of state, one can use QCD-like non-perturbative models, in particular Nambu-Jona- Lasinio (NJL) model. In... 

Worldline formalism provides an effective and intuitive method in order to obtain the full prop- agator of a system with definite degrees of freedom and the one-loop effective action of such a system interacting with a background field. The covariance of relations and results facilitates the generalization to more complex geometries and symmetries. Feynman for the first time arrived at a relation for the relativistic orbit of a quantum particle in vacuum. In the same year, Schwinger employed a differential method to address the problem of vacuum polarization. The purpose of the current research is to review both of these methods in their search for a polarized vacuum, Lorentzian and gauge... 

In the framework of the Standard Model of Particle Physics, Quantum Chromodynamics (QCD) is known to be the only theory which describes the strong nuclear force. Because of the property of asymptotic freedom, perturbative methods fail to describe QCD at low energies. Here, mesons and baryons build the main degrees of freedom of QCD. To describe the dynamics of mesons at low energies, nonperturbative methods are used. The Nambu–Jona-Lasinio (NJL) model is one of the most important effective models, which is used to study the nonperturbative phenomena of QCD at low energies. The Lagrangian density of this model includes a local four-fermion term,which descibes the interaction between the... 

Quantum Chromodynamics (QCD) is the theory of strong interaction. Two main properties of QCD in low energies are chiral symmetry breaking and confinement. At finite temperature, QCD exhibits a certain transition from a chirally broken phase to a chirally restored phase and liberation of color charge. Lattice QCD at finite temperature shows a crossover transition at vanishing or small chemical potential while the model-dependent studies, e.g. the Nambu-Jona--Lasinio model predicts a first-order phase transition at large chemical potentials. The first order and crossover transition lead to the existence of a critical point in the phase diagram of QCD. Determining the nature of the phase... 

This study explores the relationship between rigid rotation, thermodynamic instabilities, and quantum phase transitions in a relativistic Bose gas. By utilizing the thermodynamic potential derived from the Fock-Schwinger formalism, we demonstrate how angular velocity induces thermodynamic instabilities at high temperatures and in strong interaction regimes. These instabilities manifest as a negative moment of inertia, hypersonic sound velocity, and peculiar behavior in heat capacity. Furthermore, we examine how rigid rotation impacts the Bose-Einstein condensation (BEC). In both nonrelativistic and ultrarelativistic regimes, rotation decreases the critical temperature of the BEC, suppresses... 

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.
 

Using the achievements of differential geometry an extended form of descent equations is worked out which leads to a set of modified consistent anomalies. A gauge invariant partition function is also defined for gauge theories with the standard quantization results. It is shown that the (extended) descent equations and consequently the (modified) consistent anomalies and Schwinger terms can be extracted from this modified partition function naturally. Moreover Translation-invariant products are discussed in the setting of α-cohomology and it is shown that loop calculations of Translation-invariant quantum field theories are entirely determined by α-cohomology class of star product in all...