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#### Non-Relativistic Conformal Symmetries; Infinite Extensions and Logarithmic Representation

, Ph.D. Dissertation Sharif University of Technology ; Rouhani, Shahin (Supervisor)
Abstract

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

#### Schrodinger-Virasoro Algebra

, M.Sc. Thesis Sharif University of Technology ; Rouhani, Shahin (Supervisor)
Abstract

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...

#### On AdS/CFT of galilean conformal field theories

, Article Journal of High Energy Physics ; Volume 2009, Issue 8 , 2009 ; 11266708 (ISSN) ; Davody, A ; Vahedi, A ; Sharif University of Technology
2009

Abstract

We study a new contraction of a d+1 dimensional relativistic conformal algebra where n+1 directions remain unchanged. For n = 0,1 the resultant algebras admit infinite dimensional extension containing one and two copies of Virasoro algebra, respectively. For 1$">n>1 the obtained algebra is finite dimensional containing an so(2,n+1) subalgebra. The gravity dual is provided by taking a Newton-Cartan like limit of the Einstein's equations of AdS space which singles out an AdS n+2 spacetime. The infinite dimensional extension of n = 0,1 cases may be understood from the fact that the dual gravities contain AdS 2 and AdS 3 factor, respectively. We also explore how the AdS/CFT correspondence works...

####
String Theory Discription on Non-Relativistic QFT

,
Ph.D. Dissertation
Sharif University of Technology
;
Ardalan, Farhad
(Supervisor)
Abstract

In this Thesis we study the string theory discription of non-relativistic quantum ?eld theories.In other statement we study the duality between gravity and gauge theory with non-relativistic symmetry.We discuss that this duality works in non rel- ativistic sense.We study two kind of non-relativistic theories that one of them camefrom string theory and other model obtained by special transformation of original relativistic theory and we see that how duality can be work for these models.Also dual picture of semi-classical string in the background that found from string theorystudied.We also study the motion of particle in a hot plasma and we ?nd a sign of non-relativisic duality really works

#### NHEG mechanics: Laws of near horizon extremal geometry (thermo)dynamics

, Article Journal of High Energy Physics ; Vol. 2014, issue. 3 , 2014 ; ISSN: 11266708 ; Seraj, A ; Sheikh-Jabbari, M. M ; Sharif University of Technology
Abstract

Near Horizon Extremal Geometries (NHEG) are solutions to gravity theories with SL(2, ℝ) × U(1) N (for some N) symmetry, are smooth geometries and have no event horizon, unlike black holes. Following the ideas by R. M. Wald, we derive laws of NHEG dynamics, the analogs of laws of black hole dynamics for the NHEG. Despite the absence of horizon in the NHEG, one may associate an entropy to the NHEG, as a Noether-Wald conserved charge. We work out "entropy" and "entropy perturbation" laws, which are respectively universal relations between conserved Noether charges corresponding to the NHEG and a system probing the NHEG. Our entropy law is closely related to Sen's entropy function. We also...

#### Characterization of qutrit channels in terms of their covariance and symmetry properties

, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 84, Issue 1 , July , 2011 ; 10502947 (ISSN) ; Mani, A ; Memarzadeh, L ; Sharif University of Technology
2011

Abstract

We characterize the completely positive trace-preserving maps on qutrits (qutrit channels) according to their covariance and symmetry properties. Both discrete and continuous groups are considered. It is shown how each symmetry group restricts arbitrariness in the parameters of the channel to a very small set. Although the explicit examples are related to qutrit channels, the formalism is sufficiently general to be applied to qudit channels

#### Special Lagrangian sub-manifolds and super-symmetry

, Article International Journal of Geometric Methods in Modern Physics ; Volume 10, Issue 7 , 2013 ; 02198878 (ISSN) ; Sharif University of Technology
2013

Abstract

Special Lagrangian sub-manifolds of Calabi-Yau (CY) 3-folds are used to describe membrane instanton solutions of N = 1, 11-dimensional super-gravity theories. Super-symmetry is the essential ingredient that relates super-gravity branes to special Lagrangian sub-manifolds [K. Becker, M. Becker and A. Strominger, Fivebranes, membranes and non-perturbative string theory, Nucl. Phys. B 456(1-2) (1995) 135-152]. In this note we would like to explain this relation, more explicitly and with more details than in the current literature

#### Analyzing symmetry in photonic band structure of gyro-magnetic photonic crystals

, Article Proceedings of SPIE - The International Society for Optical Engineering ; Volume 8096 , 2011 ; 0277786X (ISSN) ; 9780819487063 (ISBN) ; Khorasani, S ; Gholami, F ; Sharif University of Technology
2011

Abstract

In the band structure analysis of photonic crystals it is normally assumed that the full photonic gaps could be found by scanning high-symmetry paths along the edges of Irreducible Brillouin Zones (IBZ). We have recently shown [1] that this assumption is wrong in general for sufficiently symmetry breaking geometries, so that the IBZ is exactly half of the complete BZ. That minimal required symmetry arises from the requirement on time-reversal symmetry. In this paper we show that even that requirement might be broken by using gyro-magnetic materials in the composition of photonic structures we can observe that the IBZ extends fully to the boundaries of the complete BZ, that is IBZ must be as...

#### Wiggling throat of extremal black holes

, Article Journal of High Energy Physics ; Volume 2015, Issue 10 , October , 2015 ; 11266708 (ISSN) ; Hajian, K ; Seraj, A ; Sheikh Jabbari, M. M ; Sharif University of Technology
Springer Verlag
2015

Abstract

Abstract: We construct the classical phase space of geometries in the near-horizon region of vacuum extremal black holes as announced in [arXiv:1503.07861]. Motivated by the uniqueness theorems for such solutions and for perturbations around them, we build a family of metrics depending upon a single periodic function defined on the torus spanned by the U(1) isometry directions. We show that this set of metrics is equipped with a consistent symplectic structure and hence defines a phase space. The phase space forms a representation of an infinite dimensional algebra of so-called symplectic symmetries. The symmetry algebra is an extension of the Virasoro algebra whose central extension is the...

#### Synthesis and crystal structure of non-symmetric tetradentate complexes of Ni(II), Cu(II), Co(II), and Zn(II)

, Article Synthesis and Reactivity in Inorganic, Metal-Organic and Nano-Metal Chemistry ; Volume 40, Issue 6 , Jul , 2010 , Pages 373-377 ; 15533174 (ISSN) ; Boghaei, D. M ; Shivapour, Z ; Seraj, S ; Sharif University of Technology
2010

Abstract

The non-symmetrical tetradentate Schiff-base H2L have been obtained using the half-unit N-(1-hydroxy-2-acetonaphthone)-1-amino-2- phenyleneimine (HL1) with 2-hydroxyl-1-naphthaldehyde. ML complexes(M = Ni(1), Cu(2), Co(3) and Zn(4)) were prepared and characterized by atomic absorption, IR, UV, 1H NMR spectroscopy, and a single crystal X-ray structure. Crystal data for (1) are triclinic space group P-1, a = 7.9784 (3) A, b = 10.2417 (4) A, c = 13.4090 (5) A, α = 103.8480 (10)°, β = 97.0540 (10)°, γ = 92.2400 (10)° and z = 2. Crystal data for (2): Triclinic space group P-1, a = 7.9991 (6) A, b = 10.0520 (7) A, c = 13.6974 (10) A, α = 103.6500 (10)°, β = 95.9650 (10)°, γ = 90.3160 (10)° and z =...

####
Study ofthe NJL-Model Phase Diagram at Finite Temperature and Chemical Potential

,
M.Sc. Thesis
Sharif University of Technology
;
Rouhani, Shahin
(Supervisor)
;
Sadooghi, Neda
(Supervisor)
Abstract

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.

#### Application of the Coset Construction Method in Theories of Spontaneous Symmetry Breaking: Gravitation as an Example

, M.Sc. Thesis Sharif University of Technology ; Torabian, Mahdi (Supervisor)
Abstract

In this manuscript we used the method of coset construction to describe theories of spontaneous symmetry breaking. The mathematical details are included in chapter 2. The utility of the method is that without any knowledge of the UV part of a theory we can construct IR part by just knowing the symmetry breaking pattern. We used the method for some symmetry breaking patterns to construct general relativity, massive gravity and also some symmetry breaking patterns corresponding to conformal gravity

#### Symmetry fractionalization: Symmetry-protected topological phases of the bond-alternating spin-1/2 Heisenberg chain

, Article Journal of Physics Condensed Matter ; Vol. 26, issue. 45 , 2014 ; ISSN: 09538984 ; Langari, A ; Rezakhani, A. T ; Sharif University of Technology
Abstract

We study different phases of the one-dimensional bond-alternating spin-1/2 Heisenberg model by using the symmetry fractionalization mechanism. We employ the infinite matrix-product state representation of the ground state (through the infinite-size density matrix renormalization group algorithm) to obtain inequivalent projective representations and commutation relations of the (unbroken) symmetry groups of the model, which are used to identify the different phases. We find that the model exhibits trivial as well as symmetry-protected topological phases. The symmetry-protected topological phases are Haldane phases on even/odd bonds, which are protected by the time-reversal (acting on the spin...

#### Symmetry and partial order reduction techniques in model checking Rebeca

, Article Acta Informatica ; Volume 47, Issue 1 , 2010 , Pages 33-66 ; 00015903 (ISSN) ; Sirjani, M ; Mousavi, M.R ; Khamespanah, E ; Movaghar, A ; Sharif University of Technology
2010

Abstract

Rebeca is an actor-based language with formal semantics which is suitable for modeling concurrent and distributed systems and protocols. Due to its object model, partial order and symmetry detection and reduction techniques can be efficiently applied to dynamic Rebeca models. We present two approaches for detecting symmetry in Rebeca models: One that detects symmetry in the topology of inter-connections among objects and another one which exploits specific data structures to reflect internal symmetry in the internal structure of an object. The former approach is novel in that it does not require any input from the modeler and can deal with the dynamic changes of topology. This approach is...

#### Nonreciprocal behaviour between photon and phonon in coupled optomechanical systems

, Article Journal of Modern Optics ; Volume 64, Issue 5 , 2017 , Pages 507-514 ; 09500340 (ISSN) ; Zandi, M. H ; Bahrampour, A ; Sharif University of Technology
Taylor and Francis Ltd
2017

Abstract

It is shown that the asymmetry coupling between two coupled optomechanical cavities leads to special class of PT-symmetric model for optomechanical structure. Under these conditions, Hamiltonian is considered in blue and red sideband regime. In these cases, the asymmetric coupling between two cavities has been transferred such that the asymmetric beam-splitter or squeezing interaction is generated between optical and mechanical modes. Then, the amount of entanglement between the different optical and mechanical modes is calculated. The results define that PT-symmetry can improve the entanglement in special conditions. The proposed system provides good condition to investigate the...

#### The Role of Symmetry in Quantifying Information

, M.Sc. Thesis Sharif University of Technology ; Shafie, Afshin (Supervisor)
Abstract

In this thesis we want to discuss about a new approach about information. Using this approach, Scott Muller builds his formalism on two basic concepts: distinguishablity and symmetry. His claim is that there is an inverse relation between symmetry and information. It means that if we have a symmetric system we need less information (Than an asymmetric system) to describe it. Here, we are going to explore the role and significance of symmetry in probabilistic distributions of the double-slit experiment, and we want to show if there is a predetermined relation between symmetry and information or not.

#### Will The (Super)Symmetry Survive?

, M.Sc. Thesis Sharif University of Technology ; Golshani, Mehdi (Supervisor)
Abstract

The concept of symmetry has long been the focus of numerous debates in different fields; some have come up with an artistic approach looking for a beautiful notion germane to the concept of symmetry. Others have examined this issue from a philosophical viewpoint and studied the ontology of symmetry and philosophers like Kant moved beyond the limits and have given their symmetry a transcendental position. On the other hand, in an anti-realist position relying on the fact that the goal of science is not truth but merely it’s an empirical adequacy, Van Fraassen argued that “science was rapidly gaining autonomy not only from theology but from all of philosophy, and was exploiting concepts and...

#### Gauge invariant cutoff QED

, Article Physica Scripta ; Volume 87, Issue 3 , 2013 ; 00318949 (ISSN) ; Arfaei, H ; Ghasemkhani, M ; Sadooghi, N ; Sharif University of Technology
2013

Abstract

A hidden generalized gauge symmetry of a cutoff QED is used to show the renormalizability of QED. In particular, it is shown that the corresponding Ward identities are valid all along the renormalization group flow. The exact renormalization group flow equation corresponding to the effective action of a cutoff λψ4 theory is also derived. Generalization to any gauge group is indicated

#### Discrimination of target and chaff in marine applications based on symmetry feature

, Article MRRS 2017 - 2017 IEEE Microwaves, Radar and Remote Sensing Symposium, Proceedings, 29 August 2017 through 31 August 2017 ; 2017 , Pages 131-135 ; 9781509053919 (ISBN) ; Aalami, H ; Nayebi, M. M ; Amin, A. R ; Danaei, M. R ; Yanovsky, F ; Rudiakova, A ; Averyanova, Y ; Sharif University of Technology
Abstract

Among the various techniques of electronic warfare in the sea, chaff has particular importance due to its easy application and its impact on the victim radar. Despite the great history of chaff, the significant research has not been published on its recognition. It is difficult to study the behavior of chaff because of the impossibility of chaff tests in an unechoic chamber. Therefore simulation would be a suitable alternative. In this paper, the simulations of symmetric feature of chaff and target are presented and it is used to propose a processing structure, based on various classifiers, for discrimination between chaff and target. Moreover the comparison between discrimination capability...

#### Biased random satisfiability problems: From easy to hard instances

, Article Physical Review E - Statistical, Nonlinear, and Soft Matter Physics ; Volume 71, Issue 6 , 2005 ; 15393755 (ISSN) ; Moghimi Araghi, S ; Sharif University of Technology
2005

Abstract

In this paper we study biased random K-satisfiability (K-SAT) problems in which each logical variable is negated with probability p. This generalization provides us a crossover from easy to hard problems and would help us in a better understanding of the typical complexity of random K-SAT problems. The exact solution of 1-SAT case is given. The critical point of K-SAT problems and results of replica method are derived in the replica symmetry framework. It is found that in this approximation αcp-(K-1) for p→0. Solving numerically the survey propagation equations for K=3 we find that for p