arXiv subjects

S. Rouhani

Publications and source records attributed to S. Rouhani.

At least 37 records · Page 2Linked to original sources

arXiv2009

Optimal Entanglement Provision over Underlying Networks of Group Association Schemes

We investigate creation of optimal entanglement in symmetric networks. The proposed network is one in which the connections are organized by a group table in other words a group association scheme. We show that optimal entanglement can be provided over such networks by adjusting couplings and initial state. We find that the optimal initial state is a simple local excited state. Moreover we obtain an analytic formula for entanglement achievable between vertex pairs located in the same strata and calculate their relevant optimal couplings. For those pairs located in different strata two upper bounds are presented. These results are also checked numerically.

quant-ph↗

arXiv2009

Scaling and Multiscaling Behavior of the Perimeter of Diffusion-Limited Aggregation (DLA) Generated by the Hastings-Levitov Method

In this paper, we analyze the scaling behavior of \emph{Diffusion Limited Aggregation} (DLA) simulated by Hastings-Levitov method. We obtain the fractal dimension of the clusters by direct analysis of the geometrical patterns in a good agreement with one obtained from analytical approach. We compute the two-point density correlation function and we show that in the large-size limit, it agrees with the obtained fractal dimension. These support the statistical agreement between the patterns and DLA clusters. We also investigate the scaling properties of various length scales and their fluctuations, related to the boundary of cluster. We find that all of the length scales do not have a simple scaling with same correction to scaling exponent. The fractal dimension of the perimeter is obtained equal to that of the cluster. The growth exponent is computed from the evolution of the interface width equal to $β=0.557(2)$. We also show that the perimeter of DLA cluster has an asymptotic multiscaling behavior.

cond-mat.stat-mech↗

arXiv2008

Direct Evidence for Conformal Invariance of Avalanche Frontier in Sandpile Models

Appreciation of Stochastic Loewner evolution (SLE$_κ$), as a powerful tool to check for conformal invariant properties of geometrical features of critical systems has been rising. In this paper we use this method to check conformal invariance in sandpile models. Avalanche frontiers in Abelian sandpile model (ASM) are numerically shown to be conformally invariant and can be described by SLE with diffusivity $κ=2$. This value is the same as value obtained for loop erased random walks (LERW). The fractal dimension and Schramm's formula for left passage probability also suggest the same result. We also check the same properties for Zhang's sandpile model.

cond-mat.stat-mech↗

arXiv2008

Scaling of Clusters and Winding Angle Statistics of Iso-height Lines in two-dimensional KPZ Surface

We investigate the statistics of Iso-height lines of (2+1)-dimensional Kardar-Parisi-Zhang model at different level sets around the mean height in the saturation regime. We find that the exponent describing the distribution of the height-cluster size behaves differently for level cuts above and below the mean height, while the fractal dimensions of the height-clusters and their perimeters remain unchanged. The winding angle statistics also confirms again the conformal invariance of these contour lines in the same universality class of self-avoiding random walks (SAWs).

cond-mat.stat-mech↗

arXiv2008

Power Spectrum in Krein Space Quantization

The power spectrum of scalar field and space-time metric perturbations produced in the process of inflation of universe, have been presented in this paper by an alternative approach to field quantization namely, Krein space quantization [1,2]. Auxiliary negative norm states, the modes of which do not interact with the physical world, have been utilized in this method. Presence of negative norm states play the role of an automatic renormalization device for the theory.

gr-qc↗

arXiv2008

Conformally Invariant "Massless" Spin-2 Field in de Sitter Universe

''Massless'' spin-2 field equation in de Sitter space, which is invariant under the conformal transformation, has been obtained. The frame work utilized is the symmetric rank-2 tensor field of the conformal group. Our method is based on the group theoretical approach and six-cone formalism, initially introduced by Dirac. Dirac's six-cone is used to obtain conformally invariant equations on de Sitter space. The solution of the physical sector of massless spin-2 field (linear gravity) in de Sitter ambient space is written as a product of a generalized polarization tensor and a massless minimally coupled scalar field. Similar to the minimally coupled scalar field, for quantization of this sector, the Krein space quantization is utilized. We have calculated the physical part of the linear graviton two-point function. This two-point function is de Sitter invariant and free of pathological large distance behavior.

gr-qc↗

arXiv2008

Conformal Invariance of Iso-height Lines in two-dimensional KPZ Surface

The statistics of the iso-height lines in (2+1)-dimensional Kardar-Parisi-Zhang (KPZ) model is shown to be conformal invariant and equivalent to those of self-avoiding random walks. This leads to a rich variety of new exact analytical results for the KPZ dynamics. We present direct evidence that the iso-height lines can be described by the family of conformal invariant curves called Schramm-Loewner evolution (or $SLE_κ$) with diffusivity $κ=8/3$. It is shown that the absence of the non-linear term in the KPZ equation will change the diffusivity $κ$ from 8/3 to 4, indicating that the iso-height lines of the Edwards-Wilkinson (EW) surface are also conformally invariant, and belong to the universality class of the domain walls in the O(2) spin model.

physics.data-an↗

arXiv2007

Conformal Curves on $WO_3$ Surface

We have studied the iso-height lines on the $\mathrm{WO_3}$ surface as a physical candidate for conformally invariant curves. We have shown that these lines are conformally invariant with the same statistics of domain walls in the critical Ising model. They belong to the family of conformal invariant curves called Schramm-Loewner evolution (or $SLE_κ$), with diffusivity of $κ\sim 3$. This can be regarded as the first experimental observation of SLE curves. We have also argued that Ballistic Deposition (BD) can serve as a growth model giving rise to contours with similar statistics at large scales.

cond-mat.stat-mech↗

arXiv2007

Casimir effect on nontrivial topology spaces in Krein space quantization

Casimir effect of a topologically nontrivial two-dimensional space-time, through Krein space quantization [1,2], has been calculated. In other words, auxiliary negative norm states have been utilized here. Presence of negative norm states play the role of an automatic renormalization device for the theory. The negative norm states (which do not interact with the physical world) could be chosen in two perspective. In the first case our method results in zero or vanishing values for energy. In the second case, however, the result are the same as the renormalization procedure.

gr-qc↗

arXiv2007

The Effect of Annealing Temperature on Statistical Properties of $WO_3$ Surface

We have studied the effect of annealing temperature on the statistical properties of $WO_3$ surface using atomic force microscopy techniques (AFM). We have applied both level crossing and structure function methods. Level crossing analysis indicates an optimum annealing temperature of around 400$^oC$ at which the effective area of the $WO_3$ thin film is maximum, whereas composition of the surface remains stoichiometric. The complexity of the height fluctuation of surfaces was characterized by roughness, roughness exponent and lateral size of surface features. We have found that there is a phase transition at around 400$^oC$ from one set to two sets of roughness parameters. This happens due to microstructural changes from amorphous to crystalline structure in the samples that has been already found experimentally.

physics.data-an↗

arXiv2006

Some Aspects of c=-2 Theory

We investigate some aspects of the c=-2 logarithmic conformal field theory. These include the various representations related to this theory, the structures which come out of the Zhu algebra and the W algebra related to this theory. We try to find the fermionic representations of all of the fields in the extended Kac table especially for the untwisted sector case. In addition, we calculate the various OPEs of the fields, especially the energy-momentum tensor. Moreover, we investigate the important role of the zero modes in this model. We close the paper by considering the perturbations of this theory and their relationship to integrable models and generalization of Zamolodchikov's $c-$theorem.

hep-th↗

arXiv2006

"Massless" vector field in de Sitter Universe

In the present work the massless vector field in the de Sitter (dS) space has been quantized. "Massless" is used here by reference to conformal invariance and propagation on the dS light-cone whereas "massive" refers to those dS fields which contract at zero curvature unambiguously to massive fields in Minkowski space. Due to the gauge invariance of the massless vector field, its covariant quantization requires an indecomposable representation of the de Sitter group and an indefinite metric quantization. We will work with a specific gauge fixing which leads to the simplest one among all possible related Gupta-Bleuler structures. The field operator will be defined with the help of coordinate independent de Sitter waves (the modes) which are simple to manipulate and most adapted to group theoretical matters. The physical states characterized by the divergencelessness condition will for instance be easy to identify. The whole construction is based on analyticity requirements in the complexified pseudo-Riemanian manifold for the modes and the two-point function.

gr-qc↗

arXiv2006

A Naturally Renormalized Quantum Field Theory

It was shown that quantum metric fluctuations smear out the singularities of Green's functions on the light cone [1], but it does not remove other ultraviolet divergences of quantum field theory. We have proved that the quantum field theory in Krein space, {\it i.e.} indefinite metric quantization, removes all divergences of quantum field theory with exception of the light cone singularity [2,3]. In this paper, it is discussed that the combination of quantum field theory in Krein space together with consideration of quantum metric fluctuations, results in quantum field theory without any divergences.

gr-qc↗

arXiv2006

Casimir Effect In Krein Space Quantization

An explicit calculation of Casimir effect through an alternative approach of field quantization [1, 2], has been presented in this paper. In this method, the auxiliary negative norm states have been utilized, the modes of which do not interact with the physical states or real physical world. Naturally these modes cannot be affected by the physical boundary conditions. Presence of negative norm states play the rule of an automatic renormalization device for the theory.

gr-qc↗

arXiv2006

Perturbed Logarithmic CFT and Integrable Models

Perturbation of logarithmic conformal field theories is investigated using Zamolodchikov's method. We derive conditions for the perturbing operator, such that the perturbed model be integrable. We also consider an example where integrable models arise out of perturbation of known logarithmic conformal field theories.

hep-th↗

arXiv2005

SLE($κ,ρ$)and Boundary Coulomb Gas

We consider the coulomb gas model on the upper half plane with different boundary conditions, namely Drichlet, Neuman and mixed. We related this model to SLE($κ,ρ$) theories. We derive a set of conditions connecting the total charge of the coulomb gas, the boundary charges, the parameters $κ$ and $ρ$. Also we study a free fermion theory in presence of a boundary and show with the same methods that it would lead to logarithmic boundary changing operators.

hep-th↗

arXiv2005

Discrete Symmetries for Spinor Field in de Sitter Space

Discrete symmetries, parity, time reversal, antipodal, and charge conjugation transformations for spinor field in de Sitter space, are presented in the ambient space notation, i.e. in a coordinate independent way. The PT and PCT transformations are also discussed in this notation. The five-current density is studied and their transformation under the discrete symmetries is discussed.

gr-qc↗

arXiv2005

SLE with Jumps and Conformal Null Vectors

Ordinary SLE$_{k}$ is defined using a Wiener noise and is related to CFT's which have null vector at level two of conformal tower. In this paper we introduce stochastic variables which are made up of jumps and extend the ordinary SLE to have such stochastic variables. The extended SLE can be related to CFT's which have null vectors in higher levels of Virasoro module.

cond-mat.stat-mech↗