arXiv subjects

M. Alimohammadi

Publications and source records attributed to M. Alimohammadi.

At least 37 records · Page 2Linked to original sources

arXiv2003

Spin 0 and spin 1/2 particles in a constant scalar-curvature background

We study the Klein-Gordon and Dirac equations in the presence of a background metric ds^2 = -dt^2 + dx^2 + e^{-2gx}(dy^2 + dz^2) in a semi-infinite lab (x>0). This metric has a constant scalar curvature R=6g^2 and is produced by a perfect fluid with equation of state p=-ρ/3. The eigenfunctions of spin-0 and spin-1/2 particles are obtained exactly, and the quantized energy eigenvalues are compared. It is shown that both of these particles must have nonzero transverse momentum in this background. We show that there is a minimum energy E^2_{min}=m^2c^4 + g^2c^2\hbar^2$ for bosons E_{KG} > E_{min}, while the fermions have no specific ground state E_{Dirac}>mc^2.

gr-qc↗

arXiv2003

Spin 0 and spin 1/2 quantum relativistic particles in a constant gravitational field

The Klein-Gordon and Dirac equations in a semi-infinite lab ($x > 0$), in the background metric $\ds^2 = u^2(x) (-\dt^2 + \dx^2) + \dy^2 + \dz^2$, are investigated. The resulting equations are studied for the special case $ u(x) = 1 + g x$. It is shown that in the case of zero transverse-momentum, the square of the energy eigenvalues of the spin-1/2 particles are less than the squares of the corresponding eigenvalues of spin-0 particles with same masses, by an amount of $mg\hbar c$. Finally, for nonzero transverse-momentum, the energy eigenvalues corresponding to large quantum numbers are obtained, and the results for spin-0 and spin-1/2 particles are compared to each other.

gr-qc↗

arXiv2001

Exactly solvable models through the empty interval method, for more-than-two-site interactions

Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in them more than two neighboring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for $E_n(t)$'s, the probability that $n$ consecutive sites are empty at time $t$. The general method of solving the time evolution equation is discussed. As an example, a system with next-nearest-neighbor interaction is studied.

cond-mat↗

arXiv2001

Berry phase for spin--1/2 particles moving in a spacetime with torsion

Berry phase for a spin--1/2 particle moving in a flat spacetime with torsion is investigated in the context of the Einstein-Cartan-Dirac model. It is shown that if the torsion is due to a dense polarized background, then there is a Berry phase only if the fermion is massless and its momentum is perpendicular to the direction of the background polarization. The order of magnitude of this Berry phase is discussed in other theoretical frameworks.

gr-qc↗

arXiv2001

Exactly solvable models through the empty interval method

The most general one dimensional reaction-diffusion model with nearest-neighbor interactions, which is exactly-solvable through the empty interval method, has been introduced. Assuming translationally-invariant initial conditions, the probability that $n$ consecutive sites are empty ($E_n$), has been exactly obtained. In the thermodynamic limit, the large-time behavior of the system has also been investigated. Releasing the translational invariance of the initial conditions, the evolution equation for the probability that $n$ consecutive sites, starting from the site $k$, are empty ($E_{k,n}$) is obtained. In the thermodynamic limit, the large time behavior of the system is also considered. Finally, the continuum limit of the model is considered, and the empty-interval probability function is obtained.

cond-mat↗

arXiv2001

Massive Schwinger model and its confining aspects on curved space-time

Using a covariant method to regularize the composite operators, we obtain the bosonized action of the massive Schwinger model on a classical curved background. Using the solution of the bosonic effective action, the energy of two static external charges with finite and large distance separation on a static curved space-time is obtained. The confining behavior of this model is also explicitly discussed.

hep-th↗

arXiv2001

p-species integrable reaction-diffusion processes

We consider a process in which there are p-species of particles, i.e. A_1,A_2,...,A_p, on an infinite one-dimensional lattice. Each particle $A_i$ can diffuse to its right neighboring site with rate $D_i$, if this site is not already occupied. Also they have the exchange interaction A_j+A_i --> A_i+A_j with rate $r_{ij}.$ We study the range of parameters (interactions) for which the model is integrable. The wavefunctions of this multi--parameter family of integrable models are found. We also extend the 2--species model to the case in which the particles are able to diffuse to their right or left neighboring sites.

cond-mat↗

arXiv2000

On the phase structure of two--dimensional generalized Yang--Mills theories

The phase structure of the generalized Yang--Mills theories is studied, and it is shown that {\it almost} always, it is of the third order. As a specific example, it is shown that all of the models with the interaction $\sum_j (n_j-j+N)^{2k}$ exhibit third order phase transition. ($n_j$ is the length of the $j$-th row of the Yang tableau corresponding to U($N$).) The special cases where the transition is not of the third order are also considered and, as a specific example, it is shown that the model $\sum_j (n_j-j+N)^2+g\sum_j (n_j-j+N)^{4}$ exhibits a third order phase transition, except for $g=27π^2/256$, where the order of the transition is 5/2.

hep-th↗

arXiv2000

Confinement and screening of the Schwinger model on the Poincare half plane

We discuss the confining features of the Schwinger model on the Poincare half plane. We show that despite the fact that the expectation value of the large Wilson loop of massless Schwinger model displays the perimeter behavior, the system can be in confining phase due to the singularity of the metric at horizontal axis. It is also shown that in the quenched Schwinger model, the area dependence of the Wilson loop, in contrast to the flat case, is a not a sign of confinement and the model has a finite energy even for large external charges separation. The presence of dynamical fermions can not modify the screening or the confining behavior of the system. Finally we show that in the massive Schwinger model, the system is again in screening phase. The zero curvature limit of the solutions is also discussed.

hep-th↗

arXiv2000

More on generalized simplicial chiral models

By generalizing the auxiliary field term in the Lagrangian of simplicial chiral models on a (d-1)-dimensional simplex, the generalized simplicial chiral models has been introduced in \c{Ali}. These models can be solved analytically only in d=0 and d=2 cases at large-N limit. In d=0 case, we calculate the eigenvalue density function in strong regime and show that the partition function computed from this density function is consistent with one calculated by path integration directly. In d=2 case, it is shown that all $V= {\rm Tr}(AA^{\d})^n$ models have a third order phase transition, same as the 2-dimensional Yang-Mills theory.

hep-th↗

arXiv2000

A new class of integrable diffusion-reaction processes

We consider a process in which there are two types of particles, A and B, on an infinite one-dimensional lattice. The particles hop to their adjacent sites, like the totally asymmetric exclusion process (ASEP), and have also the following interactions: A+B -> B+B and B+A -> B+B, all occur with equal rate. We study this process by imposing four boundary conditions on ASEP master equation. It is shown that this model is integrable, in the sense that its N-particle S-matrix is factorized into a product of two-particle S-matrices and, more importantly, the two-particle S-matrix satisfy quantum Yang-Baxter equation. Using coordinate Bethe-ansatz, the N-particle wavefunctions and the two-particle conditional probabilities are found exactly. Further, by imposing four reasonable physical conditions on two-species diffusion-reaction processes (where the most important ones are the equality of the reaction rates and the conservation of the number of particles in each reaction), we show that among the 4096 types of the interactions which have these properties and can be modeled by a master equation and an appropriate set of boundary conditions, there are only 28 independent interactions which are integrable. We find all these interactions and also their corresponding wave functions. Some of these may be new solutions of quantum Yang-Baxter equation.

cond-mat↗

arXiv2000

Large-N limit of the generalized 2D Yang-Mills theory on cylinder

Using the collective field theory approach of large-N generalized two-dimensional Yang-Mills theory on cylinder, it is shown that the classical equation of motion of collective field is a generalized Hopf equation. Then, using the Itzykson-Zuber integral at the large-N limit, it is found that the classical Young tableau density, which satisfies the saddle-point equation and determines the large-N limit of free energy, is the inverse of the solution of this generalized Hopf equation, at a certain point.

hep-th↗

arXiv1999

Quantum reflection of massless neutrinos from a torsion-induced potential

In the context of the Einstein-Cartan-Dirac model, where the torsion of the space-time couples to the axial currents of the fermions, we study the effects of this quantum-gravitational interaction on a massless neutrino beam crossing through a medium with high number density of fermions at rest. We calculate the reflection amplitude and show that a specific fraction of the incident neutrinos reflects from this potential if the polarization of the medium is different from zero. We also discuss the order of magnitude of the fermionic number density in which this phenomenon is observable, in other theoretical contexts, for example the strong-gravity regime and the effective field theory approach.

gr-qc↗

arXiv1999

A two--parametric family of asymmetric exclusion processes and its exact solution

A two--parameter family of asymmetric exclusion processes for particles on a one-dimensional lattice is defined. The two parameters of the model control the driving force and an effect which we call pushing, due to the fact that particles can push each other in this model. We show that this model is exactly solvable via the coordinate Bethe Ansatz and show that its {\it N}-particle $S$-matrix is factorizable. We also study the interplay of the above effects in determining various steady state and dynamical characteristics of the system.

cond-mat↗

arXiv1999

Coulomb gas representation of quantum Hall effect on Riemann surfaces

Using the correlation function of chiral vertex operators of the Coulomb gas model, we find the Laughlin wavefunctions of quantum Hall effect, with filling factor $ν=1/m$, on Riemann sufaces with Poincare metric. The same is done for quasihole wavefunctions. We also discuss their plasma analogy.

hep-th↗

arXiv1999

Phase structure of the generalized two dimensional Yang-Mills theories on sphere

We find a general expression for the free energy of $G(ϕ)=ϕ^{2k}$ generalized 2D Yang-Mills theories in the strong ($A>A_c$) region at large $N$. We also show that in this region, the density function of Young tableau of these models is a three-cut problem. In the specific $ϕ^6$ model, we show that the theory has a third order phase transition, like $ϕ^2$ (YM_2) and $ϕ^4$ models. We have some comments for $k \geq 4$ cases. At the end, we study the phase structure of $ϕ^2 + g ϕ^4$ model for $g \leq A/4$ region.

hep-th↗

arXiv1998

Large-N limit of the generalized 2-dimensional Yang-Mills theories

Using the standard saddle-point method, we find an explicit relation for the large-N limit of the free energy of an arbitrary generalized 2D Yang-Mills theory in the weak ($A A_c$) region, we investigate carefully the specific fourth Casimir theory, and show that the ordinary integral equation of the density function is not adequate to find the solution. There exist, however, another equation which restricts the parameters. So one can find the free energy in strong region and show that the theory has a third order phase transition.

hep-th↗

arXiv1998

Exact solution of a one-parameter family of asymmetric exclusion processes

We define a family of asymmetric processes for particles on a one-dimensional lattice, depending on a continuous parameter $λ\in [0,1] $, interpolating between the completely asymmetric processes [1] (for $λ=1$) and the n=1 drop-push models [2] (for $ λ=0$). For arbitrary $\la$, the model describes an exclusion process, in which a particle pushes its right neighbouring particles to the right, with rates depending on the number of these particles. Using the Bethe ansatz, we obtain the exact solution of the master equation .

cond-mat↗