arXiv subjects

V. Karimipour

Publications and source records attributed to V. Karimipour.

At least 37 records · Page 2Linked to original sources

arXiv2005

Entanglement of bosonic modes in symmetric graphs

The ground and thermal states of a quadratic hamiltonian representing the interaction of bosonic modes or particles are always Gaussian states. We investigate the entanglement properties of these states for the case where the interactions are represented by harmonic forces acting along the edges of symmetric graphs, i.e. 1, 2, and 3 dimensional rectangular lattices, mean field clusters and platonic solids. We determine the Entanglement of Formation (EoF) as a function of the interaction strength, calculate the maximum EoF in each case and compare these values with the bounds found in \cite{wolf} which are valid for any quadratic hamiltonian.

quant-ph↗

arXiv2004

Thermal entanglement of spins in the Heisenberg model at low temperatures

We calculate the entanglement between two spins in the ferromagnetic Heisenberg chain at low temperatures, and show that when only the ground state and the one particle states are populated, the entanglement profile is a gaussian with a characteristic length depending on the temperature and the coupling between spins. The magnetic field only affects the amplitude of the profile and not its characteristic length.

quant-ph↗

arXiv2004

Thermal entanglement of spins in a nonuniform magnetic field

We study the effect of inhomogeneities in the magnetic field on the thermal entanglement of a two spin system. We show that in the ferromagnetic case a very small inhomogeneity is capable to produce large values of thermal entanglement. This shows that the absence of entanglement in the ferromagnetic Heisenberg system is highly unstable against inhomogeneoity of magnetic fields which is inevitably present in any solid state realization of qubits.

quant-ph↗

arXiv2004

Simple models of small world networks with directed links

We investigate the effect of directed short and long range connections in a simple model of small world network. Our model is such that we can determine many quantities of interest by an exact analytical method. We calculate the function $V(T)$, defined as the number of sites affected up to time $T$ when a naive spreading process starts in the network. As opposed to shortcuts, the presence of un-favorable bonds has a negative effect on this quantity. Hence the spreading process may not be able to affect all the network. We define and calculate a quantity named the average size of accessible world in our model. The interplay of shortcuts, and un-favorable bonds on the small world properties is studied.

cond-mat.dis-nn↗

arXiv2004

Correlation effects in a simple model of small-world network

We analyze the effect of correlations in a simple model of small world network by obtaining exact analytical expressions for the distribution of shortest paths in the network. We enter correlations into a simple model with a distinguished site, by taking the random connections to this site from an Ising distribution. Our method shows how the transfer matrix technique can be used in the new context of small world networks.

cond-mat.dis-nn↗

arXiv2004

Investigation of a Protein Complex Network

The budding yeast {\it Saccharomyces cerevisiae} is the first eukaryote whose genome has been completely sequenced. It is also the first eukaryotic cell whose proteome (the set of all proteins) and interactome (the network of all mutual interactions between proteins) has been analyzed. In this paper we study the structure of the yeast protein complex network in which weighted edges between complexes represent the number of shared proteins. It is found that the network of protein complexes is a small world network with scale free behavior for many of its distributions. However we find that there are no strong correlations between the weights and degrees of neighboring complexes. To reveal non-random features of the network we also compare it with a null model in which the complexes randomly select their proteins. Finally we propose a simple evolutionary model based on duplication and divergence of proteins.

cond-mat.dis-nn↗

arXiv2004

On a suggestion relating topological and quantum mechanical entanglements

We analyze a recent suggestion \cite{kauffman1,kauffman2} on a possible relation between topological and quantum mechanical entanglements. We show that a one to one correspondence does not exist, neither between topologically linked diagrams and entangled states, nor between braid operators and quantum entanglers. We also add a new dimension to the question of entangling properties of unitary operators in general.

quant-ph↗

arXiv2003

Symmetrization and Entanglement of Arbitrary States of Qubits

Given two arbitrary pure states $ |ϕ>$ and $ |ψ>$ of qubits or higher level states, we provide arguments in favor of states of the form $ \frac{1}{\sqrt{2}}(|ψ> |ϕ> + i |ϕ> |ψ>) $ instead of symmetric or anti-symmetric states, as natural candidates for optimally entangled states constructed from these states. We show that such states firstly have on the average a high value of concurrence, secondly can be constructed by a universal unitary operator independent of the input states. We also show that these states are the only ones which can be produced with perfect fidelity by any quantum operation designed for intertwining two pure states with a relative phase. A probabilistic method is proposed for producing any pre-determined relative phase into the combination of any two arbitrary states.

quant-ph↗

arXiv2002

Generating correlated networks from uncorrelated ones

In this paper we consider a transformation which converts uncorrelated networks to correlated ones(here by correlation we mean that coordination numbers of two neighbors are not independent). We show that this transformation, which converts edges to nodes and connects them according to a deterministic rule, nearly preserves the degree distribution of the network and significantly increases the clustering coefficient. This transformation also enables us to relate percolation properties of the two networks.

cond-mat.dis-nn↗

arXiv2002

On the Phase Covariant Quantum Cloning

It is known that in phase covariant quantum cloning the equatorial states on the Bloch sphere can be cloned with a fidelity higher than the optimal bound established for universal quantum cloning. We generalize this concept to include other states on the Bloch sphere with a definite $z$ component of spin. It is shown that once we know the $z$ component, we can always clone a state with a fidelity higher than the universal value and that of equatorial states. We also make a detailed study of the entanglement properties of the output copies and show that the equatorial states are the only states which give rise to separable density matrix for the outputs.

quant-ph↗

arXiv2001

A new class of models for surface relaxation with exact mean-field solutions

We introduce a class of discrete models for surface relaxation. By exactly solving the master equation which governs the microscopic dynamics of the surface, we determine the steady state of the surface and calculate its roughness. We will also map our model to a diffusive system of particles on a ring and reinterpret our results in this new setting.

cond-mat.stat-mech↗

arXiv2000

An asymmetric exclusion model with overtaking a numerical and simulation study

An asymmetric exclusion model on an open chain with random rates for hopping particles, where overtaking is also possible, is studied numerically and by computer simulation. The phase structure of the model and the density profiles near the high and low density coexistence line are obtained. The effect of a site impurity is also studied.

cond-mat.stat-mech↗

arXiv2000

Exact determination of the phase structure of the p-species asymmetric exclusion process

We consider a multi-species generalization of the Asymmetric Simple Exclusion Process on an open chain, in which particles hop with their characteristic hopping rates and fast particles can overtake slow ones. The number of species is arbitrary and the hopping rates can be selected from a discrete or continuous distribution. We determine exactly the phase structure of this model and show how the phase diagram of the 1-species ASEP is modified. Depending on the distribution of hopping rates, the system can exist in a three-phase regime or a two phase regime. In the three- phase regime the phase structure is almost the same as in the one species case, that is, there are the low density, the high density and the maximal current phases, while in the two-phase regime there is no high density phase.

cond-mat.stat-mech↗

arXiv1999

Some general features of matrix product states in stochastic systems

We will prove certain general relations in Matrix Product Ansatz for one dimensional stochastic systems, which are true in both random and sequential updates. We will derive general MPA expressions for the currents and current correlators and find the conditions in the MPA formalism, under which the correlators are site-independent or completely vanishing.

cond-mat.stat-mech↗

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

A Remark on Integrability of Stochastic Systems Solvable by Matrix Product Ansatz

Within the Matrix Product Formalism we have already introduced a multi- species exclusion process in which different particles hop with different rates and fast particles stochastically overtake slow ones. In this letter we show that on an open chain, the master equation of this process can be exactly solved via the coordinate Bethe ansatz. It is shown that the N-body S-matrix of this process is factorized into a product of two-body S-matrices, which in turn satisfy the quantum Yang-Baxter equation (QYBE). This solution is to our knowledge, a new solution of QYBE.

cond-mat.stat-mech↗

arXiv1998

A multi-species asymmetric simple exclusion process and its relation to traffic flow

Using the matrix product formalism we formulate a natural p-species generalization of the asymmetric simple exclusion process. In this model particles hop with their own specific rate and fast particles can overtake slow ones with a rate equal to their relative speed. We obtain the algebraic structure and study the properties of the representations in detail. The uncorrelated steady state for the open system is obtained and in the ($p \to \infty)$ limit, the dependence of its characteristics on the distribution of velocities is determined. It is shown that when the total arrival rate of particles exceeds a certain value, the density of the slowest particles rises abroptly.

cond-mat.stat-mech↗

arXiv1998

Quantum Renormalization Group for 1 Dimensional Fermion Systems

Inspired by the superblock method of White, we introduce a simple modification of the standard Renormalization Group (RG) technique for the study of quantum lattice systems. Our method which takes into account the effect of Boundary Conditions(BC), may be regarded as a simple way for obtaining first estimates of many properties of quantum lattice systems. By applying this method to the 1-dimensional free and interacting fermion system, we obtain the ground state energy with much higher accuracy than the standard RG. We also calculate the density-density correlation function in the free-fermion case which shows good agreement with the exact result.

cond-mat.stat-mech↗