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F. Shahbazi

Publications and source records attributed to F. Shahbazi.

11 recordsLinked to original sources
arXiv2014

Quantum Decoherence Timescales for Ionic Superposition States in Ion Channels

There are many controversial and challenging discussions about quantum effects in microscopic structures in neurons of the human brain. The challenge is mainly because of quick decoherence of quantum states due to hot, wet and noisy environment of the brain which forbids long life coherence for brain processing. Despite these critical discussions, there are only a few number of published papers about numerical aspects of decoherence in neurons. Perhaps the most important issue is offered by Max Tegmark who has calculated decoherence times for the systems of "ions" and "microtubules" in neurons of the brain. In fact, Tegmark did not consider ion channels which are responsible for ions displacement through the membrane and are the building blocks of electrical membrane signals in the nervous system. Here, we would like to re-investigate decoherence times for ionic superposition states by using the data obtained via molecular dynamics simulations. Our main approach is according to what Tegmark has used before. In fact, Tegmark didn't consider the ion channel structure and his estimates are only simple approximations. In this paper, we focus on the small nano-scale part of KcsA ion channels which is called "selectivity filter" and has a key role in the operation of an ion channel. Our results for superposition states of potassium ions indicate that decoherence times are in the order of picoseconds which are 10-100 million times bigger than the order calculated by Tegmark. This decoherence time is still not enough for cognitive processing in the brain, however it can be adequate for quantum states of cooled ions in the filter to leave their quantum traces on the filter and action potentials.

physics.bio-ph↗
arXiv2011

Plaquette valence-bond ordering in J_1-J_2 Heisenberg antiferromagnet on the honeycomb lattice

We study S=1/2 Heisenberg model on the honeycomb lattice with first and second neighbor antiferromagnetic exchange (J_{1}-J_{2} model), employing exact diagonalization in both S_z=0 basis and nearest neighbor singlet valence bond (NNVB) basis. We find that for 0.2<J_2/J_1<0.3, NNVB basis gives a proper description of the ground state in comparison with the exact results. By analyzing the dimer-dimer as well as plaquette-plaquette correlations and also defining appropriate structure factors, we investigate possible symmetry breaking states as the candidate for the ground state in the frustrated region. We provide body of evidences in favor of plaquette valence bond ordering for 0.2<J_2/J_1<0.3. By further increasing the ratio J_2/J_1, this state undergoes a transition to the staggered dimerized state.

cond-mat.str-el↗
arXiv2009

Classical Analogue of the Ionic Hubbard Model

In our earlier work [M. Hafez, {\em et al.}, Phys. Lett. A {\bf 373} (2009) 4479] we employed the flow equation method to obtain a classic effective model from a quantum mechanical parent Hamiltonian called, the ionic Hubbard model (IHM). The classical ionic Hubbard model (CIHM) obtained in this way contains solely Fermionic occupation numbers of two species corresponding to particles with $\up$ and $\down$ spin, respectively. In this paper, we employ the transfer matrix method to analytically solve the CIHM at finite temperature in one dimension. In the limit of zero temperature, we find two insulating phases at large and small Coulomb interaction strength, $U$, mediated with a gap-less metallic phase, resulting in two continuous metal-insulator transitions. Our results are further supported with Monte Carlo simulations.

cond-mat.stat-mech↗
arXiv2008

Anderson Transition in Disordered Graphene

We use the regularized kernel polynomial method (RKPM) to numerically study the effect disorder on a single layer of graphene. This accurate numerical method enables us to study very large lattices with millions of sites, and hence is almost free of finite size errors. Within this approach, both weak and strong disorder regimes are handled on the same footing. We study the tight-binding model with on-site disorder, on the honeycomb lattice. We find that in the weak disorder regime, the Dirac fermions remain extended and their velocities decrease as the disorder strength is increased. However, if the disorder is strong enough, there will be a {\em mobility edge} separating {\em localized states around the Fermi point}, from the remaining extended states. This is in contrast to the scaling theory of localization which predicts that all states are localized in two-dimensions (2D).

cond-mat.str-el↗
arXiv2007

Roughness of undoped graphene and its short-range induced gauge field

We present both numerical and analytical study of graphene roughness with a crystal structure including $500 \times 500$ atoms. The roughness can effectively result in a random gauge field and has important consequences for its electronic structure. Our results show that its height fluctuations in small scales have scaling behavior with a temperature dependent roughness exponent in the interval of $ 0.6 < χ< 0.7 $. The correlation function of height fluctuations depends upon temperature with characteristic length scale of $ \approx 90 Å$ (at room temperature). We show that the correlation function of the induced gauge field has a short-range nature with correlation length of about $\simeq 2-3 Å$. We also treat the problem analytically by using the Martin-Siggia-Rose method. The renormalization group flows did not yield any delocalized-localized transition arising from the graphene roughness. Our results are in good agreement with recent experimental observations.

cond-mat.mtrl-sci↗
arXiv2005

Zero tension Kardar-Parisi-Zhang equation in (d+1)- Dimensions

The joint probability distribution function (PDF) of the height and its gradients is derived for a zero tension $d+1$-dimensional Kardar-Parisi-Zhang (KPZ) equation. It is proved that the height`s PDF of zero tension KPZ equation shows lack of positivity after a finite time $t_{c}$. The properties of zero tension KPZ equation and its differences with the case that it possess an infinitesimal surface tension is discussed. Also potential relation between the time scale $t_{c}$ and the singularity time scale $t_{c, ν\to 0}$ of the KPZ equation with an infinitesimal surface tension is investigated.

nlin.CD↗
arXiv2005

Localization of elastic waves in heterogeneous media with off-diagonal disorder and long-range correlations

Using the Martin-Siggia-Rose method, we study propagation of acoustic waves in strongly heterogeneous media which are characterized by a broad distribution of the elastic constants. Gaussian-white distributed elastic constants, as well as those with long-range correlations with non-decaying power-law correlation functions, are considered. The study is motivated in part by a recent discovery that the elastic moduli of rock at large length scales may be characterized by long-range power-law correlation functions. Depending on the disorder, the renormalization group (RG) flows exhibit a transition to localized regime in {\it any} dimension. We have numerically checked the RG results using the transfer-matrix method and direct numerical simulations for one- and two-dimensional systems, respectively.

cond-mat.stat-mech↗
arXiv2002

Level Crossing Analysis of Growing surfaces

We investigate the average frequency of positive slope $ν_α^{+} $, crossing the height $α= h- \bar h$ in the surface growing processes. The exact level crossing analysis of the random deposition model and the Kardar-Parisi-Zhang equation in the strong coupling limit before creation of singularities are given.

cond-mat↗
arXiv2002

Strong Coupling Limit of the Kardar-Parisi-Zhang Equation in 2+1 Dimensions

A master equation for the Kardar-Parisi-Zhang (KPZ) equation in 2+1 dimensions is developed. In the fully nonlinear regime we derive the finite time scale of the singularity formation in terms of the characteristics of forcing. The exact probability density function of the one point height field is obtained correspondingly.

cond-mat↗
arXiv2001

Statistical Theory for the Kardar-Parisi-Zhang Equation in 1+1 Dimension

The Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimension dynamically develops sharply connected valley structures within which the height derivative {\it is not} continuous. There are two different regimes before and after creation of the sharp valleys. We develop a statistical theory for the KPZ equation in 1+1 dimension driven with a random forcing which is white in time and Gaussian correlated in space. A master equation is derived for the joint probability density function of height difference and height gradient $P(h-\bar h,\partial_{x}h,t)$ when the forcing correlation length is much smaller than the system size and much bigger than the typical sharp valley width. In the time scales before the creation of the sharp valleys we find the exact generating function of $h-\bar h$ and $\partial_x h$. Then we express the time scale when the sharp valleys develop, in terms of the forcing characteristics. In the stationary state, when the sharp valleys are fully developed, finite size corrections to the scaling laws of the structure functions $<(h-\bar h)^n (\partial_x h)^m>$ are also obtained.

cond-mat.stat-mech↗