arXiv subjects

A. Iqbal

Publications and source records attributed to A. Iqbal.

29 records · Page 2Linked to original sources

arXiv2010

The Fourth Element: Characteristics, Modelling, and Electromagnetic Theory of the Memristor

In 2008, researchers at HP Labs published a paper in {\it Nature} reporting the realisation of a new basic circuit element that completes the missing link between charge and flux-linkage, which was postulated by Leon Chua in 1971. The HP memristor is based on a nanometer scale TiO$_2$ thin-film, containing a doped region and an undoped region. Further to proposed applications of memristors in artificial biological systems and nonvolatile RAM (NVRAM), they also enable reconfigurable nanoelectronics. Moreover, memristors provide new paradigms in application specific integrated circuits (ASICs) and field programmable gate arrays (FPGAs). A significant reduction in area with an unprecedented memory capacity and device density are the potential advantages of memristors for Integrated Circuits (ICs). This work reviews the memristor and provides mathematical and SPICE models for memristors. Insight into the memristor device is given via recalling the quasi-static expansion of Maxwell's equations. We also review Chua's arguments based on electromagnetic theory.

cond-mat.mes-hall↗

arXiv2004

Stability of mixed Nash equilibria in symmetric quantum games

In bi-matrix games the Bishop-Cannings theorem of the classical evolutionary game theory does not permit pure evolutionarily stable strategies (ESSs) when a mixed ESS exists. We find the necessary form of two-qubit initial quantum states when a switch-over to a quantum version of the game also changes the evolutionary stability of a mixed symmetric Nash equilibrium.

quant-ph↗

arXiv2003

Quantum Foam and Topological Strings

We find an interpretation of the recent connection found between topological strings on Calabi-Yau threefolds and crystal melting: Summing over statistical mechanical configuration of melting crystal is equivalent to a quantum gravitational path integral involving fluctuations of Kahler geometry and topology. We show how the limit shape of the melting crystal emerges as the average geometry and topology of the quantum foam at the string scale. The geometry is classical at large length scales, modified to a smooth limit shape dictated by mirror geometry at string scale and is a quantum foam at area scales g_s α'.

hep-th↗

arXiv2002

Quantum games with a multi-slit electron diffraction setup

A setup is proposed to play a quantum version of the famous bimatrix game of Prisoners' Dilemma. Multi-slit electron diffraction with each player's pure strategy consisting of opening one of the two slits at his/her disposal are essential features of the setup. Instead of entanglement the association of waves with travelling material objects is suggested as another resource to play quantum games.

quant-ph↗

arXiv2002

Quantum repeated games

In a two-stage repeated classical game of prisoners' dilemma the knowledge that both players will defect in the second stage makes the players to defect in the first stage as well. We find a quantum version of this repeated game where the players decide to cooperate in the first stage while knowing that both will defect in the second.

quant-ph↗

arXiv2002

Backwards-induction outcome in a quantum game

In economics duopoly is a market dominated by two firms large enough to influence the market price. Stackelberg presented a dynamic form of duopoly that is also called `leader-follower' model. We give a quantum perspective on Stackelberg duopoly that gives a backwards-induction outcome same as the Nash equilibrium in static form of duopoly also known as Cournot's duopoly. We find two qubit quantum pure states required for this purpose.

quant-ph↗

arXiv2002

Darwinism in quantum systems?

We investigate the role of quantum mechanical effects in the central stability concept of evolutionary game theory i.e. an Evolutionarily Stable Strategy (ESS). Using two and three-player symmetric quantum games we show how the presence of quantum phenomenon of entanglement can be crucial to decide the course of evolutionary dynamics in a population of interacting individuals.

quant-ph↗

arXiv2001

Quantum Cooperative Games

We study two forms of a symmetric cooperative game played by three players, one classical and other quantum. In its classical form making a coalition gives advantage to players and they are motivated to do so. However in its quantum form the advantage is lost and players are left with no motivation to make a coalition.

quant-ph↗

arXiv2001

Quantum mechanics gives stability to a Nash equilibrium

We consider a slightly modified version of the Rock-Scissors-Paper (RSP) game from the point of view of evolutionary stability. In its classical version the game has a mixed Nash equilibrium (NE) not stable against mutants. We find a quantized version of the RSP game for which the classical mixed NE becomes stable.

quant-ph↗

arXiv2001

Entanglement and Dynamic Stability of Nash Equilibria in a Symmetric Quantum Game

We study the evolutionary stability of Nash equilibria (NE) in a symmetric quantum game played by the recently proposed scheme of applying `identity' and `Pauli spin flip' operators on the initial state with classical probabilities. We show that in this symmetric game dynamic stability of a NE can be changed when the game changes its form, for example, from classical to quantum. It happens even when the NE remains intact in both forms.

quant-ph↗

arXiv2000

Evolutionarily Stable Strategies in Quantum Games

Evolutionarily Stable Strategy (ESS) in classical game theory is a refinement of Nash equilibrium concept. We investigate the consequences when a small group of mutants using quantum strategies try to invade a classical ESS in a population engaged in symmetric bimatrix game of Prisoner's Dilemma. Secondly we show that in an asymmetric quantum game between two players an ESS pair can be made to appear or disappear by resorting to entangled or unentangled initial states used to play the game even when the strategy pair remains a Nash equilibrium in both forms of the game.

quant-ph↗