Afshin Montakhab - Academia.edu (original) (raw)

Papers by Afshin Montakhab

arXiv (Cornell University), Jul 18, 2016

Physical Review A, 2022

A useful approach to characterize and identify quantum phase transitions lies in the concept of m... more A useful approach to characterize and identify quantum phase transitions lies in the concept of multipartite entanglement. In this paper, we consider well-known measures of multipartite (global) entanglement, i.e., average linear entropy of one-qubit and two-qubit reduced density matrices, in order to study topological quantum phase transition (TQPT) in the Kitaev Toric code Hamiltonian with a nonlinear perturbation. We provide an exact mapping from aforementioned measures in the above model to internal energy and energy-energy correlations in the classical Ising model. Accordingly, we find that the global entanglement shows a continuous and sharp transition from a maximum value in the topological phase to zero in the magnetized phase in a sense that its first-order derivative diverges at the transition point. In this regard, we conclude that not only can the global entanglement serve as a reasonable tool to probe quantum criticality at TQPTs, but it also can reveal the highly entangled nature of topological phases. Furthermore, we also introduce a conditional version of global entanglement which becomes maximum at the critical point. Therefore, regarding a general expectation that multipartite entanglement reaches maximum value at the critical point of quantum many-body systems, our result proposes that the conditional global entanglement can be a good measure of multipartite entanglement in TQPTs.

Attempts to establish microcanonical entropy as an adiabatic invariant date back to works of Gibb... more Attempts to establish microcanonical entropy as an adiabatic invariant date back to works of Gibbs and Hertz. More recently, a consistency relation based on adiabatic invariance has been used to argue for the validity of Gibbs (volume) entropy over Boltzmann (surface) entropy. Such consistency relation equates derivatives of thermodynamic entropy to ensemble average of the corresponding quantity in micro-state space (phase space or Hilbert space). In this work we propose to reexamine such a consistency relation when the number of particles (N) is considered as the independent thermodynamic variable. In other words, we investigate the consistency relation for the chemical potential which is a fundamental thermodynamic quantity. We show both by simple analytical calculations as well as model example that neither definitions of entropy satisfy the consistency condition when one considers such a relation for the chemical potential. This remains true regardless of the system size. Therefore, our results cast doubt on the validity of the adiabatic invariance as a required property of thermodynamic entropy. We close by providing commentary on the derivation of thermostatistics from mechanics which typically leads to controversial and inconsistent results.

Physical Review E, 2019

We study the evolution of a social network with friendly/enmity connections into a balanced state... more We study the evolution of a social network with friendly/enmity connections into a balanced state by introducing a dynamical model with an intrinsic randomness, similar to Glauber dynamics in statistical mechanics. We include the possibility of the tension promotion as well as the tension reduction in our model. Such a more realistic situation enables the system to escape from local minima in its energy landscape and thus to exit out of frozen imbalanced states, which are unwanted outcomes observed in previous models. On the other hand, in finite networks the dynamics takes the system into a balanced phase, if the randomness is lower than a critical value. For large networks, we also find a sharp phase transition at the initial positive link density of ρ * 0 = 1/2, where the system transitions from a bipolar state into a paradise. This modifies the gradual phase transition at a nontrivial value of ρ * 0 ≃ 0.65, observed in recent studies. I.

Physical Review A, 2019

It is well-known that the partition function of a classical spin model can be mapped to a quantum... more It is well-known that the partition function of a classical spin model can be mapped to a quantum entangled state where some properties on one side can be used to find new properties on the other side. However, the consequences of the existence of a classical (critical) phase transition on the corresponding quantum state has been mostly ignored. This is particularly interesting since the classical partition function exhibits non-analytic behavior at the critical point and such behavior could have important consequences on the quantum side. In this paper, we consider this problem for an important example of Kitaev toric code model which has been shown to correspond to the two-dimensional (2D) Ising model though a duality transformation. Through such duality transformation, it is shown that the temperature on the classical side is mapped to bit-flip noise on the quantum side. It is then shown that a transition from a coherent superposition of a given quantum state to a non-coherent mixture corresponds exactly to paramagnetic-ferromagnetic phase transition in the Ising model. To identify such a transition further, we define an order parameter to characterize the decoherency of such a mixture and show that it behaves similar to the order parameter (magnetization) of 2D Ising model, a behavior that is interpreted as a robust coherency in the toric code model. Furthermore, we consider other properties of the noisy toric code model exactly at the critical point. We show that there is a relative stability to noise for the toric code state at the critical noise which is revealed by a relative reduction in susceptibility to noise. We close the paper with a discussion on connection between the robust coherency as well as the critical stability with topological order of the toric code model.

Physical Review A, 2018

The correspondence between classical spin models and quantum states has attracted much attention ... more The correspondence between classical spin models and quantum states has attracted much attention in recent years. However, it remains an open problem as to which specific spin model a given (well-known) quantum state maps to. Here, we provide such an explicit correspondence for an important class of quantum states where a duality relation is proved between classical spin models and quantum Calderbank-Shor-Steane (CSS) states. In particular, we employ graph-theoretic methods to prove that the partition function of a classical spin model on a hypergraph H is equal to the inner product of a product state with a quantum CSS state on a dual hypergraphH. We next use this dual correspondence to prove that the critical behavior of the classical system corresponds to a relative stability of the corresponding CSS state to bit-flip (or phase-flip) noise, thus called critical stability. We finally conjecture that such critical stability is related to the topological order in quantum CSS states, thus providing a possible practical characterization of such states.

Physical Review D, 2017

We disclose a novel phase transition in black hole physics by investigating thermodynamics of cha... more We disclose a novel phase transition in black hole physics by investigating thermodynamics of charged dilaton black holes in an extended phase space where the charge of the black hole is regarded as a fixed quantity. Along with the usual critical (second-order) as well as the first-order phase transitions in charged black holes, we find that a finite jump in Gibbs free energy is generated by dilaton-electromagnetic coupling constant, α, for a certain range of pressure. This novel behavior indicates a small/large black hole zeroth-order phase transition in which the response functions of black holes thermodynamics diverge e.g. isothermal compressibility. Such zeroth-order transition separates the usual critical point and the standard first-order transition curve. We show that increasing the dilaton parameter(α) increases the zeroth-order portion of the transition curve. Additionally, we find that the second-order (critical) phase transition exponents are unaffected by the dilaton parameter, however, the condition of positive critical temperature puts an upper bound on the dilaton parameter (α < 1).

Physical Review B, 2018

We provide a study of various quantum phase transitions occurring in the XY Heisenberg chain in a... more We provide a study of various quantum phase transitions occurring in the XY Heisenberg chain in a transverse magnetic field using the Meyer-Wallach measure of (global) entanglement. We obtain analytic expression of the measure for finite-size systems, and show that it can be used to obtain critical exponents via finite-size scaling with great accuracy for the Ising universality class. We also calculate an analytic expression for the isotropic (XX) model and show that global entanglement can precisely identify the level-crossing points. The critical exponent for the isotropic transition is obtained exactly from an analytic expression for global entanglement in the thermodynamic limit. Next, the general behavior of the measure is calculated in the thermodynamic limit considering the important role of symmetries for this limit. The so-called oscillatory transition in the ferromagnetic regime can only be characterized by the thermodynamic limit where global entanglement is shown to be zero on the transition curve. Finally, the anisotropic transition is explored where it is shown that global entanglement exhibits an interesting behavior in the finite size limit. In the thermodynamic limit, we show that global entanglement shows a cusp-singularity across the Ising and anisotropic transition, while showing non-analytic behavior at the XX multi-critical point. It is concluded that global entanglement can be used to identify all the rich structure of the ground state Heisenberg chain.

Physical Review C, 2016

Relativistic generalization of hydrodynamic theory has attracted much attention from a theoretica... more Relativistic generalization of hydrodynamic theory has attracted much attention from a theoretical point of view. However, it has many important practical applications in high energy as well as astrophysical contexts. Despite various attempts to formulate relativistic hydrodynamics, no definitive consensus has been achieved. In this work, we propose to test the predictions of four types of first-order hydrodynamic theories for non-perfect fluids in the light of numerically exact molecular dynamics simulations of a fully relativistic particle system in the low density regime. In this regard, we study the propagation of density, velocity and heat fluctuations in a wide range of temperatures using extensive simulations and compare them to the corresponding analytic expressions we obtain for each of the proposed theories. As expected in the low temperature classical regime all theories give the same results consistent with the numerics. In the high temperature extremely relativistic regime, not all considered theories are distinguishable from one another. However, in the intermediate regime, a meaningful distinction exists in the predictions of various theories considered here. We find that the predictions of the recent formulation due to Tsumura-Kunihiro-Ohnishi are more consistent with our numerical results than the traditional theories due to Meixner, modified Eckart and modified Marle-Stewart.

The European Physical Journal C, 2016

We analytically and numerically investigate the properties of s-wave holographic superconductors ... more We analytically and numerically investigate the properties of s-wave holographic superconductors by considering the effects of scalar and gauge fields on the background geometry in five-dimensional Einstein-Gauss-Bonnet gravity. We assume the gauge field to be in the form of the power-Maxwell nonlinear electrodynamics. We employ the Sturm-Liouville eigenvalue problem for analytical calculation of the critical temperature and the shooting method for the numerical investigation. Our numerical and analytical results indicate that higher curvature corrections affect condensation of the holographic superconductors with backreaction. We observe that the backreaction can decrease the critical temperature of the holographic superconductors, while the power-Maxwell electrodynamics and Gauss-Bonnet coefficient term may increase the critical temperature of the holographic superconductors. We find that the critical exponent has the mean-field value β = 1/2, regardless of the values of Gauss-Bonnet coefficient, backreaction and power-Maxwell parameters.

International Journal of Quantum Information, 2016

Bell-like inequalities have been used in order to distinguish non-local quantum pure states by va... more Bell-like inequalities have been used in order to distinguish non-local quantum pure states by various authors. The behavior of such inequalities under Lorentz transformation (LT) has been a source of debate and controversies in the past. In this paper, we consider the two most commonly studied three-particle pure states, that of W and Greenberger–Horne–Zeilinger (GHZ) states which exhibit distinctly different types of entanglement. We discuss the various types of three-particle inequalities used in previous studies and point to their corresponding shortcomings and strengths. Our main result is that if one uses Czachor’s relativistic spin operator and Svetlichny’s inequality as the main measure of non-locality and uses the same angles in the rest frame (S) as well as the moving frame ([Formula: see text]), then maximally violated inequality in S will decrease in the moving frame, and will eventually lead to lack of non-locality (i.e. satisfaction of inequality) in the [Formula: see ...

Physical Review E, 2015

Critical dynamics of cortical neurons have been intensively studied over the past decade. Neurona... more Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that critical neuronal avalanches show mean-field behavior. There are structural as well as recently proposed [Phys. Rev. E 89, 052139 (2014)] dynamical mechanisms which can lead to mean-field behavior. In this work we consider a simple model of neuronal dynamics based on threshold self-organized critical models with synaptic noise. We investigate the role of high average connectivity, random long range connections, as well as synaptic noise in achieving mean-field behavior. We employ finite-size scaling in order to extract critical exponents with good accuracy. We conclude that relevant structural mechanisms responsible for mean-field behavior cannot be justified in realistic models of the cortex. However, strong dynamical noise, which can have realistic justifications, always leads to mean-field behavior regardless of the underlying structure. Our work provides a different (dynamical) origin than the conventionaly accepted (structural) mechanisms for mean-field behavior in neuronal avalanches.

On the closed equilibrium version of many self-organized critical(SOC) models, the hydrodynamic l... more On the closed equilibrium version of many self-organized critical(SOC) models, the hydrodynamic limits are diffusion equations exhibiting singularities at critical points. These critical points are associated with dynamical phase transitions seperating pinned and sliding states. The open driven SOC systems converge to the same critical point as the system size diverges. Singular diffusion describes this when the description applies. However, the description breaks down when fluctuations become relevant. By focusing on avalanche distributions, we have carried out a detailed study by comparing the open system to an ensemble of closed systems as a function of system size. For the prototypical BTW model, the same exponents are obtained for the open and closed system for different driving mechanism and various driving rates, even in the regime where diffusion has clearly failed. This indicates the validity of local equilibrium in this model.

In recent years, much effort has been made to understand the dynamics of spatially extended drive... more In recent years, much effort has been made to understand the dynamics of spatially extended driven systems. Spatio-temporal complexity arises in a variety of situations in nature, but an understanding of the underlying mechanisms which lead to such behavior is currently lacking. In an effort to identify and understand complexity, models for a variety of behavior in many different systems have been proposed and studied. Under certain conditions, these models exhibit self- organized criticality (SOC), where the system, under its own dynamics, self-organizes to a critical state with no characteristic time or length scales. Thus the SOC state is characterized by events of all sizes exhibiting a power-law behavior. Such scale-invariant phenomena are ubiquitous in nature. In other cases, collective periodic behavior arises in models of complex systems. Such mode- locked states are characterized by a well defined time scale and have important relevance in many biological, chemical, and phy...

Optical Materials, 2015

In this paper, we study the effects of thermal noise on the time evolution of a weak light pulse ... more In this paper, we study the effects of thermal noise on the time evolution of a weak light pulse (probe) in the presence of a strong light pulse (pump) within a gain medium which includes random scatterer particles. Suitable thermal noise term is added to a set of four coupled equations including three diffusion equations for energy densities and a rate equation for the upper level population in a four-level gain medium. These equations have been solved simultaneously by Crank-Nicholson numerical method. The main result is that the back-scattered output probe light is increased as the thermal noise strength is increased and simultaneously, with the same rate, the amplified spontaneous emission is decreased. Therefore, the amplified response of the random laser in diffusion regime for the input probe pulse is enhanced due to effect of the thermal noise.

Physical Review E, 1998

We obtain numerical evidence of local equilibrium in a family of sandpile models which exhibit se... more We obtain numerical evidence of local equilibrium in a family of sandpile models which exhibit selforganized criticality ͑SOC͒, by comparing them with closed systems which exhibit dynamical depinning transitions. In particular, we construct a mapping between the open and closed system avalanche size distributions which accounts for finite size fluctuations in the density and the critical point. Our results suggest a generalization of the singular diffusion description of SOC which transcends the point where this description was previously seen to break down.

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit s... more Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (nonconservative) local dynamics on the critical behavior of a sandpile model which can be taken to mimic the dynamics of neuronal avalanches. We find that despite the fact that noise breaks the strict local conservation required to attain criticality, our system exhibits true criticality for a wide range of noise in various dimensions, given that conservation is respected on the average. Although the system remains critical, exhibiting finite-size scaling, the value of critical exponents change depending on the intensity of local noise. Interestingly, for a sufficiently strong noise level, the critical exponents approach and saturate at their mean-field values, consistent with empirical measurements of neuronal avalanches. This is confirmed for both two and three dimensional models. However, t...

Basic and clinical neuroscience, 2014

Recent advances in brain and cognitive science studies have revolutionized concepts in neural dyn... more Recent advances in brain and cognitive science studies have revolutionized concepts in neural dynamics, regulating mechanisms, coding systems and information processing networks which govern our function and behavior. Hidden aspects of neurological and psychiatric diseases are being understood and hopes for their treatment are emerging. Although the two comprehensive mega-projects on brain mapping are in place in the United States and Europe; the proportion of science contributed by the developing countries should not be downsized. With the granted supports from the Cognitive Sciences and Technologies Council (CSTC), Iran can take its role in research on brain and cognition further. The idea of research and development in Cognitive Sciences and Technologies (CST) is being disseminated across the country by CSTC. Towards this goal, the first Shiraz interdisciplinary meeting on CST was held on 9 January 2014 in Namazi hospital, Shiraz. CST research priorities, infrastructure developme...

Physica A: Statistical Mechanics and its Applications, 2014

Recently, a morphological transition in the velocity distribution of a relativistic gas has been ... more Recently, a morphological transition in the velocity distribution of a relativistic gas has been pointed out which shows hallmarks of a critical phenomenon. Here, we provide a general framework which allows for a thermodynamic approach to such a critical phenomenon. We therefore construct a thermodynamic potential which upon expansion leads to Landau-like (mean-field) theory of phase transition. We are therefore able to calculate critical exponents and explain the spontaneous emergence of "order parameter" as a result of relativistic constraints. Numerical solutions which confirm our thermodynamic approach are also provided. Our approach provides a general understanding of such a transition as well as leading to some new results. Finally, we briefly discuss some possible physical consequences of our results as well as considering the case of quantum relativistic gases.

Classical statistical thermodynamics is one of the oldest, most well-established physical theorie... more Classical statistical thermodynamics is one of the oldest, most well-established physical theories and its basis and results have not been challenged within its domain since the time of Boltzmann. Special relativity, however, introduces some constraints as well as ambiguities into such a theory. For example, the cornerstone of classical statistical mechanics, the Maxwell-Boltzmann (MB) distribution does not respect the maximal velocity of light, the cornerstone of special relativity. Additionally, the Lorentz transformation of temperature, i.e. how a moving body's temperature compares to its rest frame value, has long caused controversies. Special relativity also introduces a new concept of proper time, which could potentially affect fundamental concepts of ergodicity and time-averaging in thermodynamics. In this work, we propose a model of a relativistic hard-sphere gas, and via molecular dynamics simulations, investigate all the above issues. In particular we show that the so-called Jüttner distribution is the correct relativistic generalization of the MB distribution. Introducing proper time averaging simply rescales such distribution by similar energy factor gamma. We also show that temperature is best understood as an invariant quantity, i.e. temperature does not change under the motion of inertial frames, and is not affected by time reparametrization. Additionally, we have studied this model under a temperature gradient and have shown that the model satisfies the minimal ingredients to study nonequilibrium transport properties, i.e. the existence of a non-equilibrium steady state and local thermal equilibrium. This will allow us to study generalizations of transport properties to relativistic regimes.