Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

We study the generation of defects when a quantum spin system is quenched through a multicritical point by changing a parameter of the Hamiltonian as t/τ, where τ is the characteristic timescale of quenching. We argue that when a quantum system is quenched across a multicritical point, the density of defects (n) in the final state is not necessarily given by the Kibble-Zurek scaling form n∼1/τdν/(zν+1), where d is the spatial dimension, and ν and z are respectively the correlation length and dynamical exponent associated with the quantum critical point. We propose a generalized scaling form of the defect density given by n∼1/τd/(2z 2), where the exponent z2 determines the behavior of the off-diagonal term of the 2 × 2 Landau-Zener matrix at the multicritical point. This scaling is valid not only at a multicritical point but also at an ordinary critical point. © 2009 IOP Publishing Ltd.

Department of Physics

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Journal of Statistical Mechanics: Theory and Experiment

Defect production due to quenching through a multicritical point

We present an exact result for the nonadiabatic transition probability and hence the defect density in the final state of a one-dimensional Kitaev model following a slow quench of the parameter J-, which estimates the anisotropy between the interactions, as J- (t) ∼- | t/τ |. Here, time t goes from - to + and τ defines the rate of change in the Hamiltonian. In other words, the spin chain initially prepared in its ground state is driven by changing J- linearly in time up to the quantum critical point, which in the model considered here occurs at t=0, reversed and then gradually decreased to its initial value at the same rate. We have thoroughly compared the reverse quenching with its counterpart forward quenching, i.e., J- ∼t/τ. Our exact calculation shows that the probability of excitations is zero for the wave vector at which the instantaneous energy gap is zero at the critical point J- =0 as opposed to the maximum value of unity in the forward quenching. It is also shown that the defect density in the final state following a reverse quenching, we propose here, is nearly half of the defects generated in the forward quenching. We argue that the defects produced when the system reaches the quantum critical point get redistributed in the wave-vector space at the final time in case of reverse quenching whereas it keeps on increasing until the final time in the forward quenching. We study the entropy density and also the time evolution of the diagonal entropy density in the case of the reverse quenching and compare it with the forward case. © 2009 The American Physical Society.

Fulltext

Physical Review B - Condensed Matter and Materials Physics

Reverse quenching in a one-dimensional Kitaev model

In this paper we review the quenching dynamics of a quantum XY spin-1/2 chain in the presence of a transverse field, when the transverse field or the anisotropic interaction is quenched at a slow but uniform rate. We also extend the results to the cases in which the system starts with any arbitrary initial condition as opposed to the initial fully magnetically aligned state which has been extensively studied earlier. The evolution is non-adiabatic in the time interval when the parameters are close to their critical values, and is adiabatic otherwise. The density of defects produced due to non-adiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem. We show that in one dimension the density of defects in the final state scales as 1/√τ irrespective of the initial condition, where τ is the quenching time-scale. However, the magnitude of density of defects is found to depend on the initial condition. © Indian Academy of Sciences.

Pramana - Journal of Physics

Quenching dynamics of a quantum XY spin-1/2 chain in the presence of transverse field by the application of a generalized Landau-Zener formula

We use a quenching scheme to study the dynamics of a one-dimensional anisotropic XY spin-1/2 chain in the presence of a transverse field which alternates between the values h+δ and h-δ from site to site. In this quenching scheme, the parameter denoting the anisotropy of interaction (γ) is linearly quenched from -∞ to +∞ as γ=t/τ, keeping the total strength of interaction J fixed. The system traverses through a gapless phase when γ is quenched along the critical surface h2 = δ2 + J2 in the parameter space spanned by h, δ, and γ. By mapping to an equivalent two-level Landau-Zener problem, we show that the defect density in the final state scales as 1/ τ1/3, a behavior that has not been observed in previous studies of quenching through a gapless phase. We also generalize the model incorporating additional alternations in the anisotropy or in the strength of the interaction and derive an identical result under a similar quenching. Based on the above results, we propose a general scaling of the defect density with the quenching rate τ for quenching along a gapless critical line. © 2008 The American Physical Society.

Quenching along a gapless line: A different exponent for defect density

We study the breakdown of a random fiber bundle model (RFBM) with n discontinuities in the threshold distribution using the global load sharing scheme. In other words, n+1 different classes of fibers identified on the basis of their threshold strengths are mixed such that the strengths of the fibers in the ith class are uniformly distributed between the values σ2i-2 and σ2i-1, where 1≤i≤n+1. Moreover, there is a gap in the threshold distribution between ith and (i+1) -th class. We show that although the critical stress depends on the parameter values of the system, the critical exponents are identical to that obtained in the recursive dynamics of a RFBM with a uniform distribution and global load sharing. The avalanche size distribution, on the other hand, shows a nonuniversal, non-power-law behavior for smaller values of avalanche sizes which becomes prominent only when a critical distribution is approached. We establish that the behavior of the avalanche size distribution for an arbitrary n is qualitatively similar to a RFBM with a single discontinuity in the threshold distribution (n=1), especially when the density and the range of threshold values of fibers belonging to strongest (n+1) -th class is kept identical in all the cases. © 2008 The American Physical Society.

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Random fiber bundle with many discontinuities in the threshold distribution

We study the quantum dynamics of a one-dimensional spin- 1 2 anisotropic XY model in a transverse field when the transverse field or the anisotropic interaction is quenched at a slow but uniform rate. The two quenching schemes are called transverse and anisotropic quenching, respectively. Our emphasis in this paper is on the anisotropic quenching scheme, and we compare the results with those of the other scheme. In the process of anisotropic quenching, the system crosses all the quantum critical lines of the phase diagram where the relaxation time diverges. The evolution is nonadiabatic in the time interval when the parameters are close to their critical values, and is adiabatic otherwise. The density of defects produced due to nonadiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem and is generally found to vary as 1 τ, where τ is the characteristic time scale of quenching, a scenario that supports the Kibble-Zurek mechanism. Interestingly, in the case of anisotropic quenching, there exists an additional nonadiabatic transition, in comparison to the transverse quenching case, with the corresponding probability peaking at an incommensurate value of the wave vector. In the special case in which the system passes through a multicritical point, the defect density is found to vary as 1 τ1 6. The von Neumann entropy of the final state is shown to maximize at a quenching rate around which the ordering of the final state changes from antiferromagnetic to ferromagnetic. © 2007 The American Physical Society.

Quenching dynamics of a quantum XY spin- 1 2 chain in a transverse field

In this article, we briefly review the critical behaviour of a long-range percolation model in which any two sites are connected with a probability that falls off algebraically with the distance. The results of this percolation transition are used to describe the quantum phase transitions in a dilute transverse Ising model at the percolation threshold pc of the long-range connected lattice. In the similar spirit, we propose a new model of a contact process defined on the same long-range diluted lattice and explore the transitions at pc. The long-range nature of the percolation transition allows us to evaluate some critical exponents exactly in both the above models. Moreover, mean field theory is valid for a wide region of parameter space. In either case, the strength of Griffiths McCoy singularities are tunable as the range parameter is varied. © 2007 Elsevier B.V. All rights reserved.

Physica A: Statistical Mechanics and its Applications

Long-range connections, quantum magnets and dilute contact processes

We study a random fiber bundle model with tips of the fibers placed on a graph having co-ordination number 3. These fibers follow local load sharing with uniformly distributed threshold strengths of the fibers. We have studied the critical behavior of the model numerically using a finite size scaling method and the mean field critical behavior is established. The avalanche size distribution is also found to exhibit a mean field nature in the asymptotic limit. © World Scientific Publishing Company.

International Journal of Modern Physics C

Fibers on a graph with local load sharing

The critical behavior of a random fiber bundle model with mixed uniform distribution of threshold strengths and global load sharing rule is studied with a special emphasis on the nature of distribution of avalanches for different parameters of the distribution. The discontinuity in the threshold strength distribution of fibers nontrivially modifies the critical stress as well as puts a restriction on the allowed values of parameters for which the recursive dynamics approach holds good. The discontinuity leads to a nonuniversal behavior in the avalanche size distribution for smaller values of avalanche size. We observe that apart from the mean field behavior for larger avalanches, a new behavior for smaller avalanche size is observed as a critical threshold distribution is approached. The phenomenological understanding of the above result is provided using the exact analytical result for the avalanche size distribution. Most interestingly, the prominence of nonuniversal behavior in avalanche size distribution depends on the system parameters. © 2007 The American Physical Society.

Effect of discontinuity in the threshold distribution on the critical behavior of a random fiber bundle

We study the zero-temperature quenching dynamics of various extensions of the transverse Ising model (TIM) for when the transverse field is linearly quenched from to (or zero) at a finite and uniform rate. The rate of quenching is dictated by a characteristic scale given by τ. The density of kinks produced in these extended models while crossing the quantum critical points during the quenching process is calculated using a many-body generalization of the Landau-Zener transition theory. The density of kinks in the final state is found to decay as τ-1/2. In the first model considered here, the transverse Ising Hamiltonian includes an additional ferromagnetic three-spin interaction term of strength J3. For J3&lt;0.5, the kink density is found to increase monotonically with J3 whereas it decreases with J3 for J3&gt;0.5. The point with J 3 = 0.5 and the transverse field h = -0.5 is multicritical, where the density shows a slower decay given by τ-1/6. We also study the effect of ferromagnetic or antiferromagnetic next nearest neighbor (NNN) interactions on the dynamics of the TIM under the same quenching scheme. In a mean field approximation, the transverse Ising Hamiltonians with NNN interactions are identical to the three-spin Hamiltonian. The NNN interactions non-trivially modify the dynamical behavior; for example an antiferromagnetic NNN interaction results in a larger number of kinks in the final state in comparison to the case when the NNN interaction is ferromagnetic. © IOP Publishing Ltd.

The effect of the three-spin interaction and the next nearest neighbor interaction on the quenching dynamics of a transverse Ising model

A random fiber bundle model with a mixed Weibull distribution is studied under the global load sharing scheme. The mixed model consists of two sets of fibers. The threshold strength of one set of fibers is randomly chosen from a Weibull distribution with a particular Weibull index, and another set of fibers with a different index. The mixing tunes the critical stress of the bundle and the variation of critical stress with the amount of mixing is determined using a probabilistic method where the external load is increased quasistatically. In a special case which we illustrate, the critical stress is found to vary linearly with the mixing parameter. The critical exponents and power-law behavior of burst avalanche size distribution is found to remain unaltered due to mixing. © 2007 The American Physical Society.

Critical behavior of random fibers with mixed Weibull distribution

The breakdown phenomena of materials is a very complex process which involves a study of formation of microscopic cracks, their evolution to the other regions of the materials via some interaction and the ultimate collapse of the structure [1]. Random Fibre Bundle Model (RFBM) [2, 3] is a paradigmatic model, simple yet subtle, which captures the essential physics of breakdown processes. It consists of N parallel, vertical fibres whose ends are connected to two horizontal rods. The upper rod is fixed and a load F is applied to the lower one so that a stress σ (= F/N) is generated on each fibre. The fibres are assigned a threshold strength chosen randomly from a cumulative distribution function P (σ) with a corresponding density function ρ (σ). © 2006 Springer.