arXiv subjects

Shreyoshi Mondal

Publications and source records attributed to Shreyoshi Mondal.

5 recordsLinked to original sources

arXiv2009

Non-equilibrium dynamics of quantum systems: order parameter evolution, defect generation, and qubit transfer

In this review, we study some aspects of the non-equilibrium dynamics of quantum systems. In particular, we consider the effect of varying a parameter in the Hamiltonian of a quantum system which takes it across a quantum critical point or line. We study both sudden and slow quenches in a variety of systems including one-dimensional ultracold atoms in an optical lattice, an infinite range ferromagnetic Ising model, and some exactly solvable spin models in one and two dimensions (such as the Kitaev model). We show that quenching leads to the formation of defects whose density has a power-law dependence on the quenching rate; the power depends on the dimensionalities of the system and of the critical surface and on some of the exponents associated with the critical point which is being crossed. We also study the effect of non-linear quenching; the power law of the defects then depends on the degree of non-linearity. Finally, we study some spin-1/2 models to discuss how a qubit can be transferred across a system.

cond-mat.stat-mech↗

arXiv2008

Theory of defect production in nonlinear quench across a quantum critical point

We study defect production in a quantum system subjected to a nonlinear power law quench which takes it either through a quantum critical or multicritical point or along a quantum critical line. We elaborate on our earlier work [D. Sen, K. Sengupta, S. Mondal, \prl 101, 016806 (2008)] and present a detailed analysis of the scaling of the defect density $n$ with the quench rate $τ$ and exponent $\al$ for each of the above-mentioned cases. We also compute the correlation functions for defects generated in nonlinear quenches through a quantum critical point and discuss the dependence of the amplitudes of such correlation functions on the exponent $\al$. We discuss several experimental systems where these theoretical predictions can be tested.

cond-mat.str-el↗

arXiv2008

Defect production in non-linear quench across a quantum critical point

We show that the defect density $n$, for a slow non-linear power-law quench with a rate $τ^{-1}$ and an exponent $α>0$, which takes the system through a critical point characterized by correlation length and dynamical critical exponents $ν$ and $z$, scales as $n \sim τ^{-ανd/ (αzν+1)}$ [$n \sim (αg^{(α-1)/α}/τ)^{νd/(zν+1)}$], if the quench takes the system across the critical point at time $t=0$ [$t=t_0 \ne 0$], where $g$ is a non-universal constant and $d$ is the system dimension. These scaling laws constitute the first theoretical results for defect production in non-linear quenches across quantum critical points and reproduce their well-known counterpart for linear quench ($α=1$) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.

cond-mat.str-el↗

arXiv2008

Quench dynamics and defect production in the Kitaev and extended Kitaev models

We study quench dynamics and defect production in the Kitaev and the extended Kitaev models. For the Kitaev model in one dimension, we show that in the limit of slow quench rate, the defect density n \sim 1/\sqrtτ where 1/τis the quench rate. We also compute the defect correlation function by providing an exact calculation of all independent non-zero spin correlation functions of the model. In two dimensions, where the quench dynamics takes the system across a critical line, we elaborate on the results of earlier work [K. Sengupta, D. Sen and S. Mondal, Phys. Rev. Lett. 100, 077204 (2008)] to discuss the unconventional scaling of the defect density with the quench rate. In this context, we outline a general proof that for a d dimensional quantum model, where the quench takes the system through a d-m dimensional gapless (critical) surface characterized by correlation length exponent νand dynamical critical exponent z, the defect density n \sim 1/τ^{m ν/(z ν+1)}. We also discuss the variation of the shape and the spatial extent of the defect correlation function with the change of both the rate of quench and the model parameters and compute the entropy generated during such a quench process. Finally, we study the defect scaling law, entropy generation and defect correlation function of the two-dimensional extended Kitaev model.

cond-mat.stat-mech↗

arXiv2008

Exact results for quench dynamics and defect production in a two-dimensional model

We show that for a d-dimensional model in which a quench with a rate τ^{-1} takes the system across a d-m dimensional critical surface, the defect density scales as n \sim 1/τ^{mν/(zν+1)}, where νand z are the correlation length and dynamical critical exponents characterizing the critical surface. We explicitly demonstrate that the Kitaev model provides an example of such a scaling with d=2 and m=ν=z=1. We also provide the first example of an exact calculation of some multispin correlation functions for a two-dimensional model which can be used to determine the correlation between the defects. We suggest possible experiments to test our theory.

cond-mat.stat-mech↗