arXiv subjects

Archak Purkayastha

Publications and source records attributed to Archak Purkayastha.

41 records · Page 3Linked to original sources

arXiv2017

Quantum transport under AC drive from the leads : A Quantum Master Equation approach

Evaluating the time-dependent dynamics of driven open quantum systems is relevant for a theoretical description of many systems, including molecular junctions, quantum dots, cavity-QED experiments, cold atoms experiments and more. Here, we formulate a rigorous microscopic theory of an out-of-equilibrium open quantum system of non-interacting particles on a lattice weakly coupled to multiple baths and driven by periodically varying thermodynamic parameters like temperature and chemical potential of the bath. The particles can be either bosonic or fermionic and the lattice can be of any dimension and geometry. Based on Redfield quantum master equation under Born-Markov approximation, we derive a complete set of linear differential equations for equal time two-point correlation functions from which various physical observables, for example, current, can be calculated. Various interesting physical effects, such as resonance, can be directly read-off from the equations. Thus, our theory is quite general gives quite transparent and easy-to-calculate results. We validate our theory by comparing with exact numerical simulations. We apply our method to a generic open quantum system, namely a double-quantum dot coupled to leads with modulating chemical potentials. Two most important experimentally relevant insights from this are : (i) time-dependent measurements of current for symmetric oscillating voltages (with zero instantaneous voltage bias) can point to the degree of asymmetry in the system, and (ii) under certain conditions, time-dependent currents can exceed time-averaged currents by several orders of magnitude, and can therefore be detected even when the average current is below the measurement threshold.

cond-mat.mes-hall↗

arXiv2016

Non-linear transport in an out-of-equilibrium single-site Bose Hubbard model: scaling, rectification and time dynamics

Recent experiments in hybrid-quantum systems facilitate the potential realization of one of the most fundamental interacting Hamiltonian-Reservoir system, namely, the single-site Bose-Hubbard model coupled to two reservoirs at different temperatures. Using Redfield equations in Born-Markov approximation, we compute non-equilibrium average particle number, energy and currents beyond linear response regime, both time-dynamics and steady state and investigate its dependence on various tunable parameters analytically. We find interesting scaling laws in high temperature regimes that are independent of choice of bath spectral functions. We also demonstrate that the system shows very interesting particle and energy current rectification properties which can be controlled via the relative strength of interaction and temperatures, as well as via the degree of asymmetry in system-bath coupling. Specifically, we find inversion of direction of thermal rectification as a function of the relative strength of the interaction strength and the temperatures. We also show that, in the limit of low-temperature and high interaction strength our results are consistent with the non-equilibrium spin-Boson model. Our results are experimentally relevant not only to hybrid quantum systems, but also in other areas such as molecular junctions.

quant-ph↗

arXiv2016

Out of equilibrium open quantum systems: a comparison of approximate Quantum Master Equation approaches with exact results

We present the Born-Markov approximated Redfield quantum master equation (RQME) description for an open system of non-interacting particles (bosons or fermions) on an arbitrary lattice of $N$ sites in any dimension and weakly connected to multiple reservoirs at different temperatures and chemical potentials. The RQME can be reduced to the Lindblad equation, of various forms, by making further approximations. By studying the $N=2$ case, we show that RQME gives results which agree with exact analytical results for steady state properties and with exact numerics for time-dependent properties, over a wide range of parameters. In comparison, the Lindblad equations have a limited domain of validity in non-equilibrium. We conclude that it is indeed justified to use microscopically derived full RQME to go beyond the limitations of Lindblad equations in out-of-equilibrium systems. We also derive closed form analytical results for out-of-equilibrium time dynamics of two-point correlation functions. These results explicitly show the approach to steady state and thermalization. These results are experimentally relevant for cold atoms, cavity QED and far-from-equilibrium quantum dot experiments.

cond-mat.stat-mech↗

arXiv2016

Entanglement spectrum and block eigenvalue spacing distribution of correlated electron states

Entanglement spectrum of finite-size correlated electron systems are investigated using the Gutzwiller projection technique. The product of largest eigenvalue and rank of the block reduced density matrix, which is a measure of distance of the state from the maximally entangled state of the corresponding rank, is seen to characterise the insulator to metal crossover in the state. The fraction of distinct eigenvalues exhibits a `chaotic' behaviour in the crossover region, and it shows a `integrable' behaviour at both insulating and metallic ends. The integrated entanglement spectrum obeys conformal field theory (CFT) prediction at the metal and insulator ends, but shows a noticeable deviation from CFT prediction in the crossover regime, thus it can also track a metal-insulator crossover. A modification of the CFT result for the entanglement spectrum for finite size is proposed which holds in the crossover regime also. The adjacent level spacing distribution of unfolded non-zero eigenvalues for intermediate values of Gutzwiller projection parameter $g$ is the same as that of an ensemble of random matrices obtained by replacing each block of reduced density matrix by a random real symmetric Toeplitz matrix. It is strongly peaked at zero, with an exponential tail proportional to $e^{-(n/R)s}$, where $s$ is the adjacent level spacing, $n$ is number of distinct eigenvalues and $R$ is the rank of the reduced density matrix.

cond-mat.str-el↗

arXiv2014

Block entanglement and fluctuations in finite size correlated electron systems

The block entanglement entropy and fluctuations are investigated in one dimension in finite size correlated electron systems using the Gutzwiller wave function as a prototype correlated electron state. Entanglement entropy shows logarithmic divergence for all values of the correlation projection parameter $g$, as predicted by conformal field theories for critical systems, but the central charge requires finite size corrections. There is an infinite correlation length corresponding to correlation between same kinds of spins, for all values of $g$. A scaling form for the block entropy, as a function of $g$ and the system size $N$, is proposed which predicts a metal-insulator crossover at $N^{1/3} g\approx 0.24$. Bipartite fluctuations in the number of particles in a block, and the spin fluctuations also obey an approximate scaling. A relation is found between the block entropy and the bipartite spin fluctuations. Our results show some correspondence with an experiment on Ni nanochains.

cond-mat.str-el↗