The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Mark Jarrell - One of the best experts on this subject based on the ideXlab platform.
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continuous Time Quantum monte carlo and maximum entropy approach to an imaginary Time formulation of strongly correlated steady state transport
Physical Review E, 2010Co-Authors: Andreas Dirks, Mark Jarrell, Philipp Werner, Thomas PruschkeAbstract:Recently, Han and Heary [Phys. Rev. Lett. 99, 236808 (2007)] proposed an approach to steady-state Quantum transport through mesoscopic structures, which maps the nonequilibrium problem onto a family of auxiliary Quantum impurity systems subject to imaginary voltages. We employ continuous-Time Quantum Monte-Carlo solvers to calculate accurate imaginary Time data for the auxiliary models. The spectral function is obtained from a maximum entropy analytical continuation in both Matsubara frequency and complexified voltage. To enable the analytical continuation we construct a kernel which is compatible with the analytical structure of the theory. While it remains a formidable task to extract reliable spectral functions from this unbiased procedure, particularly for large voltages, our results indicate that the method in principle yields results in agreement with those obtained by other methods.
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Analytic continuation of Quantum Monte Carlo data by stochastic analytical inference.
Physical Review E, 2010Co-Authors: Sebastian Fuchs, Thomas Pruschke, Mark JarrellAbstract:We present an algorithm for the analytic continuation of imaginary-Time Quantum Monte Carlo data which is strictly based on principles of Bayesian statistical inference. Within this framework we are able to obtain an explicit expression for the calculation of a weighted average over possible energy spectra, which can be evaluated by standard Monte Carlo simulations, yielding as by-product also the distribution function as function of the regularization parameter. Our algorithm thus avoids the usual ad hoc assumptions introduced in similar algorithms to fix the regularization parameter. We apply the algorithm to imaginary-Time Quantum Monte Carlo data and compare the resulting energy spectra with those from a standard maximum-entropy calculation.
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bayesian inference and the analytic continuation of imaginary Time Quantum monte carlo data
Physics Reports, 1996Co-Authors: Mark Jarrell, J E GubernatisAbstract:Abstract We present a way to use Bayesian statistical inference and the principle of maximum entropy to analytically continue imaginary-Time Quantum Monte Carlo data. We supply the details that are lacking in the seminal literature but are important for the motivated reader to understand the assumptions and approximations embodied in these methods. First, we summarize the general relations between Quantum correlation functions and spectral densities. We then review the basic principles, formalism, and philosophy of Bayesian inference and discuss the application of this approach in the context of the analytic continuation problem. Next, we present a detailed case study for the symmetric, infinite-dimension Anderson Hamiltonian. We chose this Hamiltonian because the qualitative features of its spectral density are well established and because a particularly convenient algorithm exists to produce the imaginary-Time Green's function data. Shown are all the intermediate steps of data and solution qualification. The importance of careful data preparation and error propagation in the analytic continuation is discussed in the context of this example. Then, we review the different physical systems and physical quantities to which these, or related, procedures have been applied. Finally, we describe other features concerning the application of our methods, their possible improvement, and areas for additional study.
Dario Poletti - One of the best experts on this subject based on the ideXlab platform.
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occurrence of discontinuities in the performance of finite Time Quantum otto cycles
Physical Review E, 2016Co-Authors: Yuanjian Zheng, Peter Hanggi, Dario PolettiAbstract:: We study a Quantum Otto cycle in which the strokes are performed in finite Time. The cycle involves energy measurements at the end of each stroke to allow for the respective determination of work. We then optimize for the work and efficiency of the cycle by varying the Time spent in the different strokes and find that the optimal value of the ratio of Time spent on each stroke goes through sudden changes as the parameters of this cycle vary continuously. The position of these discontinuities depends on the optimized quantity under consideration such as the net work output or the efficiency.
Thomas Pruschke - One of the best experts on this subject based on the ideXlab platform.
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continuous Time Quantum monte carlo and maximum entropy approach to an imaginary Time formulation of strongly correlated steady state transport
Physical Review E, 2010Co-Authors: Andreas Dirks, Mark Jarrell, Philipp Werner, Thomas PruschkeAbstract:Recently, Han and Heary [Phys. Rev. Lett. 99, 236808 (2007)] proposed an approach to steady-state Quantum transport through mesoscopic structures, which maps the nonequilibrium problem onto a family of auxiliary Quantum impurity systems subject to imaginary voltages. We employ continuous-Time Quantum Monte-Carlo solvers to calculate accurate imaginary Time data for the auxiliary models. The spectral function is obtained from a maximum entropy analytical continuation in both Matsubara frequency and complexified voltage. To enable the analytical continuation we construct a kernel which is compatible with the analytical structure of the theory. While it remains a formidable task to extract reliable spectral functions from this unbiased procedure, particularly for large voltages, our results indicate that the method in principle yields results in agreement with those obtained by other methods.
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Analytic continuation of Quantum Monte Carlo data by stochastic analytical inference.
Physical Review E, 2010Co-Authors: Sebastian Fuchs, Thomas Pruschke, Mark JarrellAbstract:We present an algorithm for the analytic continuation of imaginary-Time Quantum Monte Carlo data which is strictly based on principles of Bayesian statistical inference. Within this framework we are able to obtain an explicit expression for the calculation of a weighted average over possible energy spectra, which can be evaluated by standard Monte Carlo simulations, yielding as by-product also the distribution function as function of the regularization parameter. Our algorithm thus avoids the usual ad hoc assumptions introduced in similar algorithms to fix the regularization parameter. We apply the algorithm to imaginary-Time Quantum Monte Carlo data and compare the resulting energy spectra with those from a standard maximum-entropy calculation.
Andrew M Childs - One of the best experts on this subject based on the ideXlab platform.
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spatial search by continuous Time Quantum walks on crystal lattices
Physical Review A, 2014Co-Authors: Andrew M ChildsAbstract:We consider the problem of searching a general $d$-dimensional lattice of $N$ vertices for a single marked item using a continuous-Time Quantum walk. We demand locality, but allow the walk to vary periodically on a small scale. By constructing lattice Hamiltonians exhibiting Dirac points in their dispersion relations and exploiting the linear behavior near a Dirac point, we develop algorithms that solve the problem in a Time of $O(\sqrt{N})$ for $dg2$ and $O(\sqrt{N}\phantom{\rule{0.16em}{0ex}}logN)$ in $d=2$. In particular, we show that such algorithms exist even for hypercubic lattices in any dimension. Unlike previous continuous-Time Quantum walk algorithms on hypercubic lattices in low dimensions, our approach does not use external memory.
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on the relationship between continuous and discrete Time Quantum walk
Communications in Mathematical Physics, 2010Co-Authors: Andrew M ChildsAbstract:Quantum walk is one of the main tools for Quantum algorithms. Defined by analogy to classical random walk, a Quantum walk is a Time-homogeneous Quantum process on a graph. Both random and Quantum walks can be defined either in continuous or discrete Time. But whereas a continuous-Time random walk can be obtained as the limit of a sequence of discrete-Time random walks, the two types of Quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-Time case.
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on the relationship between continuous and discrete Time Quantum walk
arXiv: Quantum Physics, 2008Co-Authors: Andrew M ChildsAbstract:Quantum walk is one of the main tools for Quantum algorithms. Defined by analogy to classical random walk, a Quantum walk is a Time-homogeneous Quantum process on a graph. Both random and Quantum walks can be defined either in continuous or discrete Time. But whereas a continuous-Time random walk can be obtained as the limit of a sequence of discrete-Time random walks, the two types of Quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-Time case. In this article, I describe a precise correspondence between continuous- and discrete-Time Quantum walks on arbitrary graphs. Using this correspondence, I show that continuous-Time Quantum walk can be obtained as an appropriate limit of discrete-Time Quantum walks. The correspondence also leads to a new technique for simulating Hamiltonian dynamics, giving efficient simulations even in cases where the Hamiltonian is not sparse. The complexity of the simulation is linear in the total evolution Time, an improvement over simulations based on high-order approximations of the Lie product formula. As applications, I describe a continuous-Time Quantum walk algorithm for element distinctness and show how to optimally simulate continuous-Time query algorithms of a certain form in the conventional Quantum query model. Finally, I discuss limitations of the method for simulating Hamiltonians with negative matrix elements, and present two problems that motivate attempting to circumvent these limitations.
Hui Dong - One of the best experts on this subject based on the ideXlab platform.
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achieve higher efficiency at maximum power with finite Time Quantum otto cycle
Physical Review E, 2019Co-Authors: Jin-fu Chen, Hui DongAbstract:: The optimization of heat engines was intensively explored to achieve higher efficiency while maintaining the output power. However, most investigations were limited to a few finite-Time cycles, e.g., the Carnot-like cycle, due to the complexity of the finite-Time thermodynamics. In this paper, we propose a class of finite-Time engine with Quantum Otto cycle, and demonstrate a higher achievable efficiency at maximum power. The current model can be widely utilized, benefitting from the general C/τ^{2} scaling of extra work for a finite-Time adiabatic process with long control Time τ. We apply the adiabatic perturbation method to the Quantum piston model and calculate the efficiency at maximum power, which is validated with an exact solution.
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achieve higher efficiency at maximum power with finite Time Quantum otto cycle
arXiv: Quantum Physics, 2019Co-Authors: Jin-fu Chen, Hui DongAbstract:The optimization of finite-Time thermodynamic heat engines was intensively explored recently, yet limited to few cycles, e.g. finite-Time Carnot-like cycle. In this Letter, we supplement a new type of finite-Time engine with Quantum Otto cycle and show the better performance. The current model can be widely utilized benefited from the general \mathcal{C}/\tau^{2} scaling of extra work for finite-Time adiabatic process with long control Time \tau. Such scaling allows analytical optimization of the generic finite-Time Quantum Otto cycle to surpass the efficiency at maximum power for the Carnot-like engine. We apply the current perturbation method to the Quantum piston model and calculate the efficiency at maximum power, which is validated with exact solution.
