共查询到20条相似文献，搜索用时 15 毫秒
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A novel path integral Monte Carlo (PIMC) approach for correlated many‐particle systems with arbitrary pair interaction in continuous space at low temperatures is presented. It is based on a representation of the N ‐particle density operator in a basis of (anti‐)symmetrized N ‐particle states (configurations of occupation numbers). The path integral is transformed into a sum over trajectories with the same topology and, finally, the limit of M → ∞, where M is the number of high‐temperature factors, is analytically performed. This yields exact expressions for the thermodynamic quantities and allows to perform efficient simulations for fermions at low temperature and weak to moderate coupling. Our method is expected to be applicable to dense quantum plasmas in the regime of strong degeneracy where conventional PIMC fails due to the fermion sign problem (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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G. Düring;J. Kurchan 《Europhysics letters》2010,92(5)
Monte Carlo sampling of any system may be analyzed in terms of an associated glass model —a variant of the Random Energy Model— with, whenever there is a sign problem, complex fields. This model has three types of phases (liquid, frozen and “chaotic”), as is characteristic of glass models with complex parameters. Only the liquid one yields the correct answers for the original problem, and the task is to design the simulation to stay inside it. The statistical convergence of the sampling to the correct expectation values may be studied in these terms, yielding a general lower bound for the computer time as a function of the free energy difference between the true system, and a reference one. In this way, importance sampling strategies may be optimized.https://doi.org/10.1209/0295-5075/92/50004 相似文献
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In Lagrangian formulation, it is extremely difficult to compute the excited spectrum and wavefunctions ora quantum theory via Monte Carlo methods. Recently, we developed a Monte Carlo Hamiltonian method for investigating this hard problem and tested the algorithm in quantum-mechanical systems in 1 1 and 2t1 dimensions. In this paper we apply it to the study of thelow-energy quantum physics of the (3 1)-dimensional harmonic oscillator.`` 相似文献
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We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method,in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. Weconsider two quantum mechanical models: a symmetric one V(x) = |x|/2; and an asymmetric one V(x) = ∞, forx ＜ 0 and V(x) = x, for x ≥ 0. The results for the spectrum, wave functions and thermodynamical observables are inagreement with the analytical or Runge-Kutta calculations. 相似文献
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《Europhysics letters》1997,38(2):113-118
Recent work on the complete wetting transition for three-dimensional systemswith short-ranged forces has emphasized the role played by the coupling of order-parameter fluctuations near the wall and depinning interface.It has been proposed that an effective two-fieldHamiltonian, which predicts a renormalisation of the wetting parameter,could explain the controversy between the RG analysis of the capillary-wave model and Monte Carlo simulations on the Ising model. In this letter results of extensive Monte Carlo simulations of the two-field model are presented. The results are in agreement withprediction of a renormalized wetting parameter . https://doi.org/10.1209/epl/i1997-00210-x 相似文献
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We study the equilibrium properties of a single quantum particle interacting with a classical lattice gas. We develop a path-integral formalism in which the quantum particle is represented by a closed, variable-step random walk on the lattice. After demonstrating that a Metropolis algorithm correctly predicts the properties of a free particle, we extend it to investigate the behavior of the quantum particle interacting with the lattice gas. Evidence of weak localization is observed under conditions of quenched disorder, while self-trapping clearly occurs for the fully annealed system. Compared with continuous space systems, convergence of Monte Carlo simulations in this minimum model is orders of magnitude faster in cpu time. Therefore the system behavior can be investigated for a much larger domain of thermodynamic parameters (e.g., density and temperature) in a reasonable time. 相似文献
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The Monte Carlo Hamiltonian method developed recentlyallows to investigate the groundstate and low-lying excited states of a quantum system, using MonteCarlo (MC) algorithm with importance sampling. However, conventional MC algorithmhas some difficulties when applied to inverse potentials. We propose to use effective potential andextrapolation method to solve the problem. We present examples from the hydrogensystem. 相似文献
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A method for introducing relativistic quantum mechanics to energy students is described. The method complements existing modern
physics courses and relies on Feynman’s relativistic path integral approach to display a relationship between classical dynamics,
quantum theory, and relativistic quantum theory. 相似文献
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We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of control variates from classical Monte Carlo integration. We illustrate it using two models of nonequilibrium transport. 相似文献
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Antonino La Magna 《Surface science》2007,601(2):308-314
The shape relaxation of supported crystallites is studied by means of kinetic Monte Carlo simulations, initialising the system with different configurations. At low temperature, when the facet nucleation limits the relaxation, the simulations show that the equilibration mechanism and the equilibration time scaling laws depend strongly on the initialisation. In this regime, the adhesion strongly increases the stability of intermediate configurations with large contact area. The relationship between the different equilibration pathways and the equilibration scaling laws is discussed considering the dependence of the nucleation barrier energy G∗ on the particle energetics in the regions with the largest kinks and steps density. 相似文献
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Francis J. Alexander Gregory L. Eyink Juan M. Restrepo 《Journal of statistical physics》2005,119(5-6):1331-1345
Asbstract By casting stochastic optimal estimation of time series in path integral form, one can apply analytical and computational techniques of equilibrium statistical mechanics. In particular, one can use standard or accelerated Monte Carlo methods for smoothing, filtering and/or prediction. Here we demonstrate the applicability and efficiency of generalized (nonlocal) hybrid Monte Carlo and multigrid methods applied to optimal estimation, specifically smoothing. We test these methods on a stochastic diffusion dynamics in a bistable potential. This particular problem has been chosen to illustrate the speedup due to the nonlocal sampling technique, and because there is an available optimal solution which can be used to validate the solution via the hybrid Monte Carlo strategy. In addition to showing that the nonlocal hybrid Monte Carlo is statistically accurate, we demonstrate a significant speedup compared with other strategies, thus making it a practical alternative to smoothing/filtering and data assimilation on problems with state vectors of fairly large dimensions, as well as a large total number of time steps. 相似文献
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JIANG JunQin HUANG ChunQing LUO XiangQian Hamza Jirari Helmut Kr&# ger Kevin Moriarty 《理论物理通讯》2000,34(4):723-728
Using a recently developed Hamiltonian Monte Carlo method, we compute the lowlying energy spectrum and wavefunctions as well as thermodynamical observables in (2+1)-dimensional quantum mechanics, and give an estimate of the statistical errors. Our numerical results are in good agreement with the exact ones. 相似文献
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Alexander K. Hartmann;Pierre Le Doussal;Satya N. Majumdar;Alberto Rosso;Gregory Schehr 《Europhysics letters》2018,121(6)
The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling approach,the distribution is obtained over a large range of values,down to a probability density as small as in the tails. Both short and long times are investigated and compared with recent analytical predictions for the large-deviation forms of the probability of rare fluctuations. At short times the agreement with the analytical expression is spectacular. We observe that the far left and right tails,with exponents 5/2 and 3/2,respectively,are preserved also in the region of long times. We present some evidence for the predicted non-trivial crossover in the left tail from the tail exponent to the cubic tail of the Tracy-Widom distribution,although the details of the full scaling form remain beyond reach.https://doi.org/10.1209/0295-5075/121/67004 相似文献
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Hendrik Schawe;Alexander K. Hartmann;Satya N. Majumdar;Grégory Schehr 《Europhysics letters》2018,124(4)
We derive analytically the full distribution of the ground-state energy of K non-interacting fermions in a disordered environment, modelled by a Hamiltonian whose spectrum consists of N i.i.d. random energy levels with distribution (with ε ≥0), in the same spirit as the “Random Energy Model”. We show that for each fixed K , the distribution P K , N (E 0) of the ground-state energy E 0 has a universal scaling form in the limit of large N . We compute this universal scaling function and show that it depends only on K and the exponent α characterizing the small ε behaviour of . We compared the analytical predictions with results from numerical simulations. For this purpose we employed a sophisticated importance-sampling algorithm that allowed us to obtain the distributions over a large range of the support down to probabilities as small as . We found asymptotically a very good agreement between analytical predictions and numerical results.https://doi.org/10.1209/0295-5075/124/40005 相似文献