Sign problem of the fermionic shadow wave function.

We present a whole series of methods to alleviate the sign problem of the fermionic shadow wave function in the context of variational Monte Carlo. The effectiveness of our techniques is demonstrated on liquid ^{3}He. We found that although the variance is reduced, the gain in efficiency is restricted by the increased computational cost.

First-passage kinetic Monte Carlo method.

We present an efficient method for Monte Carlo simulations of diffusion-reaction processes. Introduced by us in a previous paper [Phys. Rev.

Fermionic shadow wave function variational calculations of the vacancy formation energy in 3He.

We present a novel technique well suited for studying the ground state of inhomogeneous fermionic matter in a wide range of different systems. The system is described using a fermionic shadow wave function, and the energy is computed by means of the variational Monte Carlo technique. The general form of the fermionic shadow wave function is useful for describing many-body systems with the coexistence of different phases as well in the presence of defects or impurities, but it requires overcoming a significant sign problem.

First-passage Monte Carlo algorithm: diffusion without all the hops.

We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions. Using the theory of first-passage processes and time dependent Green's functions, we break the difficult N-body problem into independent single- and two-body propagations circumventing numerous diffusion hops used in standard Monte Carlo simulations. The new algorithm is exact, extremely efficient, and applicable to many important physical situations in arbitrary integer dimensions.

Quantum Monte Carlo method using a stochastic Poisson solver.

The quantum Monte Carlo (QMC) technique is an extremely powerful method to treat many-body systems. Usually the quantum Monte Carlo method has been applied in cases where the interaction potential has a simple analytic form, like the 1/r Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a nontrivial problem.

Adaptive importance sampling Monte Carlo simulation of rare transition events.

We develop a general theoretical framework for the recently proposed importance sampling method for enhancing the efficiency of rare-event simulations [W. Cai, M. H.

Calculating expectations with time-dependent perturbations in quantum Monte Carlo.

We show that a small perturbation periodic in imaginary time can be used to compute expectation values of nondifferential operators that do not commute with the Hamiltonian within the framework of quantum diffusion Monte Carlo. Some results for the harmonic oscillator and the helium atom are presented showing the validity of the proposed method.

Bilinear diffusion quantum Monte Carlo methods.

The standard method of quantum Monte Carlo for the solution of the Schrödinger equation in configuration space can be described quite generally as devising a random walk that generates-at least asymptotically-populations of random walkers whose probability density is proportional to the wave function of the system being studied. While, in principle, the energy eigenvalue of the Hamiltonian can be calculated with high accuracy, estimators of operators that do not commute the Hamiltonian cannot. Bilinear quantum Monte Carlo (BQMC) is an alternative in which the square of the wave function is sampled in a somewhat indirect way.

Importance sampling of rare transition events in Markov processes.

We present an importance sampling technique for enhancing the efficiency of sampling rare transition events in Markov processes. Our approach is based on the design of an importance function by which the absolute probability of sampling a successful transition event is significantly enhanced, while preserving the relative probabilities among different successful transition paths. The method features an iterative stochastic algorithm for determining the optimal importance function.

Exact monte carlo method for continuum fermion systems.

We offer a new proposal for the Monte Carlo treatment of many-fermion systems in continuous space. It is based upon diffusion Monte Carlo with significant modifications: correlated pairs of random walkers that carry opposite signs, different functions "guide" walkers of different signs, the Gaussians used for members of a pair are correlated, and walkers can cancel so as to conserve their expected future contributions. We report results for free-fermion systems and a fermion fluid with 14 3He atoms, where it proves stable and correct.