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A generalized version of the simulated tempering operated in the expanded ensembles of non-Boltzmann weights has been proposed to mitigate a quasiergodicity problem occurring in simulations of rough energy landscapes. In contrast to conventional simulated tempering employing the Boltzmann weight, our method utilizes a parametrized, generalized distribution as a workhorse for stochastic exchanges of configurations and subensembles transitions, which allows a considerable enhancement for the rate of convergence of Monte Carlo and molecular dynamics simulations using delocalized weights. A feature of our method is that the exploration of the parameter space encouraging subensembles transitions is greatly accelerated using the dynamic update scheme for the weight via the average guide specific to the energy distribution. The performance and characteristic feature of our method have been validated in the liquid-solid transition of Lennard-Jones clusters and the conformational sampling of alanine dipeptide by taking two types of Tsallis [C. Tsallis, J. Stat. Phys. 52, 479 (1988)] expanded ensembles associated with different parametrization schemes.

We present one effective multicanonical molecular dynamics (MCMD) algorithm accelerating the convergence of rough energy landscapes simulations via an adaptive force-biased iteration scheme. Our method utilizes several short MCMD simulations with dynamically updated weights and combines them to estimate the density of states via multiple histogram technique. The key step of our algorithm is the adaptive refinement for the derivative of multicanonical weight, which allows the system to enlarge the sampling energy range maintaining the statistical accuracy. The performance of our method has been validated for atomic Lennard-Jones clusters.

We demonstrate the importance of the consistent treatment of mutual interaction between the condensate and the thermal component by applying the semiclassical Hartree-Fock model to the 2D trapped interacting Bose system. In contrast to the case where the interaction from the thermal component is neglected, the present system shows a lowering of the critical temperature and increase of the critical chemical potential due to the short-range repulsive interaction. Recent experimental observations of Bose-Einstein condensation (BEC) [1, 2] in dilute atomic gases confined in a magnetic trap have created great theoretical interest in weakly interacting Bose gases. At zero temperature the Gross-Pitaevskii (GP) equation [3] provides satisfactory ground state properties of the condensate. For finite temperature the Hartree-Fock-Bogoliobov-Popov (HFBP) theory has been developed to describe the finite-temperature properties of BEC [4,5]. Moreover, since the elementary collective excitations do not contribute significantly to the thermodynamics [6], the HFBP theory has been further simplified to the Hartree-Fock (HF) model where the condensate is described by the GP equation combined with the Thomas-Fermi (TF) approximation, and thermal components are treated as non-interacting bosons in an effective mean potential [7]. Recently, this simple and intuitive two-fluid model has been applied to obtain a semi-analytic expression of 3D BEC by further neglecting atomic interaction from the thermal component [8]. The validity of the two-fluid model has been confirmed by comparisions with the more elaborate self-consistent calculations for the 3D case [9]. All BEC experiments on trapped Bose gases to date have been naturally performed on the 3D system. However, over the last few years, several schemes for the preparation of atomic quasi-2D gases by using various planar waveguides for atoms have been proposed [10]. Theoretical study of the 2D system is also interesting, because even though the 2D homogeneous ideal boson system does not undergo BEC, a number of studies have indicated that it might be possible if a proper confining potential is applied [11-13]. Recently, Bayindir et al showed that 2D interacting Bose gases have BEC-like behaviour similar to those of an ideal system for weak interaction by applying a simplified form of the two-fluid model which neglects the interaction from the thermal component [14]. The results of the quantum Monte Carlo (QMC) study by Pearson et al [15] also strongly support the idea that there exists BEC in two dimensions for finite N , even though, as pointed out by Krauth [16], the effect of interaction is largely underestimated.