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In the physics literature ergodicity is taken to mean that a system, including a macroscopic one, visits all microscopic states in a relatively short time. We show that this is an impossibility even if that time is billions of years. We also suggest that this feature does not contradict most physical considerations since those considerations deal with correlations of only a few particles.
Whether the number of beta-steps in the lambda-calculus can be taken as a reasonable time cost model (that is, polynomially related to the one of Turing machines) is a delicate problem, which depends on the notion of evaluation strategy. Since the ni
We use exact diagonalization to study the eigenstate thermalization hypothesis (ETH) in the quantum dimer model on the square and triangular lattices. Due to the nonergodicity of the local plaquette-flip dynamics, the Hilbert space, which consists of
We revisit the question of describing critical spin systems and field theories using matrix product states, and formulate a scaling hypothesis in terms of operators, eigenvalues of the transfer matrix, and lattice spacing in the case of field theorie
Surface force apparatus (SFA) and atomic force microscopy (AFM) can measure a force curve between a substrate and a probe in liquid. However, the force curve had not been transformed to the number density distribution of solvent molecules (colloidal
We present a method for determining the free energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting cases. Converge