{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"critpt","formal_name":"CritPt","introduction":"研究水準の物理問題で、科学的理解と多段階の推論・計算を評価するベンチマークです。公開データには70の課題があり、問題文とコード雛形を組み合わせて解答を構成します。\n\nCritPt evaluates scientific understanding and multi-step reasoning and computation on research-level physics problems. Its public dataset contains 70 challenges with problem descriptions and code templates.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://critpt.com/","indexing_mode":"noindex"},"task_id":"9f682704-9d06-5932-a4bd-92a45b23f700","task_key":"train--Challenge~5f41~5fmain","task_revision_id":"1","upstream_id":"Challenge_41_main","short_description":"In a real-space quantum Monte Carlo simulation of a crystal, only a finite…","config":"","split":"train","body":"{\"code_template\":\"def answer():\\n    r\\\"\\\"\\\"\\n    Return the value one should add to the total energy per electron.\\n\\n    Inputs\\n    ----------\\n    None\\n\\n    Outputs\\n    ----------\\n    delta_E_fs : float, the value one should add to the total energy per electron to remove finite-size effects (Hartree, two significant digits).\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    delta_E_fs = ...\\n    # ---------------------------------------------------------------\\n\\n    return delta_E_fs\\n\",\"problem_description\":\"# Problem setup:\\nIn a real-space quantum Monte Carlo simulation of a crystal, only a finite number of N electrons can be simulated on a computer. This is typically done by tiling a few unit cells of the materials into a supercell with volume $\\\\Omega$. Using periodic boundary conditions, the simulation can access only a finite number of momenta, which are compatible with the supercell. As a result, the total energy calculated in the simulation will have a finite-size error, which is the difference between the result from an infinite system and that of a finite-size one. It is possible to correct this finite-size error if given access to the many-body wave function.\\nThe density of the electron gas is typically parameterized using the Wigner-Seitz radius $r_s$. When unpolarized, the Fermi wavevector $k_F=\\\\sqrt{2}/r_s$.\\n\\n# Main problem:\\n\\nAfter performing a diffusion Monte Carlo simulation of the unpolarized two-dimensional electron gas with $N=122$ electrons at density $r_s=10$ in a square box in the Fermi liquid phase using the Slater-Jastrow wave function, what should one add to the total energy per electron to remove finite-size effects? Report the answer in Hartree and keep two significant digits.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}