{"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":"4ae8b035-20b5-5082-af8a-c7b6e94a69ed","task_key":"train--Challenge~5f45~5fmain","task_revision_id":"1","upstream_id":"Challenge_45_main","short_description":"In goniopolar materials, the thermal power can be n-type in one direction and…","config":"","split":"train","body":"{\"code_template\":\"def answer(mc_x, mc_y, mv_x, mv_y):\\n    r\\\"\\\"\\\"\\n    Return the value of the goniopolarity condition.\\n\\n    Inputs\\n    ----------\\n    mc_x, mc_y, mv_x, mv_y: float\\n        Effective masses $m_{c/v,\\\\alpha}$ with $\\\\alpha = x,y$, in unit of a typical carrier mass $m_0$ that is five times of the electron mass.\\n\\n    Outputs\\n    ----------\\n    have_goniopolarity: bool\\n        True if the material exhibits goniopolarity, otherwise False.\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    have_goniopolarity = ...\\n    # ---------------------------------------------------------------\\n\\n    return have_goniopolarity\",\"problem_description\":\"\\n\\n# Problem setup:\\nIn goniopolar materials, the thermal power can be n-type in one direction and p-type in another direction.\\n\\n# Main problem:\\nConsider a two-band 2D intrinsic semiconductor under temperature $T$. The conduction band has a dispersion $E_c= \\\\Delta/2+\\\\sum_{\\\\alpha=x,y}\\\\frac{\\\\hbar^2k_{\\\\alpha}^2}{2m_{c,\\\\alpha}}$, and the valence band has a dispersion $E_v= -\\\\Delta/2-\\\\sum_{\\\\alpha=x,y}\\\\frac{\\\\hbar^2k_{\\\\alpha}^2}{2m_{v,\\\\alpha}}$, where $\\\\Delta$ is the size of band gap. We further assume that the relaxation time of the electrons and holes are the same. What condition should the effective mass $m_{c/v,\\\\alpha}$, with $ \\\\alpha=x,y$, satisfy to exhibit goniopolarity?\\n\\n\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}