Fugu-MT 論文翻訳(概要): Scattering Cross Section Formula Derived From Macroscopic Model of Detectors

論文の概要: Scattering Cross Section Formula Derived From Macroscopic Model of Detectors

arxiv url: http://arxiv.org/abs/2601.01625v1
Date: Sun, 04 Jan 2026 18:08:22 GMT
ステータス: 翻訳完了
システム内更新日: 2026-01-06 16:25:22.577219
Title: Scattering Cross Section Formula Derived From Macroscopic Model of Detectors
Title（参考訳）: 検出器のマクロモデルから導出した散乱断面積式
Authors: Rashi Kaimal, Roderich Tumulka,
Abstract要約: 我々は、量子散乱理論で一般的に使用される(明示的または暗黙的に)ステートメントの正当化を懸念している。検出過程の異なるマクロモデルに基づいて,この式を2つの導出する。
参考スコア（独自算出の注目度）: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We are concerned with the justification of the statement, commonly (explicitly or implicitly) used in quantum scattering theory, that for a free non-relativistic quantum particle with initial wave function $Ψ_0(\boldsymbol{x})$, surrounded by detectors along a sphere of large radius $R$, the probability distribution of the detection time and place has asymptotic density (i.e., scattering cross section) $σ(\boldsymbol{x},t)= m^3 \hbar^{-3} R t^{-4} |\widehatΨ_0(m\boldsymbol{x}/\hbar t)|^2$ with $\widehatΨ_0$ the Fourier transform of $Ψ_0$. We give two derivations of this formula, based on different macroscopic models of the detection process. The first one consists of a negative imaginary potential of strength $λ>0$ in the detector volume (i.e., outside the sphere of radius $R$) in the limit $R\to\infty,λ\to 0, Rλ\to \infty$. The second one consists of repeated nearly-projective measurements of (approximately) the observable $1_{|\boldsymbol{x}|>R}$ at times $\mathscr{T},2\mathscr{T},3\mathscr{T},\ldots$ in the limit $R\to\infty,\mathscr{T}\to\infty,\mathscr{T}/R\to 0$; this setup is similar to that of the quantum Zeno effect, except that there one considers $\mathscr{T}\to 0$ instead of $\mathscr{T}\to\infty$. We also provide a comparison to Bohmian mechanics: while in the absence of detectors, the arrival times and places of the Bohmian trajectories on the sphere of radius $R$ have asymptotic distribution density given by the same formula as $σ$, their deviation from the detection times and places is not necessarily small, although it is small compared to $R$, so the effect of the presence of detectors on the particle can be neglected in the far-field regime. We also cover the generalization to surfaces with non-spherical shape, to the case of $N$ non-interacting particles, to time-dependent surfaces, and to the Dirac equation.
Abstract（参考訳）: 量子散乱理論において一般的に(明示的あるいは暗黙的に)用いられるステートメントの正当性については、初期波動関数を持つ自由な非相対論的量子粒子に対して、大半径$R$の球面に沿った検出器に囲まれている場合、検出時間と場所の確率分布は漸近密度(すなわち散乱断面)を持つ(例えば、散乱断面)$σ(\boldsymbol{x},t)= m^3 \hbar^{-3} R t^{-4} |\widehat _0(m\boldsymbol{x}/\hbar t)|^2$ である。検出過程の異なるマクロモデルに基づいて,この式を2つの導出する。 1つは、検出器の体積(すなわち半径$R$の球の外側)における強度$λ>0$の負の虚ポテンシャルで、極限$R\to\infty,λ\to 0, Rλ\to \infty$である。 2番目の測度は、観測可能な1_{|\boldsymbol{x}|>R}$ at times $\mathscr{T},2\mathscr{T},3\mathscr{T},\ldots$ in the limit $R\to\infty,\mathscr{T}\to\infty,\mathscr{T}/R\to 0$ の概射測度である。また, 検出器が存在しない場合, 半径$R$の球面上のボヘミア軌道の到達時間と位置は, σ$と同じ式で漸近分布密度を持つが, 検出時間と位置の偏差は必ずしも小さくない。また、非球形曲面への一般化、非相互作用粒子$N$、時間依存曲面への一般化、ディラック方程式への一般化もカバーする。

論文の概要: Scattering Cross Section Formula Derived From Macroscopic Model of Detectors

関連論文リスト