AI 中文总结
研究非相对论玻色子场中耗散CSL模型，在泛函薛定谔表示下建立公式，通过扇区投影获固定粒子数波函数，考虑耗散扩展，单粒子扇区再现能量平衡，多体扇区有额外项，集体对摩擦产生非广延稳态平均动能。
AI 中文摘要
我们在非相对论玻色子场的泛函薛定谔表示中，为最小耗散连续自发局域化（CSL）动力学建立公式。在该框架下，福克空间态由波函数编码，通过扇区投影获得固定粒子数的波函数。对于与涂抹质量密度的最小CSL耦合，投影在每个\(N\)粒子扇区给出标准非线性随机动力学。我们还考虑了耗散扩展，其中坍缩算符包括涂抹电流贡献。单粒子扇区再现了预期的耗散CSL能量平衡，而固定多体扇区包含额外的集体动量转移和对混合项。在领先的紧致闭合内，集体对摩擦产生非广延的稳态平均动能。
英文摘要
We formulate minimal and dissipative Continuous Spontaneous Localization (CSL) dynamics in the functional Schrödinger representation for a non-relativistic bosonic field. In this framework, the Fock-space state is encoded in a wave functional, and fixed particle-number wave functions are obtained by sector projection. For the minimal CSL coupling to the smeared mass density, this projection gives the standard nonlinear stochastic dynamics in each \(N\)-particle sector, with the collapse operator acting on the total smeared density of the configuration. This makes the amplification mechanism transparent and allows us to discuss sector superpositions, local probability balance, and the status of Bohmian equivariance at the wave-function level. We then consider a dissipative extension in which the collapse operator includes a smeared current contribution. The one-particle sector reproduces the expected dissipative CSL energy balance, while fixed many-body sectors contain additional collective momentum shifts and pair-mixing terms that are not reducible, in general, to independent one-particle contributions. Within a leading compact closure, the collective pair friction produces a non-extensive stationary mean kinetic energy: in three dimensions and for weak dissipation, $T_N^{\rm comp}\simeq 2T_β/N$, whereas the corresponding dilute energy remains extensive.
