Anton Arnold, Franco Fagnola, Lukas Neumann
In this article we try to bridge the gap between the quantum dynamical semigroup and Wigner function approaches to quantum open systems. In particular we study stationary states and the long time asymptotics for the quantum Fokker-Planck equation. Our new results apply to open quantum systems in a harmonic confinement potential, perturbed by a (large) sub-quadratic term.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
This paper is concerned with the Wigner-Poisson-Fokker-Planck system, a kinetic evolution equation for an open quantum system with a non-linear Hartree potential. Existence, uniqueness and regularity of global solutions to the Cauchy problem in 3 dimensions are established. The analysis is carried out in a weighted L^2-space, such that the linear quantum Fokker-Planck operator generates a dissipative semigroup.The non-linear potential can be controled by using the parabolic regularization of the system. The main technical difficulty for establishing global-in-time solutions is to derive a-prio…
We consider the linear Wigner-Fokker-Planck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator potential. For a certain class of perturbations we prove that the equation admits a unique stationary solution in a weighted Sobolev space. A key ingredient of the proof is a new result on the existence of spectral gaps for Fokker-Planck type operators in certain weighted $L^2$-spaces. In addition we show that the steady state corresponds to a positive density matrix operator with unit trace and that the solutions of the time-dependent problem converge …
Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the Ehrenfest equations). Numerical simulations establish that the model approximately equilibrates. These findings signific…
The time evolution of the Wigner function for Gaussian states generated by Lindblad quantum dynamics is investigated in the semiclassical limit. A new type of phase-space dynamics is obtained for the centre of a Gaussian Wigner function, where the Lindblad terms generally introduce a non-Hamiltonian flow. In addition to this, the Gaussian approximation yields dynamical equations for the covariances. The approximation becomes exact for linear Lindblad operators and a quadratic Hamiltonian. By viewing the Wigner function as a wave function on a coordinate space of doubled dimension, and the phas…
This paper has been withdrawn by the authors due to a crucial error in the proof of the main result. In a new manuscript (with two new authors) available at arXiv:1010.2791v1 this problem has been resolved.
We demonstrate a method which allows the stochastic modelling of quantum systems for which the generalised Fokker-Planck equation in the phase space contains derivatives of higher than second order. This generalises quantum stochastics far beyond the quantum-optical paradigm of three and four-wave mixing problems to which these techniques have so far only been applicable. To verify our method, we model a full Wigner representation for the optical parametric oscillator, a system where the correct results are well known and can be obtained by other methods.
A semiclassical approximation for an evolving density operator, driven by a "closed" hamiltonian operator and "open" markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by a…
We consider a class of evolution equations in Lindblad form, which model the dynamics of dissipative quantum mechanical systems with mean-field interaction. Particularly, this class includes the so-called Quantum Fokker-Planck-Poisson model. The existence and uniqueness of global-in-time, mass preserving solutions is proved, thus establishing the existence of a nonlinear conservative quantum dynamical semigroup. The mathematical difficulties stem from combining an unbounded Lindblad generator with the Hartree nonlinearity.
Long time quantum-classical correspondence for open systems in trace norm
研究了与 Markovian 环境耦合的无摩擦系统，证明在特定增长条件下，Lindblad 方程与 Fokker-Planck 方程的演化在迹范数下长时间保持一致，改进了以往弱范数下的结果。
Classical-Quantum correspondence in Lindblad evolution
本研究证明满足条件的Lindblad演化中，量子可观测量与经典Fokker–Planck演化的一致性远超埃伦费斯特时间，时间尺度与已有研究一致但方法结论不同，附数值验证。
The Dunkl-Fokker-Planck Equation in $1+1$ Dimensions
本文用 Dunkl 导数推广了 (1+1) 维 Fokker-Planck 方程，求解了谐振子加离心势的本征值问题，并在奇漂移函数下联系到 Wigner-Dunkl 超对称。
Relativistic Lindblad description of the electron's radiative dynamics
本文提出了一种相对论性Lindblad模型，用于描述电子在强激光场中的辐射动力学，结合辐射反应与真空波动，提供量子类比的Landau-Lifshitz方程。
Classical correspondence beyond the Ehrenfest time for open quantum systems with general Lindbladians
该研究证明了带一般Lindbladian的开放量子系统中，当扩散强度满足D≫ℏ^{4/3}时，量子-经典对应可超出埃伦费斯特时间，采用可变压缩高斯态半经典混合方法，论证了4/3指数的最优性，并在姊妹篇给出物理系统可直接应用的显式界。
Wigner functions, allowing for a reformulation of quantum mechanics in phase space, are of central importance for the study of the quantum-classical transition. A full understanding of the quantum-classical transition, however, also requires an explanation for the absence of macroscopic superpositions to solve the quantum measurement problem. Stochastic reformulations of quantum mechanics based on spontaneous collapses of the wavefunction are a popular approach to this issue. In this article, we derive the dynamic equations for the four most important spontaneous collapse models - Ghirardi-Rim…
Fixed-Boost Wigner Noise: Strict Trace-Distance Contraction without Quantum Degradability
研究了洛伦兹 boost 作用下大质量粒子正则自旋的迹距离收缩，通过刻画反演对称信道锥等方法求解优化问题，实现理想构造，证明无辅助自旋可区分性排序与量子统计后处理顺序无关。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。