Final-State Condition And Dissipative Quantum Mechanics

耗散量子力学：正则量子化和von Neumann方程的推广

Dissipative Quantum Mechanics: The Generalization of the Canonical Quantization and von Neumann Equation

弦论中的耗散模型可以有更广泛的应用：1）非临界弦是“耦合常数“相空间中的耗散系统。2)仿射度量曲空间中的玻色弦是耗散系统。但是，耗散系统的量子描述具有众所周知的模糊性。为了解决耗散系统的量子描述问题，我们建议在通常的（结合）算子之外引入一个算子W。所建议的算子代数并不违反海森堡代数，因为我们通过引入非完整量的算子W来扩展正则对易关系，除了通常的（完整的）坐标-动量函数的通常（结合）算子之外。为了满足广义对易关系，算子W必须是非结合非Lieble（不满足Jacobi恒等式）算子。由于这些性质，算子的乘法和换位子的总时间导数不满足Leibnitz规则。这导致耗散系统的量子运动方程和正则对易关系的兼容性。所建议的von Neumann方程的推广与耗散系统的经典Liouville方程有关。

耗散Hofstadter模型的Phase Diagram

Phase Diagram of the Dissipative Hofstadter Model

带电粒子在均匀磁场和周期势场中的耗散量子力学存在离域临界点，这一临界点对应于开弦的背景。我们研究这个系统的相图（在磁场/耗散常数平面），并找到一个分形结构，在零耗散的限制，匹配的分形能级结构的纯量子力学版本的这个问题（霍夫斯塔德模型）。

Phase Space Geometry and Chaotic Attractors in Dissipative Nambu Mechanics

Following the Nambu mechanics framework we demonstrate that the non-dissipative part of the Lorenz system can be generated by the intersection of two quadratic surfaces that form a doublet under the group SL(2,R). All manifolds are classified into four dinstict classes; parabolic, elliptical, cylindrical and hyperbolic. The Lorenz attractor is localized by a specific infinite set of one parameter family of these surfaces. The different classes correspond to different physical systems. The Lorenz system is identified as a charged rigid body in a uniform magnetic field with external torque and t…

Scaling Properties of the Lorenz System and Dissipative Nambu Mechanics

In the framework of Nambu Mechanics, we have recently argued that Non-Hamiltonian Chaotic Flows in $ R^{3} $, are dissipation induced deformations, of integrable volume preserving flows, specified by pairs of Intersecting Surfaces in $R^{3}$. In the present work we focus our attention to the Lorenz system with a linear dissipative sector in its phase space dynamics. In this case the Intersecting Surfaces are Quadratic. We parametrize its dissipation strength through a continuous control parameter $ε$, acting homogeneously over the whole 3-dim. phase space. In the extended $ε$-Lorenz system we …

受监测耗散随机电路的统计力学

Statistical Mechanics of Monitored Dissipative Random Circuits

该研究将耗散引入受监测随机电路，通过映射到二维Ising模型，揭示测量与耗散联合作用下的纠缠相变及动力学交叉行为。

Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and Rössler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotati…

Dissipative quantum mechanics and Kondo-like impurities on noncommutative two-tori

In a recent paper, by exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter $θ$ (in appropriate units), a general one-to-one correspondence between the $m$-reduced conformal field theory (CFT) describing a quantum Hall fluid (QHF) at paired states fillings $ν=% \frac{m}{pm+2}$ and an Abelian noncommutative field theory (NCFT) has been established . That allowed us to add new evidence to the relationship between noncommutativity and quantum Hall fluids\cite% {ncmanybody}. On the other hand, the $m$-re…

Nambu mechanics for stochastic magnetization dynamics

The Landau-Lifshitz-Gilbert (LLG) equation describes the dynamics of a damped magnetization vector that can be understood as a generalization of Larmor spin precession. The LLG equation cannot be deduced from the Hamiltonian framework, by introducing a coupling to a usual bath, but requires the introduction of additional constraints. It is shown that these constraints can be formulated elegantly and consistently in the framework of dissipative Nambu mechanics. This has many consequences for both the variational principle and for topological aspects of hidden symmetries that control conserved q…