M. Abolhasani, M. Golshani
In a recent paper, A.Valentini tried to obtain Born's principle as a result of a subquantum heat death, using classical H-theorem and the definition of a proper quantum H-theorem within the framwork of Bohm's theory. In this paper, we shall show the possibility of solving the problem of action-reaction asymmetry present in Bohm's theory by modifying Valentini's procedure. However, we get his main result too.
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We try to obtain Born's principle as a result of a subquantum heat death, using classical ${\cal H}$-theorem and the definition of a proper quantum ${\cal H}$-theorem, within the framwork of Bohm's theory. We shall show the possibility of solving the problem of action-reaction asymmetry present in Bohm's theory and the arrow of time problem in our procedure.
The paper is withdrawn due to an error in Section 2.
A concise review of the derivation of the Born rule and Schrödinger equation from first principles is provided. The starting point is a formalization of fundamental notions of measurement and composition, leading to a general framework for physical theories known as the positive formalism. Consecutively adding notions of spacetime, locality, absolute time and causality recovers the well established convex operational framework for classical and quantum theory. Requiring the partially ordered vector space of states to be an anti-lattice one obtains quantum theory in its standard formulation. Th…
A new formulation of quantum mechanics is proposed based on a new principle that can be considered a generalization of the Born rule. The principle is composed of a mathematical expression and an associated interpretation, and establishes a correlation between the positions of a particle at two different times. Under reasonable conditions for the wave function, this correlation implies that the particles follow quasi-classical trajectories. It is also shown that the Born rule is equivalent to a particular case of the new principle. These features allow the principle to provide a unified explan…
Using the existing classification of all alternatives to the measurement postulates of quantum theory we study the properties of bi-partite systems in these alternative theories. We prove that in all these theories the purification principle is violated, meaning that some mixed states are not the reduction of a pure state in a larger system. This allows us to derive the measurement postulates of quantum theory from the structure of pure states and reversible dynamics, and the requirement that the purification principle holds. The violation of the purification principle implies that there is so…
Efficient Simulation of Pre-Born-Oppenheimer Dynamics on a Quantum Computer
本文提出了一种在量子计算机上高效模拟预玻恩-奥普芬贝格动力学的量子算法，通过优化方法显著降低了光化学反应模拟的资源需求。
The Weyl correspondence and the related Wigner formalism lie at the core of traditional quantum mechanics. We discuss here an alternative quantization scheme, whose idea goes back to Born and Jordan, and which has recently been revived in another context, namely time-frequency analysis. We show that in particular the uncertainty principle does not enjoy full symplectic covariance properties in the Born and Jordan scheme, as opposed to what happens in the Weyl quantization.
On the Born rule in a new quantum approach
该研究在新量子基础方法中，通过跃迁概率原理这一弱条件证明了玻恩规则，并提出了比传统更简单的态概念。
The action reaction principle is violated in the standard formulation of Quantum Mechanics, so that its phase space is incomplete. Moreover, projection of state of a quantum system under indirect measurement, when there are alternative virtual paths and one of them is discarded by negative detection implies, according to the action reaction principle, a reaction on the detector, although its macroscopic state does not change. If all interactions are local, mediated by fields with relativistically causal evolution, some system, different from the particle which follows another path, must locall…
The probabilistic rule that links the formalism of Quantum Mechanics (QM) to the real world was stated by Born in 1926. Since then, there were many attempts to derive the Born postulate as a theorem, Gleason's being the most prominent. The Gleason derivation, however, is generally considered rather intricate and its physical meaning, in particular in relation with the noncontextuality of probability (NP), is not quite evident. More recently, we are witnessing a revival of interest in possible demonstrations of the Born rule, like Zurek's and Deutsch's based on the decoherence and on the theory…
We explore excitonic energy transfer dynamics in a molecular dimer system coupled to both structured and unstructured oscillator environments. By extending the reaction coordinate master equation technique developed in [J. Iles-Smith, N. Lambert, and A. Nazir, Phys. Rev. A 90, 032114 (2014)], we go beyond the commonly used Born-Markov approximations to incorporate system-environment correlations and the resultant non-Markovian dynamical effects. We obtain energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierar…
Deriving the Generalised Born Rule from First Principles
本文从基本原理出发，探讨了广义玻尔兹曼规则的合理性，通过过程理论分析，展示了其与概率计算的关系，并指出引入噪声可加强标量与概率的关联。
Complex phase factors are viewed not only as redundancies of the quantum formalism but instead as remnants of unitary transformations under which the probabilistic properties of observables are invariant. It is postulated that a quantum observable corresponds to a unitary representation of an abelian Lie group, the irreducible subrepresentations of which correspond to the observable's outcomes. It is shown that this identification agrees with the conventional identification as self-adjoint operators. The upshot of this formalism is that one may 'second quantize' the representation to which an …
Diagonal Born-Oppenheimer Corrections in Condensed-Phase Ring Polymer Surface Hopping
本文研究了环状聚合物表面跃迁方法中对角本-奥普芬修正的影响，发现其在不同反应区域和温度下对模拟准确性有显著影响，尤其在低温下表现不一。
Born's rule from epistemic assumptions
本研究从本体论完备性、本体论极简主义及概率定则普遍有效性三类认识论假设出发，无需预设量子力学希尔伯特空间结构，推导得出玻恩定则的合理性，为其提供了基于第一性原理的新推导路径。
Violation of the action-reaction principle is shown to occur in the van der Waals interaction between two atoms, one of which is excited. It is accompanied by the transfer of linear momentum to the electromagnetic vacuum. The vacuum momentum results from the asymmetric interference of the virtual photons scattered off each atom along the interatomic direction, which is in itself a manifestation of the optical theorem. This momentum, of equal strength and opposite direction to the momentum gained by the two-atom system, is ultimately released through directional spontaneous emission. A quantita…
Madelung transform and variational asymptotics in Born-Oppenheimer molecular dynamics
该研究基于哈密顿变分原理与欧拉-庞加莱约化构建BOMD的几何表述，借助马德隆变换的拉格朗日流体路径，通过渐近方法从连续模型变分原理推导BOMD，验证bohmion方案的即时实现，并拓展至混合量子-经典动力学模型。
Timeless Histories: Quantum Measurement and the Maximum Entropy Principle
该研究针对量子测量问题，将其与最大熵原理结合，提出「永恒的历史」量子力学表述，以玻恩-玻尔兹曼规则为基础，结合退相干解释经典性涌现，避免了退相干需自证规则的问题。
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