相关论文: Duality and Conditional Expectations in the Nakaji…
Motivated by Barr{\'\i}a-Halmos's \cite[Question 19]{barria1982asymptotic} and Halmos's \cite[Problem 237]{Halmos1978A}, we explore projections in Toeplitz algebra on the Hardy space. We show that the product of two Toeplitz (Hankel)…
The shell model solve the nuclear many-body problem in a restricted model space and takes into account the restricted nature of the space by using effective interactions and operators. In this paper two different methods for generating the…
The principle of relativity is extended to accommodate finite-mass observers with quantum properties by introducing two operational requirements: (i) equivalence of observers at the level of transition amplitudes, and (ii) the impossibility…
We present a discussion of the extended Wigner's friend thought experiment proposed by Frauchiger and Renner in [1]. We show by using various arguments, including textbook quantum mechanics and the ontological approach of Contexts, Systems,…
In this paper, a new generalized Bernstein-Bezier type operators is constructed.The estimates of the moments of these operators are investigated. The rate of convergence in terms of modulus of continuity is given. Then, the equivalent…
Let $(X,d,\mu )$ be a space of homogeneous type in the sense of Coifman and Weiss, i.e. $d$ is a quasi metric on $X$ and $\mu $ is a positive measure satisfying the doubling condition. Suppose that $u$ and $v$ are two locally finite…
The kinematical foundations of Schwinger's algebra of selective measurements were discussed in a previous paper (arXiv:1905.12274) and, as a consequence of this, a new picture of quantum mechanics based on groupoids was proposed. In this…
We derive an exact equation of motion for the reduced density matrices of individual subsystems of quantum many-body systems of any lattice dimension and arbitrary system size. Our projection operator based theory yields a highly efficient…
The problem of construction of projection operators on eigen-subspaces of symmetry operators is considered. This problem arises in many approximate methods for solving time-independent and time-dependent quantum problems, and its solution…
The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements cannot be viewed as revealing pre-existing properties of…
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but…
The quantum measurement problem can be regarded as the tension between the two alternative dynamics prescribed by quantum mechanics: the unitary evolution of the wave function and the state-update rule (or "collapse") at the instant a…
The application of principles of Quantum Mechanics in areas outside of physics has been getting increasing attention in the scientific community in an emergent discipline called Quantum Cognition. These principles have been applied to…
We show that the correct mathematical foundation of quantum decision theory, dealing with uncertain events, requires the use of positive operator-valued measure that is a generalization of the projection-valued measure. The latter is…
We point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position…
Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…
The underlying probabilistic theory for quantum mechanics is non-Kolmogorovian. The order in which physical observables will be important if they are incompatible (non-commuting). In particular, the notion of conditioning needs to be…
In this paper, we try to give a new approach to the quantum mechanics(QM) on the framework of quantum field theory(QFT). Firstly, we make a detail study on the (non-relativistic) Schr\"odinger field theory, obtaining the Schr\"odinger…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…
By a further study of the mechanism of the hyperbolic regularization of the moment system for Boltzmann equation proposed in [Z. Cai, Y. Fan, R. Li, Comm. Math. Sci. 11(2): 547-571, 2013], we point out that the key point is treating the…