相关论文: Duality and Conditional Expectations in the Nakaji…

We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are the multi-time probability distributions estimated from the results of…

Natural philosophy integrates scientific observation with abstract frameworks, often using a mathematical Ansatz to hypothesise about physical phenomena. Exploring the possibility of other universes, however, challenges assumptions that…

In this work we discuss the notion of observable - both quantum and classical - from a new point of view. In classical mechanics, an observable is represented as a function (measurable, continuous or smooth), whereas in (von Neumann's…

We give an alternative definition of quantum fidelity for two density operators on qudits in terms of the Hilbert-Schmidt inner product between them and their purity. It can be regarded as the well-defined operator fidelity for the two…

Frames in a Hilbert space that are generated by operator orbits are vastly studied because of the applications in dynamic sampling and signal recovery. We demonstrate in this paper a representation theory for frames generated by operator…

Classical mechanics is presented here in a unary operator form, constructed using the binary multiplication and Poisson bracket operations that are given in a phase space formalism, then a Gibbs equilibrium state over this unary operator…

Dynamic equations concerning physical expectation values have been examined in terms of the real Hilbert space approach to quantum mechanics. The considered cases involve complex wave functions, as well as quaternionic wave functions. The…

The Nekrasov partition function in supersymmetric quantum gauge theory is mathematically formulated as an equivariant integral over certain moduli spaces of sheaves on a complex surface. In ``Seiberg-Witten Theory and Random Partitions'',…

A new technique to derive delay models from systems of partial differential equations, based on the Mori-Zwanzig formalism, is used to derive a delay difference equation model for the Atlantic Multidecadal Oscillation. The Mori-Zwanzig…

Through the H theorem, Bolzmann attempted to validate the foundations of statistical mechanics. However, it is incompatible with the fundamental laws of mechanics because its deduction requires the introduction of probability. In this paper…

We propose a scheme that can realize a class of positive-operator-valued measures (POVMs) by performing a sequence of projective measurements on the original system, in the sense that for an arbitrary input state the probability…

It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints…

By making use of the Weyl-Wigner-Groenewold-Moyal association rules, a commutative product and a new quantum bracket are constructed in the ring of operators \cal{F}(H). In this way, an isomorphism between Lie algebra of classical…

We review and analyze the hybrid quantum-classical NMR computing methodology referred to as Type-II quantum computing. We show that all such algorithms considered so far within this paradigm are equivalent to some classical…

The Jordan algebra structure of the bounded real quantum observables was recognized already in the early days of quantum mechanics. While there are plausible reasons for most parts of this structure, the existence of the distributive…

It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…

The algebraic approach to operator perturbation method has been applied to two quantum--mechanical systems ``The Stark Effect in the Harmonic Oscillator'' and ``The Generalized Zeeman Effect''. To that end, two realizations of the…

We propose a novel framework for the quantum geometry of expectation values over arbitrary sets of operators and establish a link between this geometry and the eigenstates of Hamiltonian families generated by these operators. We show that…

The physical meaning of the operators is not reducible to the intrinsic relations of the quantum system, since unitary transformations can find other operators satisfying the exact same relations. The physical meaning is determined…

A recent concept in theoretical physics, motivated in string duality and M-theory, is the notion that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical…