相关论文: Generalized uncertainty relations: Theory, example…
We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement and the resultant observation (observer) effect of statistical nature. Owing to its simplicity and operational tangibility, our general…
It is generally argued that the combined effect of Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We…
We propose a mathematically rigorous unified framework for hybrid quantum mechanics that systematically combines algebraic deformation and spatial non-locality within a single operator formalism. By constructing a self-adjoint hybrid…
Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…
The generalized uncertainty connection between the fluctuations of a quantum observable and its temporal derivative is derived in this study, we demonstrate that the product of an observable's uncertainties and its time derivative is…
In two articles, the authors claim that the Heisenberg uncertainty principle limits the precision of simultaneous measurements of the position and velocity of a particle and refer to experimental evidence that supports their claim. It is…
Heisenberg's uncertainty relation for measurement noise and disturbance states that any position measurement with noise epsilon brings the momentum disturbance not less than hbar/2epsilon. This relation holds only for restricted class of…
The Heisenberg Uncertainty Principle (HUP) limits the accuracy in the simultaneous measurements of the position and momentum variables of any quantum system. This is known to be true in the context of non-relativistic quantum mechanics.…
Quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose every physical meaning. In quantum mechanics, the insurgence of such minimal length can be…
Uncertainty relations for Hermitian operators have been confirmed through many experiments. However, previous experiments have only tested the special case of non-Hermitian operators, i.e., uncertainty relations for unitary operators. In…
We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the…
We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by Fourier transform. The physical examples discussed here are standard position and momentum, number and angle, finite qudit systems, and…
Textbook quantum mechanics treats time as a classical parameter, and not as a quantum observable with an associated Hermitian operator. For this reason, to make sense of usual time-energy uncertainty relations such as $\Delta {t}\Delta…
The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
We construct uncertainty relation for arbitrary finite dimensional PT invariant non-Hermitian quantum systems within a special inner product framework. This construction is led by good observables which are a more general class of…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…
Non-Hermitian Hamiltonians play a crucial role in describing open quantum systems and nonequilibrium dynamics. In this paper, we derive trade-off relations for systems governed by non-Hermitian Hamiltonians, focusing on the…
It is shown that, in the framework of non-relativistic quantum mechanics, any conserved Hermitian operator (which may depend explicitly on the time) is the generator of a one-parameter group of unitary symmetries of the Hamiltonian and…
Heisenberg's uncertainty relation is commonly regarded as defining a level of unpredictability that is fundamentally incompatible with the deterministic laws embodied in classical field theories such as Einstein's general relativity. We…