相关论文: A q-deformed Uncertainty Relation
Corresponding to two ways of realizing the q-deformed Heisenberg algebra by the undeformed variables there are two q-perturbative Hamiltonians with the additional momentum-dependent interactions, one originates from the perturbative…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
In this paper, the deformed Special Relativity, which leads to an essentially new theoretical context of quantum mechanics, is presented. The formulation of the theory arises from a straightforward analogy with the Special Relativity, but…
q-Expectation value of a physical quantity is widely used in nonextensive statistical mechanics. Here, it is shown that the q-expectation value is not stable under small deformations of a probability distribution function, in general,…
What does it take for real-deterministic c-valued (i.e., classical, commuting) variables to comply with the Heisenberg uncertainty principle? Here, we construct a class of real-deterministic c-valued variables out of the weak values…
The problem of a correct description of the physical phenomena of the Heisenberg uncertainty relation is solved by using a variable hidden in Newtonian mehcanics.
Some properties of the $q$-Fourier-sine transform are studied and $q$-analogues of the Heisenberg uncertainty principle is derived for the $q$-Fourier-cosine transform studied in \cite{FB} and for the $q$-Fourier-sine transform.
A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…
Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are…
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…
A $q$-deformed Weyl-Heisenberg algebra is used to define a deformed displacement operator giving rise to a naturally normalized nonlinear coherent states type. Robust maximally entangled deformed coherent states are studied and the effect…
We uncover an inconsistency in the uniform WKB quantization of deformed quantum mechanics.
This lecture consists of two sections. In section 1 we consider the simplest version of a q-deformed Heisenberg algebra as an example of a noncommutative structure. We first derive a calculus entirely based on the algebra and then formulate…
In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the presence in the theory of General Uncertainty Relations. Here Quantum Mechanics with Fundamental Length is…
The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We…
In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…
We described the $q$-deformed phase space. The $q$-deformed Hamilton eqations of motion are derived and discussed. Some simple models are considered.
Quantum mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Renyi entropies. The proof of these inequalities requires the use of the exact expression for the (p,q)-norm of the…
We explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…
In the paper a review of results for recovering of the weak equivalence principle in a space with deformed commutation relations for operators of coordinates and momenta is presented. Different types of deformed algebras leading to a space…