Heisenberg Uncertainty Principle and DNA Dynamics.

Sharvari Gogte Sharvari Gogte

Quantum Cryptography (QC) is an emerging security technique in which two parties communicate via a quantum channel.The fundamentals of quantum cryptography are No-cloning theorem and Heisenberg's uncertainty principle.This research paper proposes a simulation of quantum key exchange and authentication followed by an implementation of DNA based algorithm for secure message exchange.

Santanu Mondal, R. Cabrera‐Trujillo

Abstract In quantum physics, the scattering of a free particle by an impurity leads to the Ramsauer-Townsend effect, characterized by resonances in the cross section for transmission and reflection of the incident particle. In this work, we analyze this problem within the context of quantum information theory. In particular, we study the Shannon and Fisher entropy, as well as the Heisenberg uncertainty relations, to analyze the fragmentation of a wave packet in collision dynamics. As a primary contribution of this work, we note that these properties are directly related to each other through the same reflection and transmission coefficients as those of the Ramsauer-Townsend effect. Furthermore, we observe that the Heisenberg uncertainty principle satisfies the minimum value, i.e. ℏ /2, for the transmitted wave packet at resonance transmission and a maximum at higher fragmentation of the wave packet. We obtain that at resonance transmission, the reflected contribution to the uncertainty principle is zero with no violation of the Heisenberg principle. This leads, consequently, to the violation of it by the reflected wave packet, as there is no reflection. Moreover, the Shannon and Fisher quantum information entropy is found to be directly connected to Heisenberg’s uncertainty principle for a dynamical system. Finally, we establish that these effects require the proper description of the time-dependent spreading of the wave packet to account for the proper dynamics.

Charles H. Holbrow, James N. Lloyd, Joseph C. Amato

Ruggero María Santilli

We propose a unified form of possible generalizations of Heisenberg uncertainty principle for strong interactions, which is based on the product of the envelope of the dynamical equations representing wave packets under conditions of mutual overlapping and nonlocal non-Hamiltonian forces. For conventional associative products of operators, we recover the conventional Heisenberg relations for particles under long range electromagnetic interactions and no appreciable wave overlapping. For nonassociative Lie-admissible products of operators we have (a) a number of generalizations of Heisenberg's equations of increasing algebraic complexity; (b) the capability of representing a correspondingly progressive increase of conditions of wave overlapping and nonlocal, non-Hamiltonian forces; and (c) a corresponding, rather inevitable sequence of generalizations of Heisenberg uncertainty relations. All these possibilities are expressed in a unified way by postulating generalized uncertainty relations whereby the product of operators is that of the envelope of the dynamical equations. For conditions of minimal wave overlapping under strong interactions, such as in the nuclear structure, we expect a very small nonlocal non-Hamiltonian component of the force and a minimal departure from Heisenberg principle. For progressive increase of wave overlappings, such as in the structure of hadrons, or in the structure of stars undergoing gravitational collapse, we expectmore » a corresponding progressive replacement of Heisenberg principle with more general principles. The problem of the experimental resolution of the exact or only approximate validity of Heisenberg principle under strong interactions is considered for a more detailed treatment in a separate paper.« less

Charles H. Holbrow, James N. Lloyd, Joseph C. Amato +2 more