scholarly journals Stability of Quantum Eigenstates and Collapse of Superposition of States in a Fluctuating Vacuum: The Madelung Hydrodynamic Approach

2021 ◽  
Vol 3 (5) ◽  
pp. 11-28
Author(s):  
P. Chiarelli ◽  
S. Chiarelli
Keyword(s):  
Quantum Mechanics ◽  
Mass Density ◽  
Classical System ◽  
Coarse Grained ◽  
Maximum Speed ◽  
Uncertainty Relations ◽  
Quantum Superposition ◽  
Hydrodynamic Approach ◽  
Stationary Configuration ◽  
Superposition Of States

The paper investigates the quantum fluctuating dynamics by using the stochastic generalization of the Madelung quantum-hydrodynamic approach. By using the discrete approach, the path integral solution is derived in order to investigate how the final stationary configuration is obtained from the initial quantum superposition of states. The model shows that the quantum eigenstates remain stationary configurations with a very small perturbation of their mass density distribution and that any eigenstate, contributing to a quantum superposition of states, can be reached in the final stationary configuration. When the non-local quantum potential acquires a finite range of interaction, the work shows that the macroscopic coarse-grained description of the theory can lead to a really classical system. The minimum uncertainty attainable in the stochastic Madelung model is shown to be compatible with maximum speed of transmission of information and interactions. The theory shows that, in the quantum deterministic limit, the uncertainty relations of quantum mechanics are obtained. The connections with the decoherence theory and the Copenhagen interpretation of quantum mechanics are also discussed.

Fundamentals of Quantum Mechanics

2020 ◽  
pp. 73-80
Author(s):  
M. Suhail Zubairy
Keyword(s):  
Quantum Mechanics ◽  
Formal Theory ◽  
Uncertainty Relations ◽  
Quantum Superposition ◽  
Conceptual Foundation ◽  
Classical Physics ◽  
Max Born ◽  
Erwin Schrödinger ◽  
Heisenberg Uncertainty ◽  
Probabilistic Nature

The laws of quantum mechanics were formulated in the year 1925 through the work of Werner Heisenberg, followed by Max Born, Pascual Jordan, Paul Dirac, and Wolfgang Pauli. A separate but equivalent approach was independently developed by Erwin Schrödinger in early 1926. The laws governing quantum mechanics were highly mathematical and their aim was to explain many unresolved problems within the framework of a formal theory. The conceptual foundation emerged in the subsequent 2–3 years that indicated how radically different the new laws were from classical physics. In this chapter some of these salient features of quantum mechanics are discussed. The topics include the quantization of energy, wave–particle duality, the probabilistic nature of quantum mechanics, Heisenberg uncertainty relations, Bohr’s principle of complementarity, and quantum superposition and entanglement. This discussion should indicate how different and counterintuitive its fundamentals are from those of classical physics.

Relational Blockworld and Quantum Mechanics

2018 ◽  
Author(s):  
Michael Silberstein ◽  
W.M. Stuckey ◽  
Timothy McDevitt
Keyword(s):  
Quantum Mechanics ◽  
Measurement Problem ◽  
Quantum Nonlocality ◽  
Global Constraints ◽  
Quantum Superposition ◽  
Delayed Choice ◽  
Counterfactual Definiteness ◽  
Main Thread ◽  
Block Universe ◽  
Contextual Emergence

The main thread of chapter 4 introduces some of the major mysteries and interpretational issues of quantum mechanics (QM). These mysteries and issues include: quantum superposition, quantum nonlocality, Bell’s inequality, entanglement, delayed choice, the measurement problem, and the lack of counterfactual definiteness. All these mysteries and interpretational issues of QM result from dynamical explanation in the mechanical universe and are dispatched using the authors’ adynamical explanation in the block universe, called Relational Blockworld (RBW). A possible link between RBW and quantum information theory is provided. The metaphysical underpinnings of RBW, such as contextual emergence, spatiotemporal ontological contextuality, and adynamical global constraints, are provided in Philosophy of Physics for Chapter 4. That is also where RBW is situated with respect to retrocausal accounts and it is shown that RBW is a realist, psi-epistemic account of QM. All the relevant formalism for this chapter is provided in Foundational Physics for Chapter 4.

scholarly journals Quantum Computers - An Emerging Cybersecurity Threat

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Dajana Jelčić Dubček
Keyword(s):  
Information Processing ◽  
Quantum Coherence ◽  
Quantum Physics ◽  
Quantum Computers ◽  
Practical Implementation ◽  
Quantum Superposition ◽  
Processing And Storage ◽  
And Storage ◽  
Superposition Of States

Quantum computational supremacy may potentially endanger the current cryptographic protection methods. Although quantum computers are still far from a practical implementation in information processing and storage, they should not be overlooked in the context of cybersecurity. Quantum computers operate with qubits - units of information that are governed by the fundamental principles of quantum physics, such as quantum superposition of states and quantum coherence. In order to address the new challenge that quantum computers pose to cybersecurity, the very principles of their operation have to be understood and are overviewed in this contribution.

Quantum Mechanics

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Variational Principles ◽  
Free Particle ◽  
Uncertainty Relations ◽  
Probabilistic Interpretation ◽  
Historical Account ◽  
Potential Wells ◽  
Harmonic Oscillator Potential ◽  
Ground State Energies

In this chapter, the main features of quantum theory are presented. The chapter begins with a historical account of the invention of quantum mechanics. The meaning of position and momentum in quantum mechanics is discussed and non-commuting operators are introduced. The Schrödinger equation is presented and solved for a free particle and for a harmonic oscillator potential in one dimension. The meaning of the wavefunction is considered and the probabilistic interpretation is presented. The mathematical machinery and language of quantum mechanics are developed, including Hermitian operators, observables and expectation values. The uncertainty principle is discussed and the uncertainty relations are presented. Scattering and tunnelling by potential wells and barriers is considered. The use of variational principles to estimate ground state energies is explained and illustrated with a simple example.

Quantum mechanics, interpretation of

2018 ◽  
Author(s):  
Allen Stairs
Keyword(s):  
Quantum Mechanics ◽  
Microscopic Level ◽  
Quantum States ◽  
Quantum Mechanical ◽  
Quantum Superposition ◽  
Ordinary Objects ◽  
Making Sense ◽  
Interpretations Of Quantum Mechanics ◽  
The World

Quantum mechanics developed in the early part of the twentieth century in response to the discovery that energy is quantized, that is, comes in discrete units. At the microscopic level this leads to odd phenomena: light displays particle-like characteristics and particles such as electrons produce wave-like interference patterns. At the level of ordinary objects such effects are usually not evident, but this generalization is subject to striking exceptions and puzzling ambiguities. The fundamental quantum mechanical puzzle is ’superposition of states’. Quantum states can be added together in a manner that recalls the superposition of waves, but the effects of quantum superposition show up only probabilistically in the statistics of many measurements. The details suggest that the world is indefinite in odd ways; for example, that things may not always have well-defined positions or momenta or energies. However, if we accept this conclusion, we have difficulty making sense of such straightforward facts as that measurements have definite results. Interpretations of quantum mechanics are, in one way or another, attempts to understand the superposition of quantum states. The range of interpretations stretches from the metaphysically daring to the seemingly innocuous. But, so far, no single interpretation has commanded anything like universal agreement.

scholarly journals ENTANGLEMENT QUANTISTICO

2020 ◽  
Author(s):  
Alberto Rimini
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Measurement ◽  
First Principles ◽  
Measurement Problem ◽  
Entangled State ◽  
Uncertainty Relations ◽  
Entanglement State ◽  
State Uncertainty ◽  
Einstein Podolsky Rosen

This extended note deals with a pedagogical description of the entangled state of two particles, starting from first principles. After some general remarks about quantum mechanics and physical theories, the single particle case is discussed by defining state, uncertainty relations and wave function in the state space. The system of two particles is then considered, with its possible states, starting from the original papers by Einstein Podolsky Rosen and by Schroedinger. The quantum measurement problem is then introduced, together with its role in the entanglement state. Finally the orthodox solution and the relevant conclusions are drawn.

scholarly journals Uncertainty Relations for Coarse–Grained Measurements: An Overview

Entropy ◽  
2018 ◽  
Vol 20 (6) ◽  
pp. 454 ◽  
Author(s):  
Fabricio Toscano ◽  
Daniel Tasca ◽  
Łukasz Rudnicki ◽  
Stephen Walborn
Keyword(s):  
Coarse Grained ◽  
Uncertainty Relations

scholarly journals Explaining electric conductivity using the particle-in-a-box model: quantum superposition is the key

2017 ◽  
Vol 95 (12) ◽  
pp. 1181-1188
Author(s):  
Umaseh Sivanesan ◽  
Kin Tsang ◽  
Artur F. Izmaylov
Keyword(s):  
Quantum Mechanics ◽  
Charged Particle ◽  
Electric Conductivity ◽  
Excited States ◽  
Constant Electric Field ◽  
Particle Dynamics ◽  
Model System ◽  
Linear Potential ◽  
Quantum Superposition ◽  
Oscillatory Dynamics

Most of the textbooks explaining electric conductivity in the context of quantum mechanics provide either incomplete or semi-classical explanations that are not connected with the elementary concepts of quantum mechanics. We explain electric conductivity using the simplest model system in quantum mechanics, a particle in a box (PIB). To stimulate the particle dynamics, a linear potential tilting the bottom of the box is introduced, which is equivalent to imposing a constant electric field for a charged particle. Although the PIB model represents a closed system that cannot have a flow of electrons through it, we consider the oscillatory dynamics of the particle probability density as the analogue of the electric current. Relating the amplitude and other parameters of the particle oscillatory dynamics with the gap between the ground and excited states of the PIB model allows us to demonstrate one of the most basic dependencies of electric conductivity on the valence–conduction band gap of the material.

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