arXiv subjects

Bryan J Dalton

Publications and source records attributed to Bryan J Dalton.

5 recordsLinked to original sources

arXiv2024

Can quantum theory be underpinned by a non-local hidden variable theory ?

In this paper we consider the description by a general Bell-type non-local hidden variable theory (NLHVT) of bipartite quantum states with two observables per sub-system. We derive Bell inequalities of the Collins-Gisin.-Liden-Massar-Popescu (CGLMP) type which involve combinations of the probabilities of related outcomes for measurements for the four pairs of sub-system observables. It is shown that the corresponding quantum theory expressions violate the Bell inequalities in the case of the maximally entangled state of the bipartitite system. The CHSH Bell inequality is also derived from this general CGLMP Bell-type non-local hidden variable theory. This shows that quantum theory can not be underpinned by a Bell-type non-local hidden variable theory. So as a general Bell-type local hidden variable theory has already been shown to conflict with quantum theory, it follows that quantum theory can not be understood in terms of any CGLMP Bell-type hidden variable theory - local or non-local.

quant-ph↗

arXiv2024

The sounds of science a symphony for many instruments and voices part II

Despite its amazing quantitative successes and contributions to revolutionary technologies, physics currently faces many unsolved mysteries ranging from the meaning of quantum mechanics to the nature of the dark energy that will determine the future of the Universe. It is clearly prohibitive for the general reader, and even the best informed physicists, to follow the vast number of technical papers published in the thousands of specialized journals. For this reason, we have asked the leading experts across many of the most important areas of physics to summarise their global assessment of some of the most important issues. In lieu of an extremely long abstract summarising the contents, we invite the reader to look at the section headings and their authors, and then to indulge in a feast of stimulating topics spanning the current frontiers of fundamental physics from The Future of Physics by William D Phillips and What characterises topological effects in physics? by Gerard t Hooft through the contributions of the widest imaginable range of world leaders in their respective areas. This paper is presented as a preface to exciting developments by senior and young scientists in the years that lie ahead, and a complement to the less authoritative popular accounts by journalists.

physics.soc-ph↗

arXiv2021

Many-Body Effects and Quantum Fluctuations for Discrete Time Crystals in Bose-Einstein Condensates

We present a fully comprehensive multi-mode quantum treatment based on the truncated Wigner approximation (TWA) to study many-body effects and quantum fluctuations on the formation of a discrete time crystal (DTC) in a Bose-Einstein condensate (BEC) bouncing resonantly on an atom mirror, driven at period T. Our theoretical approach avoids the restrictions both of mean-field theory, where all bosons are assumed to remain in a single mode, and of time-dependent Bogoliubov theory, which assumes boson depletion from the condensate mode is small. For realistic initial conditions corresponding to a harmonic trap condensate mode function, our TWA calculations performed for period-doubling agree broadly with recent mean-field calculations for times out to at least 2000 T, except at interaction strengths very close to the threshold value for DTC formation where the position probability density differs significantly from that determined from mean-field theory. For typical attractive interaction strengths above the threshold value for DTC formation and for the chosen trap and driving parameters, the TWA calculations indicate a quantum depletion due to quantum many-body fluctuations of less than about two atoms out of 600 atoms at times corresponding to 2000 T, in agreement with time-dependent Bogoliubov theory calculations. On the other hand, for interaction strengths very close to the threshold value for DTC formation, the TWA calculations predict a large quantum depletion - as high as about 260 atoms out of 600. We also show that the mean energy of the DTC does not increase significantly for times out to at least 2000 mirror oscillations, so TWA theory predicts that thermalisation is absent. Finally, we find that the dynamical behaviour is similar for attractive or repulsive boson-boson interactions, and that a stable DTC based on repulsive interactions can be created.

cond-mat.quant-gas↗

arXiv2020

Quantum Theory and Local Hidden Variable Theory: General Features and Tests for EPR Steering

In a previous paper tests for entanglement for two mode systems involving identical massive bosons were obtained. In the present paper we consider sufficiency tests for EPR steering in such systems. We find that spin squeezing in any spin component, a Bloch vector test, the Hillery-Zubairy planar spin variance test and squeezing in two mode quadratures all show that the quantum state is EPR steerable. We also find a generalisation of the Hillery-Zubairy planar spin variance test for EPR steering. The relation to previous correlation tests is discussed. This paper is based on a detailed classification of quantum states for bipartite systems. States for bipartite composite systems are categorised in quantum theory as either separable or entangled, but the states can also be divided differently into Bell local or Bell non-local states in terms of local hidden variable theory (LHVT). For the Bell local states there are three cases depending on whether both, one of or neither of the LHVT probabilities for each sub-system are also given by a quantum probability involving sub-system density operators. Cases where one or both are given by a quantum probability are known as local hidden states (LHS) and such states are non-steerable. The steerable states are the Bell local states where there is no LHS, or the Bell non-local states. The relationship between the quantum and hidden variable theory classification of states is discussed.

quant-ph↗

arXiv2016

Grassmann Phase Space Methods for Fermions. II. Field Theory

In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum - atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker-Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. Solutions for spin 1/2 fermions either free or in lattices are found.

quant-ph↗