Bell's Theorem and Locally-Mediated Reformulations of Quantum Mechanics

Bell's Theorem rules out many potential reformulations of quantum mechanics, but within a generalized framework, it does not exclude all "locally-mediated" models. Such models describe the correlations between entangled particles as mediated by intermediate parameters which track the particle world-lines and respect Lorentz covariance. These locally-mediated models require the relaxation of an arrow-of-time assumption which is typically taken for granted. Specifically, some of the mediating parameters in these models must functionally depend on measurement settings in their future, i.e., on input parameters associated with later times. This option (often called "retrocausal") has been repeatedly pointed out in the literature, but the exploration of explicit locally-mediated toy-models capable of describing specific entanglement phenomena has begun only in the past decade. A brief survey of such models is included here. These models provide a continuous and consistent description of events associated with spacetime locations, with aspects that are solved "all-at-once" rather than unfolding from the past to the future. The tension between quantum mechanics and relativity which is usually associated with Bell's Theorem does not occur here. Unlike conventional quantum models, the number of parameters needed to specify the state of a system does not grow exponentially with the number of entangled particles. The promise of generalizing such models to account for all quantum phenomena is identified as a grand challenge.Comment: 61 pages, 2 figures; accepted for publication by Rev. Mod. Phy

Colloquium: Bell\u27s theorem and locally mediated reformulations of quantum mechanics

Bell\u27s theorem rules out many potential reformulations of quantum mechanics, but within a generalized framework it does not exclude all locally mediated models. Such models describe the correlations between entangled particles as mediated by intermediate parameters that track the particle worldlines and respect Lorentz covariance. These locally mediated models require the relaxation of an arrow-of-time assumption that is typically taken for granted. Specifically, some of the mediating parameters in these models must functionally depend on measurement settings in their future, i.e., on input parameters associated with later times. This option, often called retrocausal, has been repeatedly pointed out in the literature, but the exploration of explicit locally mediated toy models capable of describing specific entanglement phenomena has begun only in the past decade. A brief survey of such models is included here. These models provide a continuous and consistent description of events associated with spacetime locations, with aspects that are solved all at once rather than unfolding from the past to the future. The tension between quantum mechanics and relativity that is usually associated with Bell\u27s theorem does not occur here. Unlike in conventional quantum models, the number of parameters needed to specify the state of a system does not grow exponentially with the number of entangled particles. The promise of generalizing such models to account for all quantum phenomena is identified as a grand challenge

Quantum particle statistics on the holographic screen leads to Modified Newtonian Dynamics (MOND)

Employing a thermodynamic interpretation of gravity based on the holographic principle and assuming underlying particle statistics, fermionic or bosonic, for the excitations of the holographic screen leads to Modified Newtonian Dynamics (MOND). A connection between the acceleration scale $a_0$ appearing in MOND and the Fermi energy of the holographic fermionic degrees of freedom is obtained. In this formulation the physics of MOND results from the quantum-classical crossover in the fermionic specific heat. However, due to the dimensionality of the screen, the formalism is general and applies to two dimensional bosonic excitations as well. It is shown that replacing the assumption of the equipartition of energy on the holographic screen by a standard quantum-statistical-mechanics description wherein some of the degrees of freedom are frozen out at low temperatures is the physical basis for the MOND interpolating function ${\tilde \mu}$. The interpolating function ${\tilde \mu}$ is calculated within the statistical mechanical formalism and compared to the leading phenomenological interpolating functions, most commonly used. Based on the statistical mechanical view of MOND, its cosmological implications are re-interpreted: the connection between $a_0$ and the Hubble constant is described as a quantum uncertainty relation; and the relationship between $a_0$ and the cosmological constant is better understood physically

The spectral form factor is not self-averaging

The spectral form factor, k(t), is the Fourier transform of the two level correlation function C(x), which is the averaged probability for finding two energy levels spaced x mean level spacings apart. The average is over a piece of the spectrum of width W in the neighborhood of energy E0. An additional ensemble average is traditionally carried out, as in random matrix theory. Recently a theoretical calculation of k(t) for a single system, with an energy average only, found interesting nonuniversal semiclassical effects at times t approximately unity in units of {Planck's constant) /(mean level spacing). This is of great interest if k(t) is self-averaging, i.e, if the properties of a typical member of the ensemble are the same as the ensemble average properties. We here argue that this is not always the case, and that for many important systems an ensemble average is essential to see detailed properties of k(t). In other systems, notably the Riemann zeta function, it is likely possible to see the properties by an analysis of the spectrum.Comment: 4 pages, RevTex, no figures, submitted to Phys. Rev. Lett., permanent e-mail address, [email protected]

On the absence of Shapiro-like steps in certain mesoscopic S-N-S junctions

In DC transport through mesoscopic S-N-S junctions, it is known that the Josephson coupling decreases exponentially with increasing temperature, but the phase dependence of the conductance persists to much higher temperatures and decreases only as 1/T. It is pointed out here that, despite the fact that such a phase-dependent conductance does bring about an AC current for a pure DC voltage, it cannot, by itself, lead to the formation of Shapiro steps.Comment: 1 page, to be published in PRL (as Comment

Characteristic Potentials for Mesoscopic Rings Threaded by an Aharonov-Bohm Flux

Electro-static potentials for samples with the topology of a ring and penetrated by an Aharonov-Bohm flux are discussed. The sensitivity of the electron-density distribution to small variations in the flux generates an effective electro-static potential which is itself a periodic function of flux. We investigate a simple model in which the flux sensitive potential leads to a persistent current which is enhanced compared to that of a loop of non-interacting electrons. For sample geometries with contacts the sensitivity of the electro-static potential to flux leads to a flux-induced capacitance. This capacitance gives the variation in charge due to an increment in flux. The flux-induced capacitance is contrasted with the electro-chemical capacitance which gives the variation in charge due to an increment in an electro-chemical potential. The discussion is formulated in terms of characteristic functions which give the variation of the electro-static potential in the interior of the conductor due to an increment in the external control parameters (flux, electro-chemical potentials). Paper submitted to the 16th Nordic Semiconductor Meeting, Laugarvatan, Iceland, June 12-15, 1994. The proceedings will be published in Physica Scripta.Comment: 23 pages + 4 figures, revtex, IBM-RC1955

Thermodynamics as an alternative foundation for zero-temperature density functional theory and spin density functional theory

Thermodynamics provides a transparent definition of the free energy of density functional theory (DFT), and of its derivatives - the potentials, at finite temperatures T. By taking the T to 0 limit, it is shown here that both DFT and spin-dependent DFT (for ground states) suffer from precisely the same benign ambiguities: (a) charge and spin quantization lead to "up to a constant" indeterminacies in the potential and the magnetic field respectively, and (b) the potential in empty subspaces is undetermined but irrelevant. Surprisingly, these simple facts were inaccessible within the standard formulation, leading to recent discussions of apparent difficulties within spin-DFT.Comment: RevTeX, to appear in Phys. Rev.

Periodic-Orbit Theory of Anderson Localization on Graphs

We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an a-periodic Kronig-Penney model in one dimension. The exact expression for the probability to return of an initially localized state is computed in terms of classical trajectories. It saturates to a finite value due to localization, while the diagonal approximation decays diffusively. Our theory is based on the identification of families of isometric orbits. The coherent periodic-orbit sums within these families, and the summation over all families are performed analytically using advanced combinatorial methods.Comment: 4 pages, 3 figures, RevTe

Can the trace formula describe weak localisation?

We attempt to systematically derive perturbative quantum corrections to the Berry diagonal approximation of the two-level correlation function (TLCF) for chaotic systems. To this end, we develop a ``weak diagonal approximation'' based on a recent description of the first weak localisation correction to conductance in terms of the Gutzwiller trace formula. This semiclassical method is tested by using it to derive the weak localisation corrections to the TLCF for a semiclassically disordered system. Unfortunately the method is unable to correctly reproduce the ``Hikami boxes'' (the relatively small regions where classical paths are glued together by quantum processes). This results in the method failing to reproduce the well known weak localisation expansion. It so happens that for the first order correction it merely produces the wrong prefactor. However for the second order correction, it is unable to reproduce certain contributions, and leads to a result which is of a different form to the standard one.Comment: 23 pages in Latex (with IOP style files), 3 eps figures included, to be a symposium paper in a Topical Issue of Waves in Random Media, 199

Random Scattering Matrices and the Circuit Theory of Andreev Conductances

The conductance of a normal-metal mesoscopic system in proximity to superconducting electrode(s) is calculated. The normal-metal part may have a general geometry, and is described as a ``circuit'' with ``leads'' and ``junctions''. The junctions are each ascribed a scattering matrix which is averaged over the circular orthogonal ensemble, using recently-developed techniques. The results for the electrical conductance reproduce and extend Nazarov's circuit theory, thus bridging between the scattering and the bulk approaches. The method is also applied to the heat conductance.Comment: 12 pages, RevTeX, including 2 figures with eps