On the nature of continuous physical quantities in classical and quantum mechanics

Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value and a sharp momentum value. Is it possible, though, to describe a particle as possessing just a sharp position value (or just a sharp momentum value)? Some, such as Teller (Journal of Philosophy, 1979), have thought that the answer to this question is No -- that the status of individual continuous quantities is very different in quantum mechanics than in classical mechanics. On the contrary, I shall show that the same subtle issues arise with respect to continuous quantities in classical and quantum mechanics; and that it is, after all, possible to describe a particle as possessing a sharp position value without altering the standard formalism of quantum mechanics.Comment: 26 pages, LaTe

Carbon isotope ratios of Great Plains soils and in wheat-fallow systems

Includes bibliographical references (pages 1076-1077).The purposes of this study were to improve knowledge of regional vegetation patterns of C3 and C4 plants in the North American Great Plains and to use δ13C methodology and long-term research sites to determine contributions of small-grain crops to total soil organic carbon (SOC) now present. Archived and recent soil samples were used. Detailed soil sampling was in 1993 at long-term sites near Akron, CO, and Sidney, NE. After soil sieving, drying, and deliming, SOC and δ13C were determined using an automated C/N analyzer interfaced to an isotope-ratio mass spectrometer. Yield records from long-term experimental sites were used to estimate the amount of C3 plant residue C returned to the soil. Results from δ13C analyses of soils from near Waldheim, Saskatchewan, to Big Springs, TX, showed a strong north to south decrease in SOC derived from C3 plants and a corresponding increase from C4 plants. The δ13C analyses gave evidence that C3 plant residue C (possibly from shrubs) is increasing at the Big Springs, TX, and Lawton, OK, sites. Also, δ13C analyses of subsoil and topsoil layers shows evidence of a regional shift to more C3 species, possibly because of a cooler climate during the past few hundreds to thousands of years. Data from long-term research sites indicate that the efficiency of incorporation of small-grain crop residue C was about 5.4% during 84 year at Akron, CO, and about 10.5% during 20 year at Sidney, NE. The 14C age of the SOC at 0- to 10-cm depth was 193 year and at 30 to 45 cm was 4000 yr; 14C age of nonhydrolyzable C was 2000 and 7000 year for these same two respective depths. Natural partitioning of the 13C isotope by the photosynthetic pathways of C3 and C4 plants provides a potentially powerful tool to study SOC dynamics at both regional and local scales

Hyperentangled States

We investigate a new class of entangled states, which we call 'hyperentangled',that have EPR correlations identical to those in the vacuum state of a relativistic quantum field. We show that whenever hyperentangled states exist in any quantum theory, they are dense in its state space. We also give prescriptions for constructing hyperentangled states that involve an arbitrarily large collection of systems.Comment: 23 pages, LaTeX, Submitted to Physical Review

The Scalar Field Kernel in Cosmological Spaces

We construct the quantum mechanical evolution operator in the Functional Schrodinger picture - the kernel - for a scalar field in spatially homogeneous FLRW spacetimes when the field is a) free and b) coupled to a spacetime dependent source term. The essential element in the construction is the causal propagator, linked to the commutator of two Heisenberg picture scalar fields. We show that the kernels can be expressed solely in terms of the causal propagator and derivatives of the causal propagator. Furthermore, we show that our kernel reveals the standard light cone structure in FLRW spacetimes. We finally apply the result to Minkowski spacetime, to de Sitter spacetime and calculate the forward time evolution of the vacuum in a general FLRW spacetime.Comment: 13 pages, 1 figur

Models of HoTT and the Constructive View of Theories

Homotopy Type theory and its Model theory provide a novel formal semantic framework for representing scientific theories. This framework supports a constructive view of theories according to which a theory is essentially characterised by its methods. The constructive view of theories was earlier defended by Ernest Nagel and a number of other philosophers of the past but available logical means did not allow these people to build formal representational frameworks that implement this view

Excited states of linear polyenes

We present density matrix renormalisation group calculations of the Pariser- Parr-Pople-Peierls model of linear polyenes within the adiabatic approximation. We calculate the vertical and relaxed transition energies, and relaxed geometries for various excitations on long chains. The triplet (3Bu+) and even- parity singlet (2Ag+) states have a 2-soliton and 4-soliton form, respectively, both with large relaxation energies. The dipole-allowed (1Bu-) state forms an exciton-polaron and has a very small relaxation energy. The relaxed energy of the 2Ag+ state lies below that of the 1Bu- state. We observe an attraction between the soliton-antisoliton pairs in the 2Ag+ state. The calculated excitation energies agree well with the observed values for polyene oligomers; the agreement with polyacetylene thin films is less good, and we comment on the possible sources of the discrepencies. The photoinduced absorption is interpreted. The spin-spin correlation function shows that the unpaired spins coincide with the geometrical soliton positions. We study the roles of electron-electron interactions and electron-lattice coupling in determining the excitation energies and soliton structures. The electronic interactions play the key role in determining the ground state dimerisation and the excited state transition energies.Comment: LaTeX, 15 pages, 9 figure

Local Operations and Completely Positive Maps in Algebraic Quantum Field Theory

Einstein introduced the locality principle which states that all physical effect in some finite space-time region does not influence its space-like separated finite region. Recently, in algebraic quantum field theory, R\'{e}dei captured the idea of the locality principle by the notion of operational separability. The operation in operational separability is performed in some finite space-time region, and leaves unchanged the state in its space-like separated finite space-time region. This operation is defined with a completely positive map. In the present paper, we justify using a completely positive map as a local operation in algebraic quantum field theory, and show that this local operation can be approximately written with Kraus operators under the funnel property