Quantum mechanical hamiltonian models of turing machines

Quantum mechanical Hamiltonian models, which represent an aribtrary but finite number of steps of any Turing machine computation, are constructed here on a finite lattice of spin-1/2 systems. Different regions of the lattice correspond to different components of the Turing machine (plus recording system). Successive states of any machine computation are represented in the model by spin configuration states. Both time-independent and time-dependent Hamiltonian models are constructed here. The time-independent models do not dissipate energy or degrade the system state as they evolve. They operate close to the quantum limit in that the total system energy uncertainty/computation speed is close to the limit given by the time-energy uncertainty relation. However, the model evolution is time global and the Hamiltonian is more complex. The time-dependent models do not degrade the system state. Also they are time local and the Hamiltonian is less complex.     

The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines

In this paper a microscopic quantum mechanical model of computers as represented by Turing machines is constructed. It is shown that for each numberN and Turing machineQ there exists a HamiltonianH _N ^Q and a class of appropriate initial states such that if c is such an initial state, then _Q ^N (t)=exp(–1H _N ^Q t) _Q ^N (0) correctly describes at timest ₃,t ₆,,t _3N model states that correspond to the completion of the first, second, , Nth computation step ofQ. The model parameters can be adjusted so that for an arbitrary time interval aroundt ₃,t ₆,,t _3N, the machine part of _Q ^N (t) is stationary.     

On the discrete spectrum of the N-body quantum mechanical Hamiltonian: II

Using the Weinberg-van Winter equations we prove finiteness of the discrete spectrum of the N-body quantum mechanical Hamiltonian with pair potentials satisfying |V(x)| C(1 + |x|²)^– , > 1 in case the threshold of the continuous spectrum is negative and determined exclusively by eigenvalues of two-cluster Hamiltonians.     

From Classical Hamiltonian Flow to Quantum Theory: Derivation of the Schrödinger Equation

It is shown how the essentials of quantum theory, i.e., the Schrödinger equation and the Heisenberg uncertainty relations, can be derived from classical physics. Next to the empirically grounded quantisation of energy and momentum, the only input is given by the assumption of fluctuations in energy and momentum to be added to the classical motion. Extending into the relativistic regime for spinless particles, this procedure leads also to a derivation of the Klein-Gordon equation. Comparing classical Hamiltonian flow with quantum theory, then, the essential difference is given by a vanishing divergence of the velocity of the probability current in the former, whereas the latter results from a much less stringent requirement, i.e., that only the average over fluctuations and positions on the average divergence be identical to zero.     

Exploring the thermodynamic limit of Hamiltonian models: convergence to the Vlasov equation

We here discuss the emergence of quasistationary states (QSS), a universal feature of systems with long-range interactions. With reference to the Hamiltonian mean-field model, numerical simulations are performed based on both the original N-body setting and the continuum Vlasov model which is supposed to hold in the thermodynamic limit. A detailed comparison unambiguously demonstrates that the Vlasov-wave system provides the correct framework to address the study of QSS. Further, analytical calculations based on Lynden-Bell's theory of violent relaxation are shown to result in accurate predictions. Finally, in specific regions of parameters space, Vlasov numerical solutions are shown to be affected by small scale fluctuations, a finding that points to the need for novel schemes able to account for particle correlations.     

Statistical mechanical approach to secondary processes and structural relaxation in glasses and glass formers: a leading model to describe the onset of Johari-Goldstein processes and their relationship with fully cooperative processes

The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and structural relaxation. The study of the dynamics allows for predictions on the system relaxation above the temperature of dynamic arrest in the mean-field approximation, that are compared with the outcomes of the equations of motion directly derived within the Mode Coupling Theory (MCT) for under-cooled viscous liquids. By varying the external thermodynamic parameters, a wide range of phenomenology can be represented, from a very clear separation of structural and secondary peak in the susceptibility loss to excess wing structures.     

Application of continuous variation formulas and discrete invariance principles to black holes and neutron star models

A discussion is given of the inferences that can be drawn from the application of the principle of time reversal invariance to the equilibrium states of axisymmetric bodies in general relativity, in conjunction with the law relating energy and angular momentum variations in elastic deformations. The concepts of moments of inertia and of the mutual moments of inertia between different components of a multicomponent body are described. Particular attention is given to the case of axisymmetric perfect solid neutron star models with relaxable elastic structures, and it is shown that such bodies have equilibrium states with the special property of invariance under simultaneous time and axial angle reversal. Finally, the case of a Kerr black hole is presented as a concrete example of the application of the ensuing formulas.     

Calculation of kinetic energy terms for the vibrational Hamiltonian: Application to large-amplitude vibrations using one-, two-, and three-dimensional models

One-, two-, and three-dimensional models involving large-amplitude vibrations have been used to calculate kinetic energy terms. Principle G matrix elements as well as cross terms in the kinetic energy were determined. Calculations were done on models involving the ring-puckering and PH inversion vibrations for 3-phospholene and the ring-puckering, ring deformation, and SiH₂ in-phase rocking vibrations for 1,3-disilacyclobutane. Kinetic energy expansions for g₄₄ and g₄₅ type terms were determined. Calculations show a coordinate dependence of the principle G matrix elements as well as of the g₄₅ terms. The vectorial models used in these calculations make it possible to treat vibrations in a one-, two-, or three-dimensional model separate from the other vibrations without carrying out a coordinate transformation, which would be necessary for the Wilson GF high- or low-frequency separation.     

Algebraic programming of Hamiltonian formalism in general relativity: Application to inhomogeneous space-times

We describe the structure and the use of a program written in the algebraic programming languagereduce 2, giving the super-Hamiltonian and supermomenta constraints, as well as Hamilton's canonical equations in terms of the canonical variables, for vacuum relativistic space-times. The program uses as input the components of the spatial metric tensor and of the corresponding canonically conjugate momenta in a coordinate or in a spatial Cartan basis. The results of the application of the program to a series of inhomogeneous (cosmological as well as noncosmological) space-times are given: in particular, the constraints, the Dirac Hamiltonian and the canonical equations are explicitly written for axisymmetric space-times, constituting the starting point for the study of the dynamics and of the canonical quantization of these configurations.     

Burned bones tell their own stories: A review of methodological approaches to assess heat-induced diagenesis

One of the biggest struggles of biological anthropology is to estimate the biological profile from burned human skeletal remains. Bioanthropological methods are seriously compromised due to bone heat-induced alterations in shape and size. Therefore, it is urgent to improve our ability to estimate sex, age at death, stature, and ancestrality, to recognize peri mortem traumas and differentiate them from fractures due to fire, and to determine what was the intensity of burning, namely maximum temperature and heat exposure length. This review focuses on different methodologies to assess heat prompted changes in bone submicrostructure. Some of these are extensively used in burned bones research, namely infrared and Raman spectroscopy and X-ray diffraction, while others such as neutron spectroscopy and diffraction are rarely applied to bone samples although their contribution may be crucial for establishing new bioanthropological methods for a reliable examination of burned victims.     

Quantum structures: An attempt to explain the origin of their appearance in nature

We explain quantum structure as due to two effects: (a) a real change of state of the entity under the influence of the measurement and (b) a lack of knowledge about a deeper deterministic reality of the measurement process. We present a quantum machine, with which we can illustrate in a simple way how the quantum structure arises as a consequence of the two mentioned effects. We introduce a parameter that measures the size of the lack of knowledge of the measurement process, and by varying this parameter, we describe a continuous evolution from a quantum structure (maximal lack of knowledge) to a classical structure (zero lack of knowledge). We show that for intermediate values of we find a new type of structure that is neither quantum nor classical. We apply the model to situations of lack of knowledge about the measurement process appearing in other aspects of reality. Specifically, we investigate the quantumlike structures that appear in the situation of psychological decision processes, where the subject is influenced during the testing and forms some opinions during the testing process. Our conclusion is that in the light of this explanation, the quantum probabilities are epistemic and not ontological, which means that quantum mechanics is compatible with a determinism of the whole.     

Application of the SCC method to the multi-O(4) model: The collective Hamiltonian

The collective Hamiltonian up to the fourth order for a multi-O(4) model is derived for the first time based on the self-consistent collective-coordinate(SCC) method,which is formulated in the framework of the time-dependent Hartree-Bogoliubov(TDHB) theory.This collective Hamiltonian is valid for the spherical case where the HB equilibrium point of the multi-O(4) model is spherical as well as for the deformed case where the HB equilibrium points are deformed.Its validity is tested numerically in both the sp...     

Application of the mutual-interaction method to a class of two-scatterer systems: I. Two discrete scatterers

In a recent paper we developed a formalism that fully accommodates the mutual interactions among scatterers separable by parallel planes. The total fields propagating away from these planes are the unknowns of a system of difference equations. Each scatterer is characterized by a scattering function that expresses the scattered wave amplitude as a function of the incident and scattered wavevectors for a unit-amplitude plane wave scattered from the object in isolation. This function can be derived completely from the scattered far field with the help of analytic continuation. For a two-scatterer system the mutual-interaction equations reduce to a single Fredholm integral equation of the second kind. It turns out that analytic solutions are tractable for those scattering functions that are Dirac deltas or a sum of products of separable functions of the incident and scattered wavevectors. Scattering functions for planes and isotropic scatterers, as well as electric and magnetic dipoles all possess this property and are considered. The exact scattering functions agree with results obtained by analytic continuation. This paper consists of two parts. Part I derives analytic solutions for two discrete scatterers (isotropic scatterers. electric dipoles, magnetic dipoles). Part II is devoted to scattering from an object (isotropic or dipole scatterer) near an interface separating two semi-infinite uniforn-media. Because the results in this paper are exact, the effects of near-field interactions can be assessed. The forms of the scattering solutions can be adapted to objects that are both radiating and scattering.     

Application of the mutual-interaction method to a class of two-scatterer systems: I. Two discrete scatterers

Abstract

In a recent paper we developed a formalism that fully accommodates the mutual interactions among scatterers separable by parallel planes. The total fields propagating away from these planes are the unknowns of a system of difference equations. Each scatterer is characterized by a scattering function that expresses the scattered wave amplitude as a function of the incident and scattered wavevectors for a unit-amplitude plane wave scattered from the object in isolation. This function can be derived completely from the scattered far field with the help of analytic continuation. For a two-scatterer system the mutual-interaction equations reduce to a single Fredholm integral equation of the second kind. It turns out that analytic solutions are tractable for those scattering functions that are Dirac deltas or a sum of products of separable functions of the incident and scattered wavevectors. Scattering functions for planes and isotropic scatterers, as well as electric and magnetic dipoles all possess this property and are considered. The exact scattering functions agree with results obtained by analytic continuation. This paper consists of two parts. Part I derives analytic solutions for two discrete scatterers (isotropic scatterers. electric dipoles, magnetic dipoles). Part II is devoted to scattering from an object (isotropic or dipole scatterer) near an interface separating two semi-infinite uniforn-media. Because the results in this paper are exact, the effects of near-field interactions can be assessed. The forms of the scattering solutions can be adapted to objects that are both radiating and scattering.     

Statistical mechanical approach to secondary processes and structural relaxation in glasses and glass formers A leading model to describe the onset of Johari-Goldstein processes and their relationship with fully cooperative processes

The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and structural relaxation. The study of the dynamics allows for predictions on the system relaxation above the temperature of dynamic arrest in the mean-field approximation, that are compared with the outcomes of the equations of motion directly derived within the Mode Coupling Theory (MCT) for under-cooled viscous liquids. By varying the external thermodynamic parameters, a wide range of phenomenology can be represented, from a very clear separation of structural and secondary peak in the susceptibility loss to excess wing structures.