Canonical Quantization of Field Theories with Boundaries

The problem of canonical quantization of singular systems in a finite volume is studied by analysing a non-relativistic field theory. Firstly, we take the boundary conditions (BCs) as primary Dirac constraints. The quantization is performed canonically using Dirac’s procedure. Then, we quantize this model canonically in the classical solution space. We show that these two different quantization schemes are equivalent although they start from different settings.     

Inequivalent Quantization in the Field of a Ferromagnetic Wire

We argue that it is possible to bind neutral atom (NA) to the ferromagnetic wire (FW) by inequivalent quantization of the Hamiltonian. We follow the well known von Neumann’s method of self-adjoint extensions (SAE) to get this inequivalent quantization, which is characterized by a parameter Σ∈ℝ(mod2π). There exists a single bound state for the coupling constant η ²∈[0,1). Although this bound state should not occur due to the existence of classical scale symmetry in the problem. But since quantization procedure breaks this classical symmetry, bound state comes out as a scale in the problem leading to scaling anomaly. We also discuss the strong coupling region η ²<0, which supports bound state making the problem re-normalizable.     

Hamiltonian and Path Integral Quantization of the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of a Scalar Dilation Field

The conformally gauge-fixed Polyakov D1 brane action in the presence of a scalar dilaton field is seen to be a constrained system in the sense of Dirac. In the present work we study its Hamiltonian and path integral quantization in the instant-form of dynamics using the equal world-sheet time framework.     

Generalized Quantization Condition

On the basis of analytical transfer matrix theory, we fine a generalized quantization condition. By introducing a new type of modified momentum, our quantization condition has the same form as the Bohr Sommerfeld formula. Numerical and analytical comparisons show that the present method is exact.     

Spectroscopy of laser-produced cerium plasma for remote isotope analysis of nuclear fuel

A cerium oxide sample was ablated by 2nd harmonic radiation of Nd:YAG laser at a power density of 0.1 GW/cm². Time evolution of the ablation plume was investigated by laser absorption time-of-flight (TOF) measurement. It was found that the ablated ionic plume in vacuum consisted of two components having different velocities whereas the ablated neutral atoms had mainly a single component. The flow velocity perpendicular to the sample surface in vacuum was determined to be 3.5 km/s for neutral atoms, and 4.7 km/s and 9.3 km/s for singly charged ions. From the detailed plume evolution in ambient atmosphere with several pressures we obtained some experimental conditions suitable for isotope analysis of atomic cerium.     

Quantization of the space－time with topological defect

We present the classical solution of Lagrange equations for the black hole with a global monopole or with a cosmic string. Then we obtain the wavefunction of the space－time by solving the Wheeler－De Witt equation. De Broglie－Bohm interpretation applied to the wavefunction gives the quantum solution of the space－time. In the end, the quantum effect on Hawking radiation is studied.     

Energy Quantization and Probability Density of Electron in Intense-Field-Atom Interactions

We find that, due to the quantum correlation between the electron and the field, the electronic energy becomes quantized also, manifesting the particle aspect of light in the electron-light interaction. The probability amplitude of finding electron with a given energy is given by a generalized Bessel function, which can be represented as a coherent superposition of contributions from a few electronic quantum trajectories. This concept is illustrated by comparing the spectral density of the electron with the laser assisted recombination spectrum.     

Electronic structure of epitaxial thin films of bay-substituted perylene bisimide dyes

We have investigated epitaxial thin films of three air-stable organic n-type semiconducting perylene tetracarboxylic acid bisimides (PBIs) with fluoroalkyl groups in the imide position with a combination of X-ray, UV, and inverse photoelectron spectroscopy. We explore the applicability of film preparation by organic molecular beam deposition (OMBD) under ultra-high vacuum conditions to these compounds. By means of fluorine and chlorine substituents in the bay area a systematic torsion of the π-conjugated core of these three PBIs is achieved. Accordingly, these molecules offer a model system to analyze the interplay between the molecular conformation, the film structure, and the electronic structure. Our results show that the PBIs can be deposited intact and contamination free by OMBD and relatively smooth films with layer-to-layer growth can be established. Moreover, the valence spectra reveal the effect of the electro-negative bay substituents as well as of the twisting of the perylene core, which leads to energy shifts of the occupied and unoccupied frontier orbitals.     

Information-Geometric Indicators of Chaos in Gaussian Models on Statistical Manifolds of Negative Ricci Curvature

A new information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) is proposed. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold ℳ _s underlying an ED Gaussian model describing an arbitrary system of 3N degrees of freedom leads to linear information-geometric entropy growth and to exponential divergence of the Jacobi vector field intensity, quantum and classical features of chaos respectively.     

The Spectrum of the Billiard Laplacian of a Family of Random Billiards

Random billiards are billiard dynamical systems for which the reflection law giving the post-collision direction of a billiard particle as a function of the pre-collision direction is specified by a Markov (scattering) operator P. Billiards with microstructure are random billiards whose Markov operator is derived from a “microscopic surface structure” on the boundary of the billiard table. The microstructure in turn is defined in terms of what we call a billiard cellQ, the shape of which completely determines the operator P. This operator, defined on an appropriate Hilbert space, is bounded self-adjoint and, for the examples considered here, a Hilbert-Schmidt operator. A central problem in the statistical theory of such random billiards is to relate the geometric characteristics of Q and the spectrum of P. We show, for a particular family of billiard cell shapes parametrized by a scale invariant curvature K (Fig. 2), that the billiard Laplacian P−I is closely related to the ordinary spherical Laplacian, and indicate, by partly analytical and partly numerical means, how this provides asymptotic information about the spectrum of P for small values of K. It is shown, in particular, that the second moment of scattering about the incidence angle closely approximates the spectral gap of P.     

Quantization of the O（N） Nonlinear Sigma Model

The Hamilton-Jacobi method of quantizing singular systems is discussed.The equations of motion are obtained as total differential equations in many variables.It is shown that if the system is integrable,one can obtain the canonical phase space coordinates and set of canonical Hamilton-Jacobi partial differential equations without any need to introduce unphysical auxiliary fields.As an example we quantize the O(2) nonlinear sigma model using two different approaches:the functional Schrodinger method to obtain the wave functionals for the ground and the exited state and then we quantize the same model using the canonical path integral quantization as an integration over the canonical phase-space coordinates.     

Molecular dynamics simulations of laser-induced damage of nanostructures and solids

A theoretical approach to treat laser induced femtosecond structural changes in covalently bonded nanostructures and solids is described. Our approach consists in molecular dynamic simulations performed on the basis of time-dependent, many-body potential energy surfaces derived from tight-binding Hamiltonians. The shape and spectral composition of the laser pulse is explicitly taking into account in a non-perturbative way. We show a few examples of the application of this approach to describe the laser damage and healing of defects in carbon nanotubes with different chiralities and the ultrafast nonequilibrium melting of bulk germanium, initiated by the laser-induced softening and destabilization of transversal acoustic phonon modes.     

A Re-interpretation of the Concept of Mass and of the Relativistic Mass-Energy Relation

For over a century the definitions of mass and derivations of its relation with energy continue to be elaborated, demonstrating that the concept of mass is still not satisfactorily understood. The aim of this study is to show that, starting from the properties of Minkowski spacetime and from the principle of least action, energy expresses the property of inertia of a body. This implies that inertial mass can only be the object of a definition—the so called mass-energy relation—aimed at measuring energy in different units, more suitable to describe the huge amount of it enclosed in what we call the “rest-energy” of a body. Likewise, the concept of gravitational mass becomes unnecessary, being replaceable by energy, thus making the weak equivalence principle intrinsically verified. In dealing with mass, a new unit of measurement is foretold for it, which relies on the de Broglie frequency of atoms, the value of which can today be measured with an accuracy of a few parts in 10⁹.     

Quantization of Horizon Area of Kerr–Newman–de Sitter Black Hole

Using the adiabatic invariant action and applying the Bohr–Sommerfeld quantization rule and first law of black hole thermodynamics, a study of the quantization of the entropy and horizon area of a Kerr–Newman–de Sitter black hole is carried out. The same entropy spectrum is obtained in two different coordinate systems. It is also observed that the spacing of the entropy spectrum is independent of the black hole parameters. Also, the corresponding quantum of horizon area is in agreement with the results of Bekenstein.     

Hamilton–Jacobi Quantization of Singular Lagrangians with Linear Velocities

In this paper, constrained Hamiltonian systems with linear velocities are investigated by using the Hamilton–Jacobi method. The integrablity conditions are considered on the equations of motion and the action function as well in order to obtain the path integral quantization of singular Lagrangians with linear velocities.     

A Note on the Extrinsic Phase Space Path Integral Method for Quantization on Riemannian Manifold Particle Motions — An Application of the Nash Embedding Theorem

We use Nash embedding for Riemann smooth manifolds to propose a constrained phase space path integral for quantization of one particle motion in a Riemannian manifold.     

Ultrashort-pulse laser irradiation of metal films: the effect of a double-peak laser pulse

The optical properties of blue-violet InGaN light-emitting diodes under normal and reversed polarizations are numerically studied. The best light-emitting performance under normal and reversed polarization is obtained in a single quantum-well structure and double quantum-well structure, respectively. The key factors responsible for these phenomena are presumably the carrier concentration distribution and the amount of carriers in quantum wells. The turn-on voltage of light-emitting diodes under reversed polarization is lower than that of light-emitting diodes under normal polarization, due mainly to lower potential heights for electrons and holes in the active region.     

Condensation of the Roots of Real Random Polynomials on the Real Axis

We introduce a family of real random polynomials of degree n whose coefficients a _k are symmetric independent Gaussian variables with variance , indexed by a real α≥0. We compute exactly the mean number of real roots 〈N _n 〉 for large n. As α is varied, one finds three different phases. First, for 0≤α<1, one finds that . For 1<α<2, there is an intermediate phase where 〈N _n 〉 grows algebraically with a continuously varying exponent, . And finally for α>2, one finds a third phase where 〈N _n 〉∼n. This family of real random polynomials thus exhibits a condensation of their roots on the real line in the sense that, for large n, a finite fraction of their roots 〈N _n 〉/n are real. This condensation occurs via a localization of the real roots around the values , 1≪k≤n.     

Fluctuations of Quantum Currents and Unravelings of Master Equations

The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a rigorous result that relates the weak coupling limit of fluctuations of reservoir observables under a global unitary evolution with the statistics of the so-called quantum trajectories. These quantum trajectories are frequently considered in the context of quantum optics, but they remain useful for more general nonequilibrium systems. In contrast with the approaches found in the literature, we do not assume that the system is continuously monitored. Instead, our starting point is a relatively realistic unitary dynamics of the full system     

The Hamiltonian of Einstein affine-metric formulation of General Relativity

It is shown that the Hamiltonian of the Einstein affine-metric (first-order) formulation of General Relativity (GR) leads to a constraint structure that allows the restoration of its unique gauge invariance, four-diffeomorphism, without the need of any field dependent redefinition of gauge parameters as in the case of the second-order formulation. In the second-order formulation of ADM gravity the need for such a redefinition is the result of the non-canonical change of variables (arXiv:0809.0097). For the first-order formulation, the necessity of such a redefinition “to correspond to diffeomorphism invariance” (reported by Ghalati, arXiv:0901.3344) is just an artifact of using the Henneaux–Teitelboim–Zanelli ansatz (Nucl. Phys. B 332:169, 1990), which is sensitive to the choice of linear combination of tertiary constraints. This ansatz cannot be used as an algorithm for finding a gauge invariance, which is a unique property of a physical system, and it should not be affected by different choices of linear combinations of non-primary first class constraints. The algorithm of Castellani (Ann. Phys. 143:357, 1982) is free from such a deficiency and it leads directly to four-diffeomorphism invariance for first, as well as for second-order Hamiltonian formulations of GR. The distinct role of primary first class constraints, the effect of considering different linear combinations of constraints, the canonical transformations of phase-space variables, and their interplay are discussed in some detail for Hamiltonians of the second- and first-order formulations of metric GR. The first-order formulation of Einstein–Cartan theory, which is the classical background of Loop Quantum Gravity, is also discussed.