Tunneling Phenomenon

2021 ◽  
pp. 45-76
Author(s):  
C. Julian Chen
Keyword(s):  
Perturbation Theory ◽  
Three Dimensional ◽  
Hamiltonian Formalism ◽  
Experimental Methods ◽  
Time Dependent ◽  
Starting Point ◽  
Metal Insulator Metal ◽  
Dimensional Version ◽  
Tunneling Phenomenon ◽  
Theory Of Superconductivity

This chapter presents basic experimental methods and the basic theory of tunneling. The classical metal-insulator-metal tunneling junction experiment of Giaever, designed to verify the Bardeen-Cooper-Schrieffer theory of superconductivity, is the motivation for Bardeen to invent his perturbation theory of tunneling. That Bardeen theory then became the starting point of the most useful models of STM. Section 2.2 presents the Bardeen tunneling theory from time-dependent perturbation theory of quantum mechanics, starting from a one-dimensional case, then proceeds to three-dimensional version with wave-function corrections. The Bardeen theory in second-quantization format, the transfer-Hamiltonian formalism, is also presented. As extensions of the original Bardeen theory, the theories and experiments of inelastic tunneling and spin-polarized tunneling are discussed in depth.

scholarly journals Oscillating scalar dissipating in a medium

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Wen-Yuan Ai ◽  
Marco Drewes ◽  
Dražen Glavan ◽  
Jan Hajer
Keyword(s):  
Perturbation Theory ◽  
Quantitative Description ◽  
Early Time ◽  
Scalar Fields ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Local Equation ◽  
Starting Point ◽  
Non Linear ◽  
Non Local

Abstract We study how oscillations of a scalar field condensate are damped due to dissipative effects in a thermal medium. Our starting point is a non-linear and non-local condensate equation of motion descending from a 2PI-resummed effective action derived in the Schwinger-Keldysh formalism appropriate for non-equilibrium quantum field theory. We solve this non-local equation by means of multiple-scale perturbation theory appropriate for time-dependent systems, obtaining approximate analytic solutions valid for very long times. The non-linear effects lead to power-law damping of oscillations, that at late times transition to exponentially damped ones characteristic for linear systems. These solutions describe the evolution very well, as we demonstrate numerically in a number of examples. We then approximate the non-local equation of motion by a Markovianised one, resolving the ambiguities appearing in the process, and solve it utilizing the same methods to find the very same leading approximate solution. This comparison justifies the use of Markovian equations at leading order. The standard time-dependent perturbation theory in comparison is not capable of describing the non-linear condensate evolution beyond the early time regime of negligible damping. The macroscopic evolution of the condensate is interpreted in terms of microphysical particle processes. Our results have implications for the quantitative description of the decay of cosmological scalar fields in the early Universe, and may also be applied to other physical systems.

BETHE-SALPETER-EQUIVALENT COVARIANT THREE-DIMENSIONAL EQUATION IN AN INFINITE-MOMENTUM FRAME

1988 ◽  
Vol 03 (16) ◽  
pp. 1569-1577
Author(s):  
R.S. BHALERAO
Keyword(s):  
Perturbation Theory ◽  
Dimensional Reduction ◽  
Three Dimensional ◽  
Starting Point ◽  
Dimensional Equation ◽  
Simplified Form

Using the recently published works on (a) a covariant time-ordered perturbation theory, and (b) an exact three-dimensional reduction of the Bethe-Salpeter equation, we obtain a three-dimensional two-body equation which is exactly equivalent to the (four-dimensional) Bethe-Salpeter equation and, moreover, is covariant. The greatly simplified form that this equation assumes in an infinite-momentum frame is discussed. The final result is a new offshell two-body equation which could serve as an attractive starting point for numerical applications.

scholarly journals Second sacral sacralalar‐iliac (S2AI) screw placement in adult degenerative scoliosis (ADS) patients: an imaging study

BMC Surgery ◽  
2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Bing Wu ◽  
Kai Song ◽  
Junyao Cheng ◽  
Pengfei Chi ◽  
Zhaohan Wang ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Imaging Study ◽  
Outer Diameter ◽  
Degenerative Scoliosis ◽  
Female Patients ◽  
Lateral Angle ◽  
Adult Degenerative Scoliosis ◽  
Imaging Characteristics ◽  
Starting Point ◽  
Trajectory Length

Abstract Background The imaging characteristics of sacral sacralalar-iliac (S2AI) screw trajectory in adult degenerative scoliosis (ADS) patients will be determined. Methods S2AI screw trajectories were mapped on three-dimensional computed tomography (3DCT) reconstructions of 40 ADS patients. The starting point, placement plane, screw template, and a circle centered at the lowest point of the ilium inner cortex were set on these images. A tangent line from the starting point to the outer diameter of the circle was selected as the axis of the screw trajectory. The related parameters in different populations were analyzed and compared. Results The trajectory length of S2AI screws in ADS patients was 12.00 ± 0.99 cm, the lateral angle was 41.24 ± 3.92°, the caudal angle was 27.73 ± 6.45°, the distance from the axis of the screw trajectory to the iliosciatic notch was 1.05 ± 0.81 cm, the distance from the axis of the screw trajectory to the upper edge of the acetabulum was 1.85 ± 0.33 cm, and the iliac width was 2.12 ± 1.65 cm. Compared with females, the lateral angle of male ADS patients was decreased, but the trajectory length was increased (P < 0.05). Compared to patients without ADS in previous studies, the lateral angle of male patients was larger, the lateral angle of female patients was increased, and the caudal angle was decreased (P < 0.05). Conclusions There is an ideal trajectory of S2AI screws in ADS patients. A different direction should be noticed in the placement of S2AI screws, especially in female patients.

scholarly journals Shell-crossing in a ΛCDM Universe

2020 ◽  
Vol 501 (1) ◽  
pp. L71-L75
Author(s):  
Cornelius Rampf ◽  
Oliver Hahn
Keyword(s):  
Dark Matter ◽  
Perturbation Theory ◽  
Large Scale ◽  
Cold Dark Matter ◽  
Three Dimensional ◽  
Random Initial Data ◽  
Recursion Relations ◽  
Indispensable Tool ◽  
First Time ◽  
Very High

ABSTRACT Perturbation theory is an indispensable tool for studying the cosmic large-scale structure, and establishing its limits is therefore of utmost importance. One crucial limitation of perturbation theory is shell-crossing, which is the instance when cold-dark-matter trajectories intersect for the first time. We investigate Lagrangian perturbation theory (LPT) at very high orders in the vicinity of the first shell-crossing for random initial data in a realistic three-dimensional Universe. For this, we have numerically implemented the all-order recursion relations for the matter trajectories, from which the convergence of the LPT series at shell-crossing is established. Convergence studies performed at large orders reveal the nature of the convergence-limiting singularities. These singularities are not the well-known density singularities at shell-crossing but occur at later times when LPT already ceased to provide physically meaningful results.

scholarly journals Colourful Poincaré symmetry, gravity and particle actions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Joaquim Gomis ◽  
Euihun Joung ◽  
Axel Kleinschmidt ◽  
Karapet Mkrtchyan
Keyword(s):  
Field Theory ◽  
Free Particle ◽  
Three Dimensional ◽  
Background Field ◽  
Quantum Field ◽  
Symmetry Factor ◽  
Starting Point ◽  
Poincaré Algebra ◽  
Poincaré Symmetry ◽  
Three Space

Abstract We construct a generalisation of the three-dimensional Poincaré algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincaré gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincaré symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory.

scholarly journals A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 756
Author(s):  
Federico Lluesma-Rodríguez ◽  
Francisco Álcantara-Ávila ◽  
María Jezabel Pérez-Quiles ◽  
Sergio Hoyas
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Direct Numerical Simulations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Thermal Flow ◽  
Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

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