arXiv subjects

Asher Yahalom

Publications and source records attributed to Asher Yahalom.

At least 37 records · Page 2Linked to original sources

arXiv2020

Spontaneous and explicit parity-time-symmetry breaking in drift wave instabilities

A method of Parity-Time (PT)-symmetry analysis is introduced to study the high dimensional, complicated parameter space of drift wave instabilities. We show that spontaneous PT-symmetry breaking leads to the Ion Temperature Gradient (ITG) instability of drift waves, and the collisional instability is the result of explicit PT-symmetry breaking. A new unstable drift wave induced by finite collisionality is identified. It is also found that gradients of ion temperature and density can destabilize the ion cyclotron waves when PT symmetry is explicitly broken by a finite collisionality.

physics.plasm-ph↗

arXiv2020

Retardation Effects in Gravitation

Galaxies are huge physical systems having dimensions of many tens of thousands of light years. Thus any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects seems to be neglected in present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper we will show that taking general relativity seriously without neglecting retardation effects one can explain the radial velocities of galactic matter without postulating dark matter.

physics.gen-ph↗

arXiv2020

Noether Currents for Eulerian Variational Principles in Non Barotropic Magnetohydrodynamics and Topological Conservations Laws

We derive a Noether current for the Eulerian variational principle of ideal non-barotropic magnetohydrodynamics (MHD). It was shown previously that ideal non-barotropic MHD is mathematically equivalent to a five function field theory with an induced geometrical structure in the case that field lines cover surfaces and this theory can be described using a variational principle. Here we use various symmetries of the flow to derive topological constants of motion through the derived Noether current and discuss their implication for non-barotropic MHD.

physics.flu-dyn↗

arXiv2020

Energy Transformations in a Relativistic Engine

In a previous paper we have shown that Newton's third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot exceed the speed of light at vacuum, which in turn means that when summing the total force in the system the force does not add up to zero. This was demonstrated in a specific example of two current loops with time dependent currents, the above analysis led to suggestion of a relativistic engine. Since the system is effected by a total force for a finite period of time this means that the system acquires mechanical momentum and energy, the question then arises how can we accommodate the law of momentum and energy conservation. The subject of momentum conversation was discussed in a previous paper, while preliminary results regarding energy conservation were discussed in previous papers. Here we give a complete analysis of the exchange of energy between the mechanical part of the relativistic engine and the field part, the energy radiated from the relativistic engine is also discussed. We show that the relativistic engine effect on the energy is 4th-order in 1/c and no lower order relativistic engine effect on the energy exist.

physics.gen-ph↗

arXiv2020

Stabilization of a Time Dependent Hamiltonian System

In this paper we consider the unstable chaotic attractor of the Toda potential and stabilize it by a control in integral form. In order to obtain stability results, we propose a special technique which is based on the idea of reduction of integro-differential equations to ordinary differential equations system.

physics.class-ph↗

arXiv2018

A New Diffeomorphism Symmetry Group of Non-Barotropic Magnetohydrodynamics

The theorem of Noether dictates that for every continuous symmetry group of an Action the system must possess a conservation law. In this paper we discuss some subgroups of Arnold's labelling symmetry diffeomorphism related to non-barotropic magnetohydrodynamics (MHD) and the conservations laws associated with them. Those include but are not limited to the metage translation group and the associated topological conservations law of non-barotropic cross helicity.

physics.plasm-ph↗

arXiv2017

Entropy measures as geometrical tools in the study of cosmology

Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by $S = \ln χ(x)$ with $χ(x)$ being the distance between two nearby geodesics. We derive an equation for the entropy which by transformation to a Ricatti-type equation becomes similar to the Jacobi equation. We further show that the geodesic equation for a null geodesic in a double warped space time leads to the same entropy equation. By applying a Robertson-Walker metric for a flat three-dimensional Euclidian space expanding as a function of time, we again reach the entropy equation stressing the connection between the chosen entropy measure and time. We finally turn to the Raychaudhuri equation for expansion, which also is a Ricatti equation similar to the transformed entropy equation. Those Ricatti-type equations have solutions of the same form as the Jacobi equation. The Raychaudhuri equation can be transformed to a harmonic oscillator equation, and it has been shown that the geodesic deviation equation of Jacobi is essentially equivalent to that of a harmonic oscillator. The Raychaudhuri equations are strong geometrical tools in the study of General Relativity and Cosmology. We suggest a refined entropy measure applicable in Cosmology and defined by the average deviation of the geodesics in a congruence.

gr-qc↗

arXiv2017

Preliminary Energy Considerations in a Relativistic Engine

In a previous paper \cite{MTAY1} we have shown that Newton'n third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot exceed the speed of light at vacuum, which in turn means that when summing the total force in the system the force does not add up to zero. This was demonstrated in a specific example of two current loops with time dependent currents, the above analysis led to suggestion of a relativistic engine \cite{MTAY3,AY1}. Since the system is effected by a total force for a finite period of time this means that the system acquires mechanical momentum and energy, the question then arises if we need to abandon the law of momentum and energy conservation. The subject of momentum conversation was discussed in \cite{MTAY4}. Here some preliminary aspects of the exchange of energy between the mechanical part of the relativistic engine and the electromagnetic field are discussed. We also refer briefly to the material composition, structure and properties of metals that should be used in a relativistic engine.

physics.gen-ph↗

arXiv2017

A DLA model for Turbulence

A connection between fractal dimensions of "turbulent facets" and fractal dimensions in diffusion-limited aggregation (DLA) is shown. The theoretical correspondence is elucidated and an empirical support to the above claim is given.

math-ph↗

arXiv2017

A THz Slot Antenna Optimization Using Analytical Techniques

Slot antennas are very popular microwave antennas and slotted wave guides are used for high frequency radar systems. A thin slot in an infinite ground plane is the complement to a dipole in free space. This was described by H.G. Booker [2] who extended Babinet's principle from optics to show that the slot will have the same radiation pattern as a dipole such that the E and H fields are swapped. As a result, the polarization is rotated, so that radiation from vertical slot is polarized horizontally. In this work we show how analytical techniques can be used for optimization of THz slot antennas, the analysis is then corroborated by using a numerical simulation which validates the performance parameters predicted by the analytical technique.

physics.app-ph↗

arXiv2017

Variational Principles and Applications of Local Topological Constants of Motion for Non-Barotropic Magnetohydrodynamics

Variational principles for magnetohydrodynamics (MHD) were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of non-barotropic MHD can be derived for certain field topologies. The variational principle is given in terms of five independent functions for non-stationary non-barotropic flows. This is less then the eight variables which appear in the standard equations of barotropic MHD which are the magnetic field $\vec B$ the velocity field $\vec v$, the entropy $s$ and the density $ρ$. The case of non-barotropic MHD in which the internal energy is a function of both entropy and density was not discussed in previous works which were concerned with the simplistic barotropic case. It is important to understand the rule of entropy and temperature for the variational analysis of MHD. Thus we introduce a variational principle of non-barotropic MHD and show that five functions will suffice to describe this physical system. We will also discuss the implications of the above analysis for topological constants. It will be shown that while cross helicity is not conserved for non-barotropic MHD a variant of this quantity is. The implications of this to non-barotropic MHD stability is discussed.

physics.plasm-ph↗

arXiv2016

Second quantization of a covariant relativistic spacetime string in Steuckelberg-Horwitz-Piron theory

A relativistic 4D string is described in the framework of the covariant quantum theory first introduced by Stueckelberg (1941) [1], and further developed by Horwitz and Piron (1973) [2], and discussed at length in the book of Horwitz (2015) [3]. We describe the space-time string using the solutions of relativistic harmonic oscillator [4]. We first study the problem of the discrete string, both classically and quantum mechanically, and then turn to a study of the continuum limit, which contains a basically new formalism for the quantization of an extended system. The mass and energy spectrum are derived. Some comparison is made with known string models.

physics.gen-ph↗

arXiv2015

Simplified Variational Principles for non-Barotropic Magnetohydrodynamics

Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of non-barotropic magnetohydrodynamics can be derived. The variational principle is given in terms of five independent functions for non-stationary barotropic flows. This is less then the eight variables which appear in the standard equations of barotropic magnetohydrodynamics which are the magnetic field $\vec B$ the velocity field $\vec v$, the entropy $s$ and the density $ρ$.

physics.plasm-ph↗

arXiv2015

Tunneling as a Source for Quantum Chaos

We use an one dimensional model of a square barrier embedded in an infinite potential well to demonstrate that tunneling leads to a complex behavior of the wave function and that the degree of complexity may be quantified by use of the spatial entropy function defined by S = -\int |Ψ(x,t)|^2 ln |Ψ(x,t)|^2 dx. There is no classical counterpart to tunneling, but a decrease in the tunneling in a short time interval may be interpreted as an approach of a quantum system to a classical system. We show that changing the square barrier by increasing the height/width do not only decrease the tunneling but also slows down the rapid rise of the entropy function, indicating that the entropy growth is an essentially quantum effect.

quant-ph↗

arXiv2015

Open Systems' Density Matrix Properties in a Time Coarsened Formalism

The concept of time-coarsened density matrix for open systems has frequently featured in equilibrium and non-equilibrium statistical mechanics, without being probed as to the detailed consequences of the time averaging procedure. In this work we introduce and prove the need for a selective and non-uniform time-sampling, whose form depends on the properties (whether thermalized or not) of the bath. It is also applicable when an open microscopic sub-system is coupled to another {\it finite} system. By use of a time-periodic minimal coupling model between these two systems, we present detailed quantitative consequences of time coarsening, which include initial state independence of equilibration, deviations from long term averages, their environment size dependence and the approach to classicality, as measured by a Leggett-Garg type inequality. An interacting multiple qubit model affords comparison between the time integrating procedure and the more conventional environment tracing method.

cond-mat.stat-mech↗

arXiv2014

Quantum Field Theory of Classically Unstable Hamiltonian Dynamics

We study a class of dynamical systems for which the motions can be described in terms of geodesics on a manifold (ordinary potential models can be cast into this form by means of a conformal map). It is rigorously proven that the geodesic deviation equation of Jacobi, constructed with a second covariant derivative, is unitarily equivalent to that of a parametric harmonic oscillator, and we study the second quatization of this oscillator. The excitations of the Fock space modes correspond to the emission and absorption of quanta into the dynamical medium, thus associating unstable behavior of the dynamical system with calculable fluctuations in an ensamble with possible thermodynamic consequences.

math-ph↗

arXiv2013

Partial Decoherence and Thermalization through Time-Domain Ergodicity

An approach, differing from two commonly used methods (the stochastic \SE \ and the master equation \cite {Schlosshauer,BieleA}) but entrenched in the traditional density matrix formalism, is developed in a semi-classical setting, so as to go from the solutions of the time dependent \SE to decohering and thermalized states. This is achieved by utilizing the time-ergodicity, rather than the sampling- (or ensemble-) ergodicity, of physical systems. We introduce the formalism through a study of the Rabi model (a two level system coupled to an oscillator) and show that our semi-classical version exhibits, both qualitatively and quantitatively, many features of state truncation and equilibration \cite {AllahverdyanBN}. We then study the time evolution of two qubits in interaction with a bosonic environment, such that the energy scale of one qubit is much larger, and that of the other much smaller than the environment's energy scale. The small energy qubit decoheres to a mixture, while the high energy qubit is protected through the adiabatic theorem. However, an inter-qubit coupling generates an overall decoherence and leads for some values of the coupling to long term revivals in the state occupations.

cond-mat.stat-mech↗

arXiv2013

Gravity and Faster than Light Particles

In this paper I discuss whether superluminal particles exist in the general relativistic theory of gravity. It seems that the answer to this question is negative. In truth the result may only represent a difficulty to {\bf special} but not general relativity, the later allowing both Lorentzian and Euclidian metrics. An Euclidian metric does not restrict speed. Although only the Lorentzian metric is stable \cite{Yahaloma}, an Euclidian metric can be created under special gravitational circumstances and persist in a limited region of space-time causing possible superluminality.

gr-qc↗