Violation Of Conservation Laws Research Articles

The Relativistic Electrodynamics of Classical Charged Particles

Maxwell’s equations and the Lorentz force equation form the foundation of classical electromagnetic theory and their discovery led to the development of special relativity. Despite this achievement, their universal compatibility with the conservation of momentum and relativistic energy transformations is still debated. Incorporating effects of hidden momentum with the Lorentz force equation or using the Einstein–Laub formula are two common approaches to address some of these concerns. Which method to use, or if a change to classical electromagnetism is even required, remains controversial. A new theoretical approach is presented in this paper to address this using relativistic electromagnetic energy inertial frame transformations. These transformations identify a situation where an apparent violation of conservation laws could occur and how to consolidate this with electromagnetic theory. An explanation regarding the elementary nature of magnetism and the relationship between inertia and electromagnetic energy is also commented on.

Lehmann representation of the nonequilibrium self-energy

It is shown that the non-equilibrium self-energy of an interacting lattice-fermion model has a unique Lehmann representation. Based on the construction of a suitable non-interacting effective medium, we provide an explicit and numerically practicable scheme to construct the Lehmann representation for the self-energy, given the Lehmann representation of the single-particle non-equilibrium Green's function. This is of particular importance for an efficient numerical solution of Dyson's equation in the context of approximations where the self-energy is obtained from a reference system with a small Hilbert space. As compared to conventional techniques to solve Dyson's equation on the Keldysh contour, the effective-medium approach allows to reach a maximum propagation time which can be several orders of magnitude longer. This is demonstrated explicitly by choosing the non-equilibrium cluster-perturbation theory as a simple approach to study the long-time dynamics of an inhomogeneous initial state after a quantum quench in the Hubbard model on a 10 x 10 square lattice. We demonstrate that the violation of conservation laws is moderate for weak Hubbard interaction and that the cluster approach is able to describe prethermalization physics.

Resistivity of inhomogeneous superconducting wires

We study the contribution of quantum phase fluctuations in the superconducting order parameter to the low-temperature resistivity $\ensuremath{\rho}(T)$ of a dirty and inhomogeneous superconducting wire. In particular, we account for random spatial fluctuations of arbitrary size in wire thickness. For a typical wire thickness above the critical value for a superconductor-insulator transition, phase-slip processes can be treated perturbatively. We use a memory formalism approach, which underlines the role played by a weak violation of conservation laws in the mechanism for generating finite resistivity. Our calculations yield an expression for $\ensuremath{\rho}(T)$, which exhibits a smooth crossover from a homogeneous to a ``granular'' limit upon increase of $T$, controlled by a ``granularity parameter'' $D$ characterizing the size of thickness fluctuations. For extremely small $D$, we recover the power-law dependence $\ensuremath{\rho}(T)\ensuremath{\sim}{T}^{\ensuremath{\alpha}}$ obtained by unbinding quantum phase slips. However in the strongly inhomogeneous limit, the exponent $\ensuremath{\alpha}$ is modified and the prefactor is exponentially enhanced. We examine the dependence of the exponent $\ensuremath{\alpha}$ on an external magnetic field applied parallel to the wire. Finally, we show that the power-law dependence at low $T$ is consistent with a series of experimental data obtained in a variety of long and narrow samples, which earlier studies have attempted to fit by an exponential trial function. The values of $\ensuremath{\alpha}$ extracted from the data, and the corresponding field dependence, are consistent with known parameters of the corresponding samples.

Supertasks, dynamical attractors and indeterminism

Atkinson [2006. Losing energy in classical, relativistic and quantum mechanics. in Studies in History and Philosophy of Modern Physics, 38 To appear.] has obtained some new results on supertasks and the violation of conservation laws. I discuss these results here, extending them from a different perspective, which, by focusing on considerations of indeterminism, facilitates the natural introduction in this context of the concept of dynamical attractor.

Violations of conservation laws in viscous liquid dynamics

The laws expressing conservation of momentum and energy apply to any isolated system, but these laws are violated for highly viscous liquids under laboratory conditions because of the unavoidable interactions with the measuring equipment over the long times needed to study the dynamics. Moreover, although particle number conservation applies strictly for any liquid, the solidity of viscous liquids implies that even this conservation law is apparently violated in coarse-grained descriptions of density fluctuations.

Tau physics: theoretical perspective

The leptonic decays of the τ lepton provide relevant tests on the structure of the weak currents and the universality of their couplings to the gauge bosons. The hadronic τ decay modes constitute an ideal tool for studying low-energy effects of the strong interaction in very clean conditions. Accurate determinations of the QCD coupling and the strange quark mass have been obtained with τ decay data. New physics phenomena, such as a non-zero m ν τ or violations of conservation laws can also be searched for with τ decays.

On the nonoccurrence of two paradoxes in the measurement scheme of stochastic quantum mechanics

The internal paradoxes in the quantum measurement scheme related to violation of conservation laws, changes in entropy, absence of a dynamic description of collapse, Wigner's friend, as well as the paradox of violation of causality in the EPR experiment are shown to be partially circumvented in the measurement scheme of stochastic quantum mechanics.

Nonunique solutions of kinetic equations

Two very hard particle models are solved and the nonuniqueness of the initial value problem for these (model) kinetic equations is explicitly demonstrated, when distribution functions decaying sufficiently slowly are permitted. The intimate connection between nonuniqueness and violation of conservation laws is made evident. The associated eigenvalue problems are solved. Finally, the general implications of these results for kinetic equations with transition rates that are increasing functions of the state variable, are stated in the form of a number of conjectures. They affect the solution of the Boltzmann equation for realistic intermolecular interactions when the collision rategI(g, χ) is an increasing function of the relative velocityg.

Violation of conservation laws when solving difference equations by iteration methods

Violation of conservation laws when solving difference equations by iteration methods

Erratum: Treatment of the charge-independent pairing Hamiltonian without violation of conservation laws

Erratum: Treatment of the charge-independent pairing Hamiltonian without violation of conservation laws

Treatment of the charge-independent pairing Hamiltonian without violation of conservation laws

An equations-of-motion method is proposed for treating neutron-proton pairing correlations conserving both nucleon number $N$ and isospin $T$. This method makes it possible to find approximate solutions to the charge-independent pairing Hamiltonian by a step-by-step procedure. It is shown that for the degenerate model the exact results are obtained.NUCLEAR STRUCTURE Charge-independent treatment of pairing correlations.

Treatment of pairing correlations without violation of conservation laws

Treatment of pairing correlations without violation of conservation laws

Collective motion in many-particle systems: Part 1. The violation of conservation laws

A method for treating collective motion is proposed which allows the use of wave functions violating conservation laws which are valid for the system. The reasons for the use of such wave functions is discussed and a simple physical interpretation is given. The method is illustrated by applications to center-of-mass motion, the electron gas in the random phase approximation, nuclear rotation, and the violation of the conservation of the number of particles.

MICROSCOPIC TESTS OF SYMMETRY PRINCIPLES

A collection of experiments which put rather stringent limits on possible violations of conservation laws and related symmetry principles, those which are believed to be universally valid. The evidence for the absolute conservation laws connected with gauge transformations, i.e., the conservation of charge, of baryons, and of leptons is discussed. Finally, discussion is presented on the evidence for the equality of the charges of the various charged elementary particles, and evidence for the conservation of angular momentum, associated with symmetry under space rotations.