scholarly journals RATE OF PARITY VIOLATION FROM MEASURE CONCENTRATION

2008 ◽  
Vol 23 (03n04) ◽  
pp. 509-517 ◽  
Author(s):  
NIKOS KALOGEROPOULOS
Keyword(s):  
Phase Space ◽  
Statistical Mechanics ◽  
Parity Violation ◽  
Degrees Of Freedom ◽  
Relative Rate ◽  
Measure Concentration ◽  
Space Factor ◽  
Geometric Argument ◽  
Phase Space Factor ◽  
Opposite Chirality

We present a geometric argument determining the kinematic (phase-space) factor contributing to the relative rate at which degrees of freedom of one chirality come to dominate over degrees of freedom of opposite chirality, in models with parity violation. We rely on the measure concentration of a subset of a Euclidean cube which is controlled by an isoperimetric inequality. We provide an interpretation of this result in terms of ideas of statistical mechanics.

ON THE FOUNDATIONS OF STATISTICAL MECHANICS: A BRIEF REVIEW

2013 ◽  
Vol 27 (06) ◽  
pp. 1330003 ◽  
Author(s):  
NAVINDER SINGH
Keyword(s):  
Phase Space ◽  
Statistical Mechanics ◽  
Degrees Of Freedom ◽  
Frequency Theory ◽  
Actual System ◽  
Ergodic Hypothesis ◽  
Foundations Of Statistical Mechanics ◽  
Time Averages ◽  
Quantum Statistical ◽  
Ergodic Problem

This work is dedicated to those who are genuinely interested in the foundations of statistical mechanics. Statistical mechanics is a very successful theory. The foundations on which it is based are radically different from the foundations of Newtonian mechanics. Probability and the law of large numbers are its fundamental ingredients. In this paper we will see how the statistical mechanical synthesis which incorporates mechanics (deterministic) and probability theory (indeterministic) works. The approach consists of replacing the actual system by a hypothetical ensemble of systems under same external conditions. From the most used prescription of Gibbs, we calculate the phase space averages of dynamical quantities and find that these phase averages agree very well with experiments. Clearly, actual experiments are not done on a hypothetical ensemble. They are done on the actual system in the laboratory and these experiments take a finite amount of time. Thus, it is usually argued that actual measurements are time averages and they are equal to phase averages due to ergodic hypothesis (time averages = phase space averages). The aim of the present review is to show that ergodic hypothesis is not relevant for equilibrium statistical mechanics (with Tolman and Landau). We will see that the solution for the problem is in the very peculiar nature of the macroscopic observables and with a very large number of degrees of freedom involved in macroscopic systems as first pointed out by Boltzmann and then more quantitatively by Khinchin. Similar arguments were used by Landau based upon the approximate property of "statistical independence". We analyze these ideas in detail. We present a critique of the ideas of Jaynes who says that the ergodic problem is a conceptual one and is related to the very concept of ensemble itself which is a by-product of the frequency theory of probability, and the ergodic problem becomes irrelevant when the probabilities of various microstates are interpreted with Laplace–Bernoulli Theory of Probability (Bayesian viewpoint). At the end, we critically review various quantum approaches (quantum-statistical typicality approaches) to the foundations of statistical mechanics. The literature on quantum-statistical typicality is organized under four notions (i) kinematical canonical typicality, (ii) dynamical canonical typicality, (iii) kinematical normal typicality, and (iv) dynamical normal typicality. Analogies are seen in the Khinchin's classical approach and in the modern quantum-statistical typicality approaches.

scholarly journals Study of the Effect of Newly Calculated Phase Space Factor on β-Decay Half-Lives

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Mavra Ishfaq ◽  
Jameel-Un Nabi ◽  
Ovidiu Niţescu ◽  
Mihail Mirea ◽  
Sabin Stoica
Keyword(s):  
Phase Space ◽  
Nuclear Matrix ◽  
Matrix Elements ◽  
Β Decay ◽  
Space Factor ◽  
Comparison With Experiment ◽  
Reliable Computation ◽  
Phase Space Factor ◽  
The Subject ◽  
New Phase

We present results for β-decay half-lives based on a new recipe for calculation of phase space factors recently introduced. Our study includes fp-shell and heavier nuclei of experimental and astrophysical interests. The investigation of the kinematics of some β-decay half-lives is presented, and new phase space factor values are compared with those obtained with previous theoretical approximations. Accurate calculation of nuclear matrix elements is a prerequisite for reliable computation of β-decay half-lives and is not the subject of this paper. This paper explores if improvements in calculating the β-decay half-lives can be obtained when using a given set of nuclear matrix elements and employing the new values of the phase space factors. Although the largest uncertainty in half-lives computations come from the nuclear matrix elements, introduction of the new values of the phase space factors may improve the comparison with experiment. The new half-lives are systematically larger than previous calculations and may have interesting consequences for calculation of stellar rates.

STRUCTURELESS COMPOSITENESS AND THE LEP W+W- DATA

1998 ◽  
Vol 13 (36) ◽  
pp. 2903-2907
Author(s):  
E. H. LEMKE
Keyword(s):  
Experimental Data ◽  
Phase Space ◽  
Total Cross Section ◽  
Cross Section ◽  
Quantum Mechanical ◽  
Final State ◽  
Space Factor ◽  
Mechanical Interference ◽  
Phase Space Factor ◽  
Rule Out

We specify the electroweak scenario of structureless compositeness (SC) put forward previously to the case of identical masses m(W±)=m(Φ±) and m(Z)=m(Φ0). The resulting quantum-mechanical interference will exhibit a vector–scalar phase interlocking of exactly π. We calculate the total cross-section of e+e-→ W+W- in this scenario and compare with the SM. The experimental data is found not to rule out any of the four scenarios SM, κ an =0, SC at κ=1 and 0. Pronounced differences between these four cases show up for the σ tot contribution of the W L W L final state. The effects are illustrated in plots free of the trivial phase-space factor.

A parametrization of the phase space factor for allowed β-decay

1974 ◽  
Vol 232 (1) ◽  
pp. 58-92 ◽  
Author(s):  
D.H. Wilkinson ◽  
B.E.F. Macefield
Keyword(s):  
Phase Space ◽  
Β Decay ◽  
Space Factor ◽  
Phase Space Factor

GUP deformed phase-space and axiomatic thermodynamic self-consistency

2019 ◽  
Vol 34 (06n07) ◽  
pp. 1950039
Author(s):  
Asmaa G. Shalaby
Keyword(s):  
Phase Space ◽  
Partition Function ◽  
Generalized Uncertainty Principle ◽  
Thermodynamic Quantities ◽  
Number Density ◽  
High Frequencies ◽  
Space Factor ◽  
Phase Space Factor ◽  
Set Up ◽  
Self Consistency

Based on the generalized uncertainty principle (GUP) with a deformation of the phase-space, the partition function has recently been modified. In the present work, we analyze the self-consistency of the axiomatic thermodynamics derived from the deformed partition function. First, we set up the thermodynamic quantities such as pressure, energy density, entropy and number density, then we extend the study for testing the approval of consistency. We found that the deformed phase-space satisfies the axiomatic self-consistency of thermodynamics. We would expect the effects of GUP to be more pronounced at high frequencies, but the used deformed phase-space factor would still diverge as [Formula: see text] approaches [Formula: see text].

Shape Dynamics and the Linking Theory

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Line Element ◽  
Hamiltonian Formulation ◽  
Operational Definition ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Problem Of Time ◽  
Definition Of ◽  
Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

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