Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating Systems

We consider the statistical mechanics of a general relativistic one-dimensional self-gravitating system. The system consists of $N$-particles coupled to lineal gravity and can be considered as a model of $N$ relativistically interacting sheets of uniform mass. The partition function and one-particle distitrubion functions are computed to leading order in $1/c$ where $c$ is the speed of light; as $c\to\infty$ results for the non-relativistic one-dimensional self-gravitating system are recovered. We find that relativistic effects generally cause both position and momentum distribution functions to become more sharply peaked, and that the temperature of a relativistic gas is smaller than its non-relativistic counterpart at the same fixed energy. We consider the large-N limit of our results and compare this to the non-relativistic case.Comment: latex, 60 pages, 22 figure

Choice of Consistent Family, and Quantum Incompatibility

In consistent history quantum theory, a description of the time development of a quantum system requires choosing a framework or consistent family, and then calculating probabilities for the different histories which it contains. It is argued that the framework is chosen by the physicist constructing a description of a quantum system on the basis of questions he wishes to address, in a manner analogous to choosing a coarse graining of the phase space in classical statistical mechanics. The choice of framework is not determined by some law of nature, though it is limited by quantum incompatibility, a concept which is discussed using a two-dimensional Hilbert space (spin half particle). Thus certain questions of physical interest can only be addressed using frameworks in which they make (quantum mechanical) sense. The physicist's choice does not influence reality, nor does the presence of choices render the theory subjective. On the contrary, predictions of the theory can, in principle, be verified by experimental measurements. These considerations are used to address various criticisms and possible misunderstandings of the consistent history approach, including its predictive power, whether it requires a new logic, whether it can be interpreted realistically, the nature of ``quasiclassicality'', and the possibility of ``contrary'' inferences.Comment: Minor revisions to bring into conformity with published version. Revtex 29 pages including 1 page with figure

A Schroedinger link between non-equilibrium thermodynamics and Fisher information

It is known that equilibrium thermodynamics can be deduced from a constrained Fisher information extemizing process. We show here that, more generally, both non-equilibrium and equilibrium thermodynamics can be obtained from such a Fisher treatment. Equilibrium thermodynamics corresponds to the ground state solution, and non-equilibrium thermodynamics corresponds to excited state solutions, of a Schroedinger wave equation (SWE). That equation appears as an output of the constrained variational process that extremizes Fisher information. Both equilibrium- and non-equilibrium situations can thereby be tackled by one formalism that clearly exhibits the fact that thermodynamics and quantum mechanics can both be expressed in terms of a formal SWE, out of a common informational basis.Comment: 12 pages, no figure

The evaluation of single Bessel function sums

We examine convergent representations for the sums of Bessel functions X∞ n=1 Jν(nx) nα (x > 0) and X∞ n=1 Kν(nz) nα (<(z) > 0), together with their alternating versions, by a Mellin transform approach. We take α to be a real parameter with ν > − 1 2 for the first sum and ν ≥ 0 for the second sum. Such representations enable easy computation of the series in the limit x or z → 0+. Particular attention is given to logarithmic cases that occur for certain values of α and

Swimming of a sphere in a viscous incompressible fluid with inertia

The swimming of a sphere immersed in a viscous incompressible fluid with inertia is studied for surface modulations of small amplitude on the basis of the Navier-Stokes equations. The mean swimming velocity and the mean rate of dissipation are expressed as quadratic forms in term of the surface displacements. With a choice of a basis set of modes the quadratic forms correspond to two hermitian matrices. Optimization of the mean swimming velocity for given rate of dissipation requires the solution of a generalized eigenvalue problem involving the two matrices. It is found for surface modulations of low multipole order that the optimal swimming efficiency depends in intricate fashion on a dimensionless scale number involving the radius of the sphere, the period of the cycle, and the kinematic viscosity of the fluid.Comment: 19 pages, 4 figure

Serre presentations of Lie superalgebras

An analogue of Serre's theorem is established for finite dimensional simple Lie superalgebras, which describes presentations in terms of Chevalley generators and Serre type relations relative to all possible choices of Borel subalgebras. The proof of the theorem is conceptually transparent; it also provides an alternative approach to Serre's theorem for ordinary Lie algebras.Comment: 45 page

Frequency discriminator/phase detector

Circuit provides dual function of frequency discriminator/phase detector which reduces frequency acquisition time without adding to circuit complexity. Both frequency discriminators, in evaluated frequency discriminator/phase detector circuits, are effective two decades above and below center frequency