Notes on the Third Law of Thermodynamics.I

We analyze some aspects of the third law of thermodynamics. We first review both the entropic version (N) and the unattainability version (U) and the relation occurring between them. Then, we heuristically interpret (N) as a continuity boundary condition for thermodynamics at the boundary T=0 of the thermodynamic domain. On a rigorous mathematical footing, we discuss the third law both in Carath\'eodory's approach and in Gibbs' one. Carath\'eodory's approach is fundamental in order to understand the nature of the surface T=0. In fact, in this approach, under suitable mathematical conditions, T=0 appears as a leaf of the foliation of the thermodynamic manifold associated with the non-singular integrable Pfaffian form $\delta Q_{rev}$. Being a leaf, it cannot intersect any other leaf $S=$ const. of the foliation. We show that (N) is equivalent to the requirement that T=0 is a leaf. In Gibbs' approach, the peculiar nature of T=0 appears to be less evident because the existence of the entropy is a postulate; nevertheless, it is still possible to conclude that the lowest value of the entropy has to belong to the boundary of the convex set where the function is defined.Comment: 29 pages, 2 figures; RevTex fil

Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem

The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann's 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the long-time behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the "quantum H-theorem", is actually a much weaker statement than Boltzmann's classical H-theorem, the other theorem, which he calls the "quantum ergodic theorem", is a beautiful and very non-trivial result. It expresses a fact we call "normal typicality" and can be summarized as follows: For a "typical" finite family of commuting macroscopic observables, every initial wave function $\psi_0$ from a micro-canonical energy shell so evolves that for most times $t$ in the long run, the joint probability distribution of these observables obtained from $\psi_t$ is close to their micro-canonical distribution.Comment: 34 pages LaTeX, no figures; v2: minor improvements and additions. The English translation of von Neumann's article is available as arXiv:1003.213

Hydrodynamical Description of 200 A GeV/c S+Au Collisions: Hadron and Electromagnetic Spectra

We study relativistic S+Au collisions at 200 A GeV/c using a hydrodynamical approach. We test various equations of state (EOSs), which are used to describe the strongly interacting matter at densities attainable in the CERN-SPS heavy ion experiments. For each EOS, suitable initial conditions can be determined to reproduce the experimental hadron spectra; this emphasizes the ambiguity between the initial conditions and the EOS in such an approach. Simultaneously, we calculate the resulting thermal photon and dielectron spectra, and compare with experiments. If one allows the excitation of resonance states with increasing temperature, the electro-magnetic signals from scenarios with and without phase transition are very similar and are not resolvable within the current experimental resolution. With regard to the CERES dilepton data, none of the EOSs considered, in conjunction with the standard leading order dilepton rates, succeed in reproducing the observed excess of dileptons below the rho peak. Our work, however, suggests that an improved measurement of the photon and dilepton spectra has the potential to strongly constrain the EOS.Comment: Uses REVTeX, 48 pages, 13 Postscript figure

Search for Large Extra Spatial Dimensions in Dimuon Production with the D0 Detector

We present the results of a search for the effects of large extra spatial dimensions in $p{\bar p}$ collisions at $\sqrt{s} =$ 1.96 TeV in events containing a pair of energetic muons. The data correspond to 246 \ipb of integrated luminosity collected by the \D0 experiment at the Fermilab Tevatron Collider. Good agreement with the expected background was found, yielding no evidence for large extra dimensions. We set 95% C.L. lower limits on the fundamental Planck scale between 0.85 TeV and 1.27 TeV within several formalisms. These are the most stringent limits achieved in the dimuon channel to date.Comment: 8 pages, 3 figures, 1 table. Published in Phys. Rev. Lett. Minor changes in v2 to match the published versio

Cell-Sorting at the A/P Boundary in the Drosophila Wing Primordium: A Computational Model to Consolidate Observed Non-Local Effects of Hh Signaling

Non-intermingling, adjacent populations of cells define compartment boundaries; such boundaries are often essential for the positioning and the maintenance of tissue-organizers during growth. In the developing wing primordium of Drosophila melanogaster, signaling by the secreted protein Hedgehog (Hh) is required for compartment boundary maintenance. However, the precise mechanism of Hh input remains poorly understood. Here, we combine experimental observations of perturbed Hh signaling with computer simulations of cellular behavior, and connect physical properties of cells to their Hh signaling status. We find that experimental disruption of Hh signaling has observable effects on cell sorting surprisingly far from the compartment boundary, which is in contrast to a previous model that confines Hh influence to the compartment boundary itself. We have recapitulated our experimental observations by simulations of Hh diffusion and transduction coupled to mechanical tension along cell-to-cell contact surfaces. Intriguingly, the best results were obtained under the assumption that Hh signaling cannot alter the overall tension force of the cell, but will merely re-distribute it locally inside the cell, relative to the signaling status of neighboring cells. Our results suggest a scenario in which homotypic interactions of a putative Hh target molecule at the cell surface are converted into a mechanical force. Such a scenario could explain why the mechanical output of Hh signaling appears to be confined to the compartment boundary, despite the longer range of the Hh molecule itself. Our study is the first to couple a cellular vertex model describing mechanical properties of cells in a growing tissue, to an explicit model of an entire signaling pathway, including a freely diffusible component. We discuss potential applications and challenges of such an approach

Search for charged Higgs bosons decaying to top and bottom quarks in ppbar collisions

We describe a search for production of a charged Higgs boson, q \bar{q'} -> H^+, reconstructed in the t\bar{b} final state in the mass range 180 <= M_{H^+} <= 300 GeV. The search was undertaken at the Fermilab Tevatron collider with a center-of-mass energy sqrt{s} = 1.96 TeV and uses 0.9 fb^{-1} of data collected with the D0 detector. We find no evidence for charged Higgs boson production and set upper limits on the production cross section in the Types I, II and III two-Higgs-doublet models (2HDMs). An excluded region in the (M_{H^+},tan\beta) plane for Type I 2HDM is presented.Comment: Submitted to Phys. Rev. Letter

Measurement of the B0_s semileptonic branching ratio to an orbitally excited D_s** state, Br(B0_s -> Ds1(2536) mu nu)

In a data sample of approximately 1.3 fb-1 collected with the D0 detector between 2002 and 2006, the orbitally excited charm state D_s1(2536) has been observed with a measured mass of 2535.7 +/- 0.6 (stat) +/- 0.5 (syst) MeV via the decay mode B0_s -> D_s1(2536) mu nu X. A first measurement is made of the branching ratio product Br(b(bar) -> D_s1(2536) mu nu X).Br(D_s1(2536)->D* K0_S). Assuming that D_s1(2536) production in semileptonic decay is entirely from B0_s, an extraction of the semileptonic branching ratio Br(B0_s -> D_s1(2536) mu nu X) is made.Comment: 7 pages, 2 figures, LaTeX, version with minor changes as accepted by Phys. Rev. Let

Measurement of the forward-backward charge asymmetry and extraction of sin^2Theta^{eff}_W in ppbar -> Z/\gamma^{*}+X -> e+e+X events produced at \sqrt{s}=1.96 TeV

We present a measurement of the forward-backward charge asymmetry ($A_{FB}$) in $p\bar{p} \to Z/\gamma^{*}+X \to e^+e^-+X$ events at a center-of-mass energy of 1.96 TeV using 1.1 fb$^{-1}$ of data collected with the D0 detector at the Fermilab Tevatron collider. $A_{FB}$ is measured as a function of the invariant mass of the electron-positron pair, and found to be consistent with the standard model prediction. We use the $A_{FB}$ measurement to extract the effective weak mixing angle $sin^2Theta^{eff}_W = 0.2327 \pm 0.0018 (stat.) \pm 0.0006 (syst.)$.Comment: 7 Pages, 1 Figure, 3 Tables, Accepted by Phys. Rev. Let

Simultaneous measurement of the ratio B(t->Wb)/B(t->Wq) and the top quark pair production cross section with the D0 detector at sqrt(s)=1.96 TeV

We present the first simultaneous measurement of the ratio of branching fractions, R=B(t->Wb)/B(t->Wq), with q being a d, s, or b quark, and the top quark pair production cross section sigma_ttbar in the lepton plus jets channel using 0.9 fb-1 of ppbar collision data at sqrt(s)=1.96 TeV collected with the D0 detector. We extract R and sigma_ttbar by analyzing samples of events with 0, 1 and >= 2 identified b jets. We measure R = 0.97 +0.09-0.08 (stat+syst) and sigma_ttbar = 8.18 +0.90-0.84 (stat+syst)} +/-0.50 (lumi) pb, in agreement with the standard model prediction.Comment: submitted to Phys.Rev.Letter

Measurement of the lifetime of the B_c meson in the semileptonic decay channel

Using approximately 1.3 fb-1 of data collected by the D0 detector between 2002 and 2006, we measure the lifetime of the B_c meson in the B_c -> J/psi mu nu X final state. A simultaneous unbinned likelihood fit to the J/\psi+mu invariant mass and lifetime distributions yields a signal of 881 +/- 80 (stat) candidates and a lifetime measurement of \tau(B_c) = 0.448 +0.038 -0.036 (stat) +/- 0.032 (syst) ps.Comment: 7 pages, 2 figures, submitted to Phys. Rev. Let