Matrix product states and the quantum max-flow/min-cut conjectures

In this note we discuss the geometry of matrix product states with periodic boundary conditions and provide three infinite sequences of examples where the quantum max-flow is strictly less than the quantum min-cut. In the first we fix the underlying graph to be a 4-cycle and verify a prediction of Hastings that inequality occurs for infinitely many bond dimensions. In the second we generalize this result to a 2d-cycle. In the third we show that the 2d-cycle with periodic boundary conditions gives inequality for all d when all bond dimensions equal two, namely a gap of at least 2^{d-2} between the quantum max-flow and the quantum min-cut.Comment: 12 pages, 3 figures - Final version accepted for publication on J. Math. Phy

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

Search for Kaluza-Klein Graviton Emission in ppˉp\bar{p} Collisions at s=1.8\sqrt{s}=1.8 TeV using the Missing Energy Signature

We report on a search for direct Kaluza-Klein graviton production in a data sample of 84 ${pb}^{-1}$ of \ppb collisions at $\sqrt{s}$ = 1.8 TeV, recorded by the Collider Detector at Fermilab. We investigate the final state of large missing transverse energy and one or two high energy jets. We compare the data with the predictions from a $3+1+n$-dimensional Kaluza-Klein scenario in which gravity becomes strong at the TeV scale. At 95% confidence level (C.L.) for $n$=2, 4, and 6 we exclude an effective Planck scale below 1.0, 0.77, and 0.71 TeV, respectively.Comment: Submitted to PRL, 7 pages 4 figures/Revision includes 5 figure

Measurement of the average time-integrated mixing probability of b-flavored hadrons produced at the Tevatron

We have measured the number of like-sign (LS) and opposite-sign (OS) lepton pairs arising from double semileptonic decays of $b$ and $\bar{b}$-hadrons, pair-produced at the Fermilab Tevatron collider. The data samples were collected with the Collider Detector at Fermilab (CDF) during the 1992-1995 collider run by triggering on the existence of $\mu \mu$ and $e \mu$ candidates in an event. The observed ratio of LS to OS dileptons leads to a measurement of the average time-integrated mixing probability of all produced $b$-flavored hadrons which decay weakly, $\bar{\chi} = 0.152 \pm 0.007$ (stat.) $\pm 0.011$ (syst.), that is significantly larger than the world average $\bar{\chi} = 0.118 \pm 0.005$.Comment: 47 pages, 10 figures, 15 tables Submitted to Phys. Rev.

Search for a vector-like quark T′ → tH via the diphoton decay mode of the Higgs boson in proton-proton collisions at s \sqrt{s} = 13 TeV

A search for the electroweak production of a vector-like quark T′, decaying to a top quark and a Higgs boson is presented. The search is based on a sample of proton-proton collision events recorded at the LHC at = 13 TeV, corresponding to an integrated luminosity of 138 fb−1. This is the first T′ search that exploits the Higgs boson decay to a pair of photons. For narrow isospin singlet T′ states with masses up to 1.1 TeV, the excellent diphoton invariant mass resolution of 1–2% results in an increased sensitivity compared to previous searches based on the same production mechanism. The electroweak production of a T′ quark with mass up to 960 GeV is excluded at 95% confidence level, assuming a coupling strength κT = 0.25 and a relative decay width Γ/MT′ < 5%

Measurement of the Higgs boson inclusive and differential fiducial production cross sections in the diphoton decay channel with pp collisions at s \sqrt{s} = 13 TeV

The measurements of the inclusive and differential fiducial cross sections of the Higgs boson decaying to a pair of photons are presented. The analysis is performed using proton-proton collisions data recorded with the CMS detector at the LHC at a centre-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 137 fb$^{−1}$. The inclusive fiducial cross section is measured to be $σ_{fid}$=73.4$^{+5.4}_{−5.3}$(stat)$^{+2.4}_{−2.2}$(syst) fb, in agreement with the standard model expectation of 75.4 ± 4.1 fb. The measurements are also performed in fiducial regions targeting different production modes and as function of several observables describing the diphoton system, the number of additional jets present in the event, and other kinematic observables. Two double differential measurements are performed. No significant deviations from the standard model expectations are observed

Search for Higgs Boson Decay to a Charm Quark-Antiquark Pair in Proton-Proton Collisions at √s = 13 TeV

A search for the standard model Higgs boson decaying to a charm quark-antiquark pair, H→c¯c, produced in association with a leptonically decaying V (W or Z) boson is presented. The search is performed with proton-proton collisions at √s=13  TeV collected by the CMS experiment, corresponding to an integrated luminosity of 138  fb−1. Novel charm jet identification and analysis methods using machine learning techniques are employed. The analysis is validated by searching for Z→c¯c in VZ events, leading to its first observation at a hadron collider with a significance of 5.7 standard deviations. The observed (expected) upper limit on σ(VH)B(H→c¯c) is 0.94 (0.50+0.22−0.15)pb at 95% confidence level (C.L.), corresponding to 14 (7.6+3.4−2.3) times the standard model prediction. For the Higgs-charm Yukawa coupling modifier, κc, the observed (expected) 95% C.L. interval is 1.1<|κc|<5.5 (|κc|<3.4), the most stringent constraint to date