Infinite Infrared Regularization and a State Space for the Heisenberg Algebra

We present a method for the construction of a Krein space completion for spaces of test functions, equipped with an indefinite inner product induced by a kernel which is more singular than a distribution of finite order. This generalizes a regularization method for infrared singularities in quantum field theory, introduced by G. Morchio and F. Strocchi, to the case of singularites of infinite order. We give conditions for the possibility of this procedure in terms of local differential operators and the Gelfand- Shilov test function spaces, as well as an abstract sufficient condition. As a model case we construct a maximally positive definite state space for the Heisenberg algebra in the presence of an infinite infrared singularity.Comment: 18 pages, typos corrected, journal-ref added, reference adde

On the discrete spectrum of spin-orbit Hamiltonians with singular interactions

We give a variational proof of the existence of infinitely many bound states below the continuous spectrum for spin-orbit Hamiltonians (including the Rashba and Dresselhaus cases) perturbed by measure potentials thus extending the results of J.Bruening, V.Geyler, K.Pankrashkin: J. Phys. A 40 (2007) F113--F117.Comment: 10 pages; to appear in Russian Journal of Mathematical Physics (memorial volume in honor of Vladimir Geyler). Results improved in this versio

Effect of external pressure on the magnetic properties of RRCoAsO (RR = La, Pr, Sm): a μ\muSR study

We report on a detailed investigation of the itinerant ferromagnets LaCoAsO, PrCoAsO and SmCoAsO performed by means of muon spin spectroscopy upon the application of external hydrostatic pressures $p$ up to $2.4$ GPa. These materials are shown to be magnetically hard in view of the weak dependence of both critical temperatures $T_{C}$ and internal fields at the muon site on $p$. In the cases $R$ = La and Sm, the behaviour of the internal field is substantially unaltered up to $p = 2.4$ GPa. A much richer phenomenology is detected in PrCoAsO instead, possibly associated with a strong $p$ dependence of the statistical population of the two different crystallographic sites for the muon. Surprisingly, results are notably different from what is observed in the case of the isostructural compounds $R$CoPO, where the full As/P substitution is already inducing a strong chemical pressure within the lattice but $p$ is still very effective in further affecting the magnetic properties.Comment: 8 pages, 9 figure

CeRu4_4Sn6_6: heavy fermions emerging from a Kondo-insulating state

The combination of low-temperature specific-heat and nuclear-magnetic-resonance (NMR) measurements reveals important information of the ground-state properties of CeRu$_4$Sn$_6$, which has been proposed as a rare example of a tetragonal Kondo-insulator (KI). The NMR spin-latticerelaxation rate $1/T_1$ deviates from the Korringa law below 100 K signaling the onset of an energy gap $\Delta E_g1/k_B \simeq 30$K. This gap is stable against magnetic fields up to 10 T. Below 10 K, however, unusual low-energy excitations of in-gap states are observed, which depend strongly on the field H. The specific heat C detects these excitations in the form of an enhanced Sommerfeld coefficient $\gamma = C(T)/T$ : In zero field, $\gamma$ increases steeply below 5 K, reaching a maximum at 0.1 K, and then saturates at $\gamma = 0.6$ J/molK$^2$. This maximum is shifted to higher temperatures with increasing field suggesting a residual density of states at the Fermi level developing a spin gap $\Delta E_g2$. A simple model, based on two narrow quasiparticle bands located at the Fermi level - which cross the Fermi level in zero field at 0.022 states/meV f.u. - can account qualitatively as well as quantitatively for the measured observables. In particular, it is demonstrated that fitting our data of both specific heat and NMR to the model, incorporating a Ce magnetic moment of $\mu = \Delta E_g1/\mu_{0H} \simeq 1 \mu_B$, leads to the prediction of the field dependence of the gap. Our measurements rule out the presence of a quantum critical point as the origin for the enhanced $\gamma$ in CeRu$_4$Sn$_6$ and suggest that this arises rather from correlated, residual in-gap states at the Fermi level. This work provides a fundamental route for future investigations into the phenomenon of narrow-gap formation in the strongly correlated class of systemComment: 11 pages, 13 figure

Spin Gap in the Single Spin-1/2 Chain Cuprate Sr1.9_{1.9}Ca0.1_{0.1}CuO3_3

We report $^{63}$Cu nuclear magnetic resonance and muon spin rotation measurements on the S=1/2 antiferromagnetic Heisenberg spin chain compound Sr$_{1.9}$Ca$_{0.1}$CuO$_3$. An exponentially decreasing spin-lattice relaxation rate 1/T$_1$ indicates the opening of a spin gap. This behavior is very similar to what has been observed for the cognate zigzag spin chain compound Sr$_{0.9}$Ca$_{0.1}$CuO$_2$, and confirms that the occurrence of a spin gap upon Ca doping is independent of the interchain exchange coupling $J'$. Our results therefore generally prove the appearance of a spin gap in an antiferromagnetic Heisenberg spin chain induced by a local bond disorder of the intrachain exchange coupling $J$. A low temperature upturn of 1/T$_1$ evidences growing magnetic correlations. However, zero field muon spin rotation measurements down to 1.5 K confirm the absence of magnetic order in this compound which is most likely suppressed by the opening of the spin gap.Comment: 5 pages, 4 figure

Toward a noncytotoxic glioblastoma therapy: blocking MCP-1 with the MTZ Regimen

To improve the prognosis of glioblastoma, we developed an adjuvant treatment directed to a neglected aspect of glioblastoma growth, the contribution of nonmalignant monocyte lineage cells (MLCs) (monocyte, macrophage, microglia, dendritic cells) that infiltrated a main tumor mass. These nonmalignant cells contribute to glioblastoma growth and tumor homeostasis. MLCs comprise of approximately 10%-30% of glioblastoma by volume. After integration into the tumor mass, these become polarized toward an M2 immunosuppressive, pro-angiogenic phenotype that promotes continued tumor growth. Glioblastoma cells initiate and promote this process by synthesizing 13 kDa MCP-1 that attracts circulating monocytes to the tumor. Infiltrating monocytes, after polarizing toward an M2 phenotype, synthesize more MCP-1, forming an amplification loop. Three noncytotoxic drugs, an antibiotic - minocycline, an antihypertensive drug - telmisartan, and a bisphosphonate - zoledronic acid, have ancillary attributes of MCP-1 synthesis inhibition and could be re-purposed, singly or in combination, to inhibit or reverse MLC-mediated immunosuppression, angiogenesis, and other growth-enhancing aspects. Minocycline, telmisartan, and zoledronic acid - the MTZ Regimen - have low-toxicity profiles and could be added to standard radiotherapy and temozolomide. Re-purposing older drugs has advantages of established safety and low drug cost. Four core observations support this approach: 1) malignant glioblastoma cells require a reciprocal trophic relationship with nonmalignant macrophages or microglia to thrive;2) glioblastoma cells secrete MCP-1 to start the cycle, attracting MLCs, which subsequently also secrete MCP-1 perpetuating the recruitment cycle;3) increasing cytokine levels in the tumor environment generate further immunosuppression and tumor growth;and 4) MTZ regimen may impede MCP-1-driven processes, thereby interfering with glioblastoma growth

Parametrizations of density matrices

This article gives a brief overview of some recent progress in the characterization and parametrization of density matrices of finite dimensional systems. We discuss in some detail the Bloch-vector and Jarlskog parametrizations and mention briefly the coset parametrization. As applications of the Bloch parametrization we discuss the trace invariants for the case of time dependent Hamiltonians and in some detail the dynamics of three-level systems. Furthermore, the Bloch vector of two-qubit systems as well as the use of the polarization operator basis is indicated. As the main application of the Jarlskog parametrization we construct density matrices for composite systems. In addition, some recent related articles are mentioned without further discussion.Comment: 31 pages. v2: 32 pages, Abstract and Introduction rewritten and Conclusion section added, references adde