Reconstruction of potential energy profiles from multiple rupture time distributions

We explore the mathematical and numerical aspects of reconstructing a potential energy profile of a molecular bond from its rupture time distribution. While reliable reconstruction of gross attributes, such as the height and the width of an energy barrier, can be easily extracted from a single first passage time (FPT) distribution, the reconstruction of finer structure is ill-conditioned. More careful analysis shows the existence of optimal bond potential amplitudes (represented by an effective Peclet number) and initial bond configurations that yield the most efficient numerical reconstruction of simple potentials. Furthermore, we show that reconstruction of more complex potentials containing multiple minima can be achieved by simultaneously using two or more measured FPT distributions, obtained under different physical conditions. For example, by changing the effective potential energy surface by known amounts, additional measured FPT distributions improve the reconstruction. We demonstrate the possibility of reconstructing potentials with multiple minima, motivate heuristic rules-of-thumb for optimizing the reconstruction, and discuss further applications and extensions.Comment: 20 pages, 9 figure

Reaching optimally oriented molecular states by laser kicks

We present a strategy for post-pulse orientation aiming both at efficiency and maximal duration within a rotational period. We first identify the optimally oriented states which fulfill both requirements. We show that a sequence of half-cycle pulses of moderate intensity can be devised for reaching these target states.Comment: 4 pages, 3 figure

Evidence for competition between the superconducting and the pseudogap state in (BiPb)_2(SrLa)_2CuO_{6+\delta} from muon-spin rotation experiments

The in-plane magnetic penetration depth \lambda_{ab} in optimally doped (BiPb)_2(SrLa)_2CuO_{6+\delta} (OP Bi2201) was studied by means of muon-spin rotation. The measurements of \lambda_{ab}^{-2}(T) are inconsistent with a simple model of a d-wave order parameter and a uniform quasiparticle weight around the Fermi surface. The data are well described assuming the angular gap symmetry obtained in ARPES experiments [Phys. Rev. Lett {\bf 98}, 267004 (2007)], where it was shown that the superconducting gap in OP Bi2201 exists only in segments of the Fermi surface near the nodes. We find that the remaining parts of the Fermi surface, which are strongly affected by the pseudogap state, do not contribute significantly to the superconducting condensate. Our data provide evidence that high temperature superconductivity and pseudogap behavior in cuprates are competing phenomena.Comment: 5 pages, 3 figure

A Generalization of Mathieu Subspaces to Modules of Associative Algebras

We first propose a generalization of the notion of Mathieu subspaces of associative algebras $\mathcal A$, which was introduced recently in [Z4] and [Z6], to $\mathcal A$-modules $\mathcal M$. The newly introduced notion in a certain sense also generalizes the notion of submodules. Related with this new notion, we also introduce the sets $\sigma(N)$ and $\tau(N)$ of stable elements and quasi-stable elements, respectively, for all $R$-subspaces $N$ of $\mathcal A$-modules $\mathcal M$, where $R$ is the base ring of $\mathcal A$. We then prove some general properties of the sets $\sigma(N)$ and $\tau(N)$. Furthermore, examples from certain modules of the quasi-stable algebras [Z6], matrix algebras over fields and polynomial algebras are also studied.Comment: A new case has been added; some mistakes and misprints have been corrected. Latex, 31 page

Laser control for the optimal evolution of pure quantum states

Starting from an initial pure quantum state, we present a strategy for reaching a target state corresponding to the extremum (maximum or minimum) of a given observable. We show that a sequence of pulses of moderate intensity, applied at times when the average of the observable reaches its local or global extremum, constitutes a strategy transferable to different control issues. Among them, post-pulse molecular alignment and orientation are presented as examples. The robustness of such strategies with respect to experimentally relevant parameters is also examined.Comment: 16 pages, 9 figure

Observation of plaquette fluctuations in the spin-1/2 honeycomb lattice

Quantum spin liquids are materials that feature quantum entangled spin correlations and avoid magnetic long-range order at T = 0 K. Particularly interesting are two-dimensional honeycomb spin lattices where a plethora of exotic quantum spin liquids have been predicted. Here, we experimentally study an effective S=1/2 Heisenberg honeycomb lattice with competing nearest and next-nearest neighbor interactions. We demonstrate that YbBr$_3$ avoids order down to at least T=100 mK and features a dynamic spin-spin correlation function with broad continuum scattering typical of quantum spin liquids near a quantum critical point. The continuum in the spin spectrum is consistent with plaquette type fluctuations predicted by theory. Our study is the experimental demonstration that strong quantum fluctuations can exist on the honeycomb lattice even in the absence of Kitaev-type interactions, and opens a new perspective on quantum spin liquids.Comment: 32 pages, 7 Figure

Incommensurate Magnetic Order in TbTe3_3

We report a neutron diffraction study of the magnetic phase transitions in the charge-density-wave (CDW) TbTe$_3$ compound. We discover that in the paramagnetic phase there are strong 2D-like magnetic correlations, consistent with the pronounced anisotropy of the chemical structure. A long-range incommensurate magnetic order emerges in TbTe$_3$ at $T_{mag1}$ = 5.78 K as a result of continuous phase transitions. We observe that near the temperature $T_{mag1}$ the magnetic Bragg peaks appear around the position (0,0,0.24) (or its rational multiples), that is fairly close to the propagation vector $(0,0,0.29)$ associated with the CDW phase transition in TbTe$_3$. This suggests that correlations leading to the long-range magnetic order in TbTe$_3$ are linked to the modulations that occur in the CDW state

Continuity of the four-point function of massive ϕ44\phi_4^4-theory above threshold

In this paper we prove that the four-point function of massive \vp_4^4-theory is continuous as a function of its independent external momenta when posing the renormalization condition for the (physical) mass on-shell. The proof is based on integral representations derived inductively from the perturbative flow equations of the renormalization group. It closes a longstanding loophole in rigorous renormalization theory in so far as it shows the feasibility of a physical definition of the renormalized coupling.Comment: 23 pages; to appear in Rev. Math. Physics few corrections, two explanatory paragraphs adde