High density QCD on a Lefschetz thimble?

It is sometimes speculated that the sign problem that afflicts many quantum field theories might be reduced or even eliminated by choosing an alternative domain of integration within a complexified extension of the path integral (in the spirit of the stationary phase integration method). In this paper we start to explore this possibility somewhat systematically. A first inspection reveals the presence of many difficulties but - quite surprisingly - most of them have an interesting solution. In particular, it is possible to regularize the lattice theory on a Lefschetz thimble, where the imaginary part of the action is constant and disappears from all observables. This regularization can be justified in terms of symmetries and perturbation theory. Moreover, it is possible to design a Monte Carlo algorithm that samples the configurations in the thimble. This is done by simulating, effectively, a five dimensional system. We describe the algorithm in detail and analyze its expected cost and stability. Unfortunately, the measure term also produces a phase which is not constant and it is currently very expensive to compute. This residual sign problem is expected to be much milder, as the dominant part of the integral is not affected, but we have still no convincing evidence of this. However, the main goal of this paper is to introduce a new approach to the sign problem, that seems to offer much room for improvements. An appealing feature of this approach is its generality. It is illustrated first in the simple case of a scalar field theory with chemical potential, and then extended to the more challenging case of QCD at finite baryonic density.Comment: Misleading footnote 1 corrected: locality deserves better investigations. Formula (31) corrected (we thank Giovanni Eruzzi for this observation). Note different title in journal versio

Overtwisted energy-minimizing curl eigenfields

We consider energy-minimizing divergence-free eigenfields of the curl operator in dimension three from the perspective of contact topology. We give a negative answer to a question of Etnyre and the first author by constructing curl eigenfields which minimize $L^2$ energy on their co-adjoint orbit, yet are orthogonal to an overtwisted contact structure. We conjecture that $K$-contact structures on $S^1$-bundles always define tight minimizers, and prove a partial result in this direction.Comment: published versio

On transversally elliptic operators and the quantization of manifolds with ff-structure

An $f$-structure on a manifold $M$ is an endomorphism field \phi\in\Gamma(M,\End(TM)) such that $\phi^3+\phi=0$. Any $f$-structure $\phi$ determines an almost CR structure E_{1,0}\subset T_\C M given by the $+i$-eigenbundle of $\phi$. Using a compatible metric $g$ and connection $\nabla$ on $M$, we construct an odd first-order differential operator $D$, acting on sections of $\S=\Lambda E_{0,1}^*$, whose principal symbol is of the type considered in arXiv:0810.0338. In the special case of a CR-integrable almost $\S$-structure, we show that when $\nabla$ is the generalized Tanaka-Webster connection of Lotta and Pastore, the operator $D$ is given by D = \sqrt{2}(\dbbar+\dbbar^*), where \dbbar is the tangential Cauchy-Riemann operator. We then describe two "quantizations" of manifolds with $f$-structure that reduce to familiar methods in symplectic geometry in the case that $\phi$ is a compatible almost complex structure, and to the contact quantization defined in \cite{F4} when $\phi$ comes from a contact metric structure. The first is an index-theoretic approach involving the operator $D$; for certain group actions $D$ will be transversally elliptic, and using the results in arXiv:0810.0338, we can give a Riemann-Roch type formula for its index. The second approach uses an analogue of the polarized sections of a prequantum line bundle, with a CR structure playing the role of a complex polarization.Comment: 31 page

Comparative Study Between Solid State Welding and Radiant Energy Welding Processes for Joining Metallic Glassy Ribbons

Amorphous alloys have emerged as an important class of advanced materials that own a combination of properties, such as mechanical strength, hardness, high elasticity modulus and a very good corrosion resistance. Since the number of amorphous structures alloys increased in the last decades, ways of joining such materials were studied in order to produce complex structures or increase their size. Thus, if this kind of complex products are obtained, it will diversify their applicability in multiple and various domains. For this research two ways of joining amorphous ribbons has been studied: solid state welding and radiant energy welding. For the radiant energy welding process, it was selected electron beam welding (EBW) method and for the solid-state welding process, ultrasonic welding (UW) method was chosen. Seeing that these methods have found applicability in industries, a comparative study was done in order to see which one offers the best outcome. Recently, in the last years, such products were embedded in a polymer matrix, creating thus, composite materials that have improved mechanical properties. This raised curiosity for major industries, such as aero-space, medical and automotive. Amorphous ribbons from Ni-Fe-Cr-Si-B and Al-Ni-Nd-Co alloy families were welded by EBW method, and Cu-Zr-Al amorphous ribbons were welded by the UW method. Microstructure characterization has been performed by SEM, EDX, XRD and DSC analyses

Once more on the Witten index of 3d supersymmetric YM-CS theory

The problem of counting the vacuum states in the supersymmetric 3d Yang-Mills-Chern-Simons theory is reconsidered. We resolve the controversy between its original calculation by Witten at large volumes and the calculation based on the evaluation of the effective Lagrangian in the small volume limit. We show that the latter calculation suffers from uncertainties associated with the singularities in the moduli space of classical vacua where the Born-Oppenheimer approximation breaks down. We also show that these singularities can be accurately treated in the Hamiltonian Born-Oppenheimer method, where one has to match carefully the effective wave functions on the Abelian valley and the wave functions of reduced non-Abelian QM theory near the singularities. This gives the same result as original Witten's calculation.Comment: 27 page

Noble gas and carbon isotope systematics at the seemingly inactive Ciomadul volcano (Eastern‐Central Europe, Romania): evidence for volcanic degassing

Ciomadul is the youngest volcano in the Carpathian-Pannonian Region, Eastern-Central Europe, which last erupted 30 ka. This volcano is considered to be inactive, however, combined evidence from petrologic and magnetotelluric data, as well as seismic tomography studies suggest the existence of a subvolcanic crystal mush with variable melt content. The volcanic area is characterized by high CO2 gas output rate, with a minimum of 8.7 × 103 t yr-1. We investigated 31 gas emissions at Ciomadul to constrain the origin of the volatiles. The δ13C-CO2 and 3He/4He compositions suggest the outgassing of a significant component of mantle-derived fluids. The He isotope signature in the outgassing fluids (up to 3.10 Ra) is lower than the values in the peridotite xenoliths of the nearby alkaline basalt volcanic field (R/Ra 5.95Ra±0.01) which are representative of a continental lithospheric mantle and significantly lower than MORB values. Considering the chemical characteristics of the Ciomadul dacite, including trace element and Sr- Nd and O isotope compositions, an upper crustal contamination is less probable, whereas the primary magmas could have been derived from an enriched mantle source. The low He isotopic ratios could indicate a strongly metasomatized mantle lithosphere. This could be due to infiltration of subduction-related fluids and postmetasomatic ingrowth of radiogenic He. The metasomatic fluids are inferred to have contained subducted carbonate material resulting in a heavier carbon isotope composition (13C is in the range of -1.4 to -4.6 ‰) and an increase of CO2/3He ratio. Our study shows the magmatic contribution to the emitted gases

Vacuum microelectronics devices based on the controlled electron motion in electric and magnetic fields

Several novel field emission devices are analyzed in a unitary way. The devices involve the use of field emitter arrays in a special configuration where the emitted electrons are subject to crossed electric and magnetic fields. Due to the acting electric and (magnetic) Lorentz forces, the electrons are either deviated or have a cycloid-like confined motion. The angular deviation of the electron trajectory can be used for measuring magnetic fields. The pulsed electron current produced by a cold cathode can be used to generate electromagnetic radiation. Because the electrons have a confined motion with a long trajectory length, their chance of hitting a residual gas molecule is increased. They can either excite gas molecules, which in turn emit UV-radiation when relaxing back to the stable state, or ionize them, the ionic current being correlated with the gas pressure. Accordingly, devices for generating UV-radiation and vacuum gauges can be devised. Furthermore, if the ion generation takes place in a narrow and well-defined region, then their angular deviation can be correlated with their mass. A mass spectrometer (with miniaturized dimensions and field emission electron source) can be devised on this principle

Modelling of the field emission microtriode with emitter covered with porous silicon

Electron field emission is obtained using high enough (greater than or equal to 1 V/nm) electric fields. Such local fields are usually obtained using sharp emitters. An alternative approach is to cover the otherwise blunt emitter (BE) with a porous silicon (PS) layer. The PS is composed of many fibrils with dimensions of several nm which act as ''nano-emitters''. In this article such an emitter is considered as part of a vertical field emission microtriode (FEMT). The BE has spherical tip and conical body and protrudes through the gate circular opening, allowing the FEMT operation in the collector-assisted mode. An electric field multiplication approximation is studied using both an analytical and a numerical emitter model. The field multiplication means that the fibril increases the local electric field, which is already increased by the BE as compared with the uniform field at large distances from it. This approximation is valid as long as the fibril dimensions are much smaller than the BE ones. The fibrils mutual influence on the field is studied separately and taken into account for the FEMT case. The emission current is computed through integration of the Fowler-Nordheim J(E) current density-electric field relationship over the BE and fibrils area. Comparison is provided with the case of BE not covered with PS. The emission current is obtained as function of model parameters. FEMT modelling results include transconductance, capacitance, cut-off frequency and static gain, Reference to experimental results is provided