Dimensional Reduction and the Yang-Mills Vacuum State in 2+1 Dimensions

We propose an approximation to the ground state of Yang-Mills theory, quantized in temporal gauge and 2+1 dimensions, which satisfies the Yang-Mills Schrodinger equation in both the free-field limit, and in a strong-field zero mode limit. Our proposal contains a single parameter with dimensions of mass; confinement via dimensional reduction is obtained if this parameter is non-zero, and a non-zero value appears to be energetically preferred. A method for numerical simulation of this vacuum state is developed. It is shown that if the mass parameter is fixed from the known string tension in 2+1 dimensions, the resulting mass gap deduced from the vacuum state agrees, to within a few percent, with known results for the mass gap obtained by standard lattice Monte Carlo methods.Comment: 14 pages, 9 figures. v2: Typos corrected. v3: added a new section discussing alternative (new variables) approaches, and fixed a problem with the appearance of figures in the pdf version. Version to appear in Phys Rev

Correlations of center flux in SU(2) Yang-Mills theory

By using the method of center projection the center vortex part of the gauge field is isolated and its propagator is evaluated in the center Landau gauge, which minimizes the open 3-dimensional Dirac volumes of non-trivial center links bounded by the closed 2-dimensional center vortex surfaces. The center field propagator is found to dominate the gluon propagator (in Landau gauge) in the low momentum regime and to give rise to an OPE correction to the latter of $\sqrt{\sigma} /p^3$.The screening mass of the center vortex field vanishes above the critical temperature of the deconfinement phase transition, which naturally explains the second order nature of this transition consistently with the vortex picture. Finally, the ghost propagator of maximal center gauge is found to be infrared finite and thus shows no signal of confinement.Comment: Presented at 23rd International Symposium on Lattice Field Field: Lattice 2005, Trinity College, Dublin, Ireland, 25-30 Jul 200

The role of center vortices in Gribov's confinement scenario

The connection of Gribov's confinement scenario in Coulomb gauge with the center vortex picture of confinement is investigated. For this purpose we assume a vacuum wave functional which models the infrared properties of the theory and in particular shows strict confinement, i.e. an area law of the Wilson loop. We isolate the center vortex content of this wave functional by standard lattice methods and investigate their contributions to various static propagators of the Hamilton approach to Yang-Mills theory in Coulomb gauge. We find that the infrared properties of these quantities, in particular the infrared divergence of the ghost form factor, are dominated by center vortices.Comment: 18 pages, 5 figure

Variational solution of the Yang-Mills Schr\"odinger equation in Coulomb gauge

The Yang-Mills Schr\"odinger equation is solved in Coulomb gauge for the vacuum by the variational principle using an ansatz for the wave functional, which is strongly peaked at the Gribov horizon. A coupled set of Schwinger-Dyson equations for the gluon and ghost propagators in the Yang-Mills vacuum as well as for the curvature of gauge orbit space is derived and solved in one-loop approximation. We find an infrared suppressed gluon propagator, an infrared singular ghost propagator and a almost linearly rising confinement potential.Comment: 24 pages, revtex, 13 figure

Macro environmental analysis of the electric vehicle battery second use market

The end-of-life (EOL) strategy of repurposing degraded electric vehicle (EV) batteries in second use applications holds the potential to reduce first-cost obstacles of EVs. With a prospective EV market uptake, increasing numbers of retired batteries will be available soon for battery second use (B2U). But this emerging secondary market remains unclear from a business model perspective. This paper evaluated the evolving B2U market from a macro environmental perspective to comprehend key opportunities and threats in the future

The Path to Entrepreneurship: The Role of Social Networks in Driving Entrepreneurial Learning and Education

This research aims to examine the extent to which the way entrepreneurs learn is reflected in entrepreneurship education, highlighting the existing gap between the literature on entrepreneurial learning and the practice of entrepreneurship education. To explore entrepreneurial learning in-depth, we adopted an interpretivist-constructivist approach that involves participant observation at coworking spaces and semi-structured interviews with entrepreneurs. Data were subsequently analyzed using thematic analysis. Major findings indicate that social networks play a vital role in facilitating entrepreneurial learning, with context and network serving as essential learning mechanisms. However, these elements are often disregarded in traditional entrepreneurship education approaches. This study highlights a gap in the literature where the focus of entrepreneurial learning is primarily on entrepreneurs, while entrepreneurship education primarily focuses on students and educators. The study’s contribution is its emphasis on the importance of social networks in entrepreneurial learning and its potential for redesigning entrepreneurship education. By bridging the gap between entrepreneurial learning and entrepreneurship education, it is possible to create educational approaches that more closely mimic how entrepreneurs learn in real life, potentially leading to more impactful entrepreneurial activity

Intense Field Multiphoton Ionization via Complex Dressed States: Application to the H Atom

This is the publisher's version, also available electronically from http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.39.1195.Extension of Floquet theory to include continuum as well as bound atomic states yields a practical technique for computation of multiphoton ionization rates in the region where rms field strengths approach the strength of the internal atomic fields

Stark ionization in dc and ac fields: An L2 complex-coordinate approach

This is the published version, also available here: http://dx.doi.org/10.1103/PhysRevA.27.2946.A finite-dimensional-matrix technique valid for computation of complex eigenvalues and eigenfunctions useful for discussing time evolution in both dc and ac Stark fields is presented. The complex eigenvalue parameters are those of appropriately analytically continued, time-independent Stark Hamiltonians as obtained via the complex scale transformation r→reiθ. Such a transformation distorts the continuous spectrum away from the real axis, exposing the Stark resonances, and also allowing use of finite variational expansions employing L2 basis functions chosen from a complete discrete basis. The structure of the dc and ac Stark Hamiltonians is discussed and extensive convergence studies performed in both the dc and ac cases to fully document the utility of the method. Sudden and adiabatic dc Stark time evolution is used to illustrate the power of finite-dimensional-matrix methods in describing complex, multiple-time-scale time evolution. The relationship between the ac Stark Hamiltonian used (a time-independent truncated Floquet Hamiltonian) and continued-fraction perturbation theory follows easily via use of matrix partitioning, and provides a particularly straightforward derivation of these results. Finally, some illustrative calculations of off-resonant generalized cross sections are given at low and high intensities, indicating that the method works satisfactorily at intensities the order of internal atomic field strengths. A more detailed discussion of time evolution in two-, three-, and four-photon ionization processes appears in the following paper by Holt, Raymer, and Reinhardt

Multiconfigurational Hartree-Fock theory for identical bosons in a double well

Multiconfigurational Hartree-Fock theory is presented and implemented in an investigation of the fragmentation of a Bose-Einstein condensate made of identical bosonic atoms in a double well potential at zero temperature. The approach builds in the effects of the condensate mean field and of atomic correlations by describing generalized many-body states that are composed of multiple configurations which incorporate atomic interactions. Nonlinear and linear optimization is utilized in conjunction with the variational and Hylleraas-Undheim theorems to find the optimal ground and excited states of the interacting system. The resulting energy spectrum and associated eigenstates are presented as a function of double well barrier height. Delocalized and localized single configurational states are found in the extreme limits of the simple and fragmented condensate ground states, while multiconfigurational states and macroscopic quantum superposition states are revealed throughout the full extent of barrier heights. Comparison is made to existing theories that either neglect mean field or correlation effects and it is found that contributions from both interactions are essential in order to obtain a robust microscopic understanding of the condensate's atomic structure throughout the fragmentation process.Comment: 21 pages, 13 figure