Would Bohr be born if Bohm were born before Born?

I discuss a hypothetical historical context in which a Bohm-like deterministic interpretation of the Schrodinger equation could have been proposed before the Born probabilistic interpretation and argue that in such a context the Copenhagen (Bohr) interpretation would probably have never achieved great popularity among physicists.Comment: 5 pages, revised, accepted for publication in Am. J. Phy

Probability in relativistic quantum mechanics and foliation of spacetime

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be non-negative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of spacetime must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.Comment: 9 pages, 3 figures, revised, new references, to appear in Int. J. Mod. Phys.

Quantum Determinism from Quantum General Covariance

The requirement of general covariance of quantum field theory (QFT) naturally leads to quantization based on the manifestly covariant De Donder-Weyl formalism. To recover the standard noncovariant formalism without violating covariance, fields need to depend on time in a specific deterministic manner. This deterministic evolution of quantum fields is recognized as a covariant version of the Bohmian hidden-variable interpretation of QFT.Comment: 6 pages, revised, new references, Honorable Mention of the Gravity Research Foundation 2006 Essay Competition, version to appear in Int. J. Mod. Phys.

Comparing quasiparticle H2_2O level alignment on anatase and rutile TiO2_2

Knowledge of the molecular frontier levels' alignment in the ground state can be used to predict the photocatalytic activity of an interface. The position of the adsorbate's highest occupied molecular orbital (HOMO) levels relative to the substrate's valence band maximum (VBM) in the interface describes the favorability of photogenerated hole transfer from the VBM to the adsorbed molecule. This is a key quantity for assessing and comparing H$_2$O photooxidation activities on two prototypical photocatalytic TiO$_2$ surfaces: anatase (A)-TiO$_2$(101) and rutile (R)-TiO$_2$(110). Using the projected density of states (DOS) from state-of-the-art quasiparticle (QP) $G_0W_0$ calculations, we assess the relative photocatalytic activity of intact and dissociated H$_2$O on coordinately unsaturated (Ti$_{\textit{cus}}$) sites of idealized stoichiometric A-TiO$_2$(101)/R-TiO$_2$(110) and bridging O vacancies (O$_{\textit{br}}^{\textit{vac}}$) of defective A-TiO$_{2-x}$(101)/R-TiO$_{2-x}$(110) surfaces ($x=\frac{1}{4},\frac{1}{8}$) for various coverages. Such a many-body treatment is necessary to correctly describe the anisotropic screening of electron-electron interactions at a photocatalytic interface, and hence obtain accurate interfacial level alignments. The more favorable ground state HOMO level alignment for A-TiO$_2$(101) may explain why the anatase polymorph shows higher photocatalytic activities than the rutile polymorph. Our results indicate that (1) hole trapping is more favored on A-TiO$_2$(101) than R-TiO$_2$(110) and (2) HO@Ti$_{\textit{cus}}$ is more photocatalytically active than intact H$_2$O@Ti$_{\textit{cus}}$

Level alignment of a prototypical photocatalytic system: Methanol on TiO2(110)

Photocatalytic and photovoltaic activity depends on the optimal alignment of electronic levels at the molecule/semiconductor interface. Establishing level alignment experimentally is complicated by the uncertain chemical identity of the surface species. We address the assignment of the occupied and empty electronic levels for the prototypical photocatalytic system of methanol on a rutile TiO2 (110) surface. Using many-body quasiparticle (QP) techniques we show that the frontier levels measured in ultraviolet photoelectron and two photon photoemission spectroscopy experiments can be assigned with confidence to the molecularly chemisorbed methanol, rather than its decomposition product, the methoxy species. We find the highest occupied molecular orbital (HOMO) of the methoxy species is much closer to the valence band maximum, suggesting why it is more photocatalytically active than the methanol molecule. We develop a general semi-quantitative model for predicting many-body QP energies based on the appropriate description of electronic screening within the bulk, molecular or vacuum regions of the wavefunctions at molecule/semiconductor interfaces.Comment: 5 pages, 5 figure

AdS-inspired noncommutative gravity on the Moyal plane

We consider noncommutative gravity on a space with canonical noncommutativity that is based on the commutative MacDowell-Mansouri action. Gravity is treated as gauge theory of the noncommutative $SO(1,3)_\star$ group and the Seiberg-Witten (SW) map is used to express noncommutative fields in terms of the corresponding commutative fields. In the commutative limit the noncommutative action reduces to the Einstein-Hilbert action plus the cosmological term and the topological Gauss-Bonnet term. After the SW expansion in the noncommutative parameter the first order correction to the action, as expected, vanishes. We calculate the second order correction and write it in a manifestly gauge covariant way.Comment: 22 pages, no figures, final versio

Bayesian inference for ultralow velocity zones in the Earth's lowermost mantle: complex ULVZ beneath the east of the Philippines

Ultralow velocity zones (ULVZs) are small-scale structures with a sharp decrease in S and P wave velocity, and an increase in the density on the top of the Earth's core-mantle boundary. The ratio of S and P wave velocity reduction and density anomaly are important to understanding whether ULVZs consist of partial melt or chemically distinct material. However, existing methods such as forward waveform modeling that utilize 1-D and 2-D Earth-structure models face challenges when trying to uniquely quantify ULVZ properties because of inherent nonuniqueness and nonlinearity. This paper develops a Bayesian inversion for ULVZ parameters and uncertainties with rigorous noise treatment to address these challenges. The posterior probability density of the ULVZ parameters (the solution to the inverse problem) is sampled by the Metropolis-Hastings algorithm. To improve sampling efficiency, parallel tempering is applied by simulating a sequence of tempered Markov chains in parallel and allowing information exchange between chains. First, the Bayesian inversion is applied to simulated noisy data for a realistic ULVZ model. Then, measured data sampling the lowermost mantle under the Philippine Sea are considered. Cluster analysis and visual waveform inspection suggest that two distinct classes of ScP (S waves converted to, and reflected as, P waves) waves exist in this region. The distinct waves likely correspond to lateral variability in the lowermost mantle properties in a NE-SW direction. For the NE area, Bayesian model selection identifies a two-layer model with a gradual density increase as a function of depth as optimal. This complex ULVZ structure can be due to the percolation of iron-enriched, molten material in the lowermost mantle. The results for the SW area are more difficult to interpret, which may be due to the limited number of data available (too few waveforms to appropriately reduce noise) and/or complex 2-D and 3-D structures that cannot be explained properly by the 1-D models required by our inversion approach. In particular, the complex waveforms require highly layered 1-D models to fit the data. These models appear physically unreasonable and suggest that the SW region cannot be explained by 1-D structure.National Collaborative Research Infrastructure Strategy (NCRIS) and the Education Investment Fund (EIF3)

Inappropriateness of the Rindler quantization

It is argued that the Rindler quantization is not a correct approach to study the effects of acceleration on quantum fields. First, the "particle"-detector approach based on the Minkowski quantization is not equivalent to the approach based on the Rindler quantization. Second, the event horizon, which plays the essential role in the Rindler quantization, cannot play any physical role for a local noninertial observer.Comment: 3 pages, accepted for publication in Mod. Phys. Lett.

Discrete representations of n-dimensional wave equations and their applications to quantum mechanics

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1992.Includes bibliographical references (p. 63-67).by Hrvoje J. HrgovcÌiÄ.Ph.D