Bohmian mechanics in relativistic quantum mechanics, quantum field theory and string theory

I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle trajectories, the problem of particle creation and destruction, the Bohmian interpretation of fermionic fields and the intrinsically Bohmian quantization of fields and strings based on the De Donder-Weyl covariant canonical formalism.Comment: 6 pages, talk given at Third International Workshop DICE2006, Piombino, Italy, September 11-15, 200

Boson-fermion unification, superstrings, and Bohmian mechanics

Bosonic and fermionic particle currents can be introduced in a more unified way, with the cost of introducing a preferred spacetime foliation. Such a unified treatment of bosons and fermions naturally emerges from an analogous superstring current, showing that the preferred spacetime foliation appears only at the level of effective field theory, not at the fundamental superstring level. The existence of the preferred spacetime foliation allows an objective definition of particles associated with quantum field theory in curved spacetime. Such an objective definition of particles makes the Bohmian interpretation of particle quantum mechanics more appealing. The superstring current allows a consistent Bohmian interpretation of superstrings themselves, including a Bohmian description of string creation and destruction in terms of string splitting. The Bohmian equations of motion and the corresponding probabilistic predictions are fully relativistic covariant and do not depend on the preferred foliation.Comment: 30 pages, 1 figure, revised, to appear in Found. Phy

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.

Shot Noise Probing of Magnetic Ordering in Zigzag Graphene Nanoribbons

The nonequilibrium time-dependent fluctuations of charge current have recently emerged as a sensitive experimental tool to probe ballistic transport through evanescent wave functions introduced into clean wide and short graphene strips by the attached metallic electrodes. We demonstrate that such "pseudo-diffusive" shot noise can be substantially modified in zigzag graphene nanoribbon (ZGNR) due to the topology of its edges responsible for localized states that facilitate ferromagnetic ordering along the edge when Coulomb interaction is taken into account. Thus, the shot noise enhancement of unpolarized, and even more sensitively of spin-polarized, charge currents injected into ZGNR will act as an all-electrical and edge-sensitive probe of such low-dimensional magnetism.Comment: 5 pages, 3 color figures; references update

Quantum Transparency of Anderson Insulator Junctions: Statistics of Transmission Eigenvalues, Shot Noise, and Proximity Conductance

We investigate quantum transport through strongly disordered barriers, made of a material with exceptionally high resistivity that behaves as an Anderson insulator or a ``bad metal'' in the bulk, by analyzing the distribution of Landauer transmission eigenvalues for a junction where such barrier is attached to two clean metallic leads. We find that scaling of the transmission eigenvalue distribution with the junction thickness (starting from the single interface limit) always predicts a non-zero probability to find high transmission channels even in relatively thick barriers. Using this distribution, we compute the zero frequency shot noise power (as well as its sample-to-sample fluctuations) and demonstrate how it provides a single number characterization of non-trivial transmission properties of different types of disordered barriers. The appearance of open conducting channels, whose transmission eigenvalue is close to one, and corresponding violent mesoscopic fluctuations of transport quantities explain at least some of the peculiar zero-bias anomalies in the Anderson-insulator/superconductor junctions observed in recent experiments [Phys. Rev. B {\bf 61}, 13037 (2000)]. Our findings are also relevant for the understanding of the role of defects that can undermine quality of thin tunnel barriers made of conventional band-insulators.Comment: 9 pages, 8 color EPS figures; one additional figure on mesoscopic fluctuations of Fano facto

Comment on "Classical interventions in quantum systems II. Relativistic invariance"

In a recent paper [Phys. Rev. A 61, 022117 (2000)], quant-ph/9906034, A. Peres argued that quantum mechanics is consistent with special relativity by proposing that the operators that describe time evolution do not need to transform covariantly, although the measurable quantities need to transform covariantly. We discuss the weaknesses of this proposal.Comment: 4 pages, to appear in Phys. Rev.

Optimizing the speed of a Josephson junction

We review the application of dynamical mean-field theory to Josephson junctions and study how to maximize the characteristic voltage IcRn which determines the width of a rapid single flux quantum pulse, and thereby the operating speed in digital electronics. We study a wide class of junctions ranging from SNS, SCmS (where Cm stands for correlated metal), SINIS (where the insulating layer is formed from a screened dipole layer), and SNSNS structures. Our review is focused on a survey of the physical results; the formalism has been developed elsewhere.Comment: (36 pages, 15 figures, to appear in Int. J. Mod. Phys. B

Quantum mechanics: Myths and facts

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.Comment: 51 pages, pedagogic review, revised, new references, to appear in Found. Phy

Typical medium theory of Anderson localization: A local order parameter approach to strong disorder effects

We present a self-consistent theory of Anderson localization that yields a simple algorithm to obtain \emph{typical local density of states} as an order parameter, thereby reproducing the essential features of a phase-diagram of localization-delocalization quantum phase transition in the standard lattice models of disordered electron problem. Due to the local character of our theory, it can easily be combined with dynamical mean-field approaches to strongly correlated electrons, thus opening an attractive avenue for a genuine {\em non-perturbative} treatment of the interplay of strong interactions and strong disorder.Comment: 7 pages, 4 EPS figures, revised version to appear in Europhysics Letter