79 research outputs found
Does a functional integral really need a Lagrangian?
Path integral formulation of quantum mechanics (and also other equivalent
formulations) depends on a Lagrangian and/or Hamiltonian function that is
chosen to describe the underlying classical system. The arbitrariness presented
in this choice leads to a phenomenon called Quantization ambiguity. For example
both and L_2=e^\dot{q} are suitable Lagrangians on a
classical level (), but quantum mechanically they are
diverse. This paper presents a simple rearrangement of the path integral to a
surface functional integral. It is shown that the surface functional integral
formulation gives transition probability amplitude which is free of any
Lagrangian/Hamiltonian and requires just the underlying classical equations of
motion. A simple example examining the functionality of the proposed method is
considered.Comment: 4 pages, published version, references added, comments are welcom
Noncommutative Lagrange Mechanics
It is proposed how to impose a general type of ''noncommutativity'' within
classical mechanics from first principles. Formulation is performed in
completely alternative way, i.e. without any resort to fuzzy and/or star
product philosophy, which are extensively applied within noncommutative quantum
theories. Newton-Lagrange noncommutative equations of motion are formulated and
their properties are analyzed from the pure geometrical point of view. It is
argued that the dynamical quintessence of the system consists in its kinetic
energy (Riemannian metric) specifying Riemann-Levi-Civita connection and thus
the inertia geodesics of the free motion. Throughout the paper,
''noncommutativity'' is considered as an internal geometric structure of the
configuration space, which can not be ''observed'' per se. Manifestation of the
noncommutative phenomena is mediated by the interaction of the system with
noncommutative background under the consideration. The simplest model of the
interaction (minimal coupling) is proposed and it is shown that guiding affine
connection is modified by the quadratic analog of the Lorentz electromagnetic
force (contortion term).Comment: This is a contribution to the Proc. of the 3-rd Microconference
"Analytic and Algebraic Methods III"(June 19, 2007, Prague, Czech Republic),
published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Spin relaxation mechanism in graphene: resonant scattering by magnetic impurities
It is proposed that the observed small (100 ps) spin relaxation time in
graphene is due to resonant scattering by local magnetic moments. At
resonances, magnetic moments behave as spin hot spots: the spin-flip scattering
rates are as large as the spin-conserving ones, as long as the exchange
interaction is greater than the resonance width. Smearing of the resonance
peaks by the presence of electron-hole puddles gives quantitative agreement
with experiment, for about 1 ppm of local moments. While the local moments can
come from a variety of sources, we specifically focus on hydrogen adatoms. We
perform first-principles supercell calculations and introduce an effective
Hamiltonian to obtain realistic input parameters for our mechanism.Comment: 5 pages, 3 figures + Suppl. material (3 pages, 5 figures
Functional integral for non-Lagrangian systems
A novel functional integral formulation of quantum mechanics for
non-Lagrangian systems is presented. The new approach, which we call "stringy
quantization," is based solely on classical equations of motion and is free of
any ambiguity arising from Lagrangian and/or Hamiltonian formulation of the
theory. The functionality of the proposed method is demonstrated on several
examples. Special attention is paid to the stringy quantization of systems with
a general A-power friction force . Results for are
compared with those obtained in the approaches by Caldirola-Kanai, Bateman and
Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon
approach are discussed as well.Comment: 14 pages, 7 figures, corrected typo
Resonant scattering by magnetic impurities as a model for spin relaxation in bilayer graphene
We propose that the observed spin-relaxation in bilayer graphene is due to
resonant scattering by magnetic impurities. We analyze a resonant scattering
model due to adatoms on both dimer and non-dimer sites, finding that only the
former give narrow resonances at the charge neutrality point. Opposite to
single-layer graphene, the measured spin-relaxation rate in graphene bilayer
increases with carrier density. Although it has been commonly argued that a
different mechanism must be at play for the two structures, our model explains
this behavior rather naturally in terms of different broadening scales for the
same underlying resonant processes. Not only our results---using robust and
first-principles inspired parameters---agree with experiment, they also predict
an experimentally testable sharp decrease of the spin-relaxation rate at high
carrier densities.Comment: 6 pages, 3 figures + 2 pages Suppl. Materia
Grassmann Electrodynamics and General Relativity
The aim of this paper is to present a short introduction to supergeometry on
pure odd supermanifolds. (Pseudo)differential forms, Cartan calculus (DeRham
differential, Lie derivative, "inner" product), metric, inner product,
Killing's vector fields, Hodge star operator, integral forms, co-differential
and connection on odd Riemannian supermanifolds are introduced. The
electrodynamics and Einstein relativity with anti-commuting variables only are
formulated modifying the geometry beyond classical (even, bosonic) theories
appropriately. Extension of these ideas to general supermanifolds is
straightforward. All this "odd business" (in both meanings of the word "odd")
is based on classical geometrical analogy.Comment: 16 pages. submitted to Journal of Geometry and Physic
Trivial and inverted Dirac bands, and emergence of quantum spin Hall states in graphene on transition-metal dichalcogenides
Proximity orbital and spin-orbital effects of graphene on monolayer
transition-metal dichalcogenides (TMDCs) are investigated from
first-principles. The Dirac band structure of graphene is found to lie within
the semiconducting gap of TMDCs for sulfides and selenides, while it merges
with the valence band for tellurides. In the former case the proximity-induced
staggered potential gaps and spin-orbit couplings (all on the meV scale) of the
Dirac electrons are established by fitting to a phenomenological effective
Hamiltonian. While graphene on MoS, MoSe, and WS has a
topologically trivial band structure, graphene on WSe exhibits inverted
bands. Using a realistic tight-binding model we find topologically protected
helical edge states for graphene zigzag nanoribbons on WSe, demonstrating
the quantum spin Hall effect. This model also features "half-topological
states", which are protected against time-reversal disorder on one edge only.Comment: 10 pages, 11 figure
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