3,506 research outputs found
Quantum mechanics without quanta
In this paper, I argue that light is a continuous classical electromagnetic
wave, while the observed so-called quantum nature of the interaction of light
with matter is connected to the discrete (atomic) structure of matter and to
the specific nature of the light-atom interaction. From this point of view, the
Born rule for light is derived, and the double-slit experiment is analysed in
detail. I show that the double-slit experiment can be explained without using
the concept of a "photon", solely on the basis of classical electrodynamics. I
show that within this framework, the Heisenberg uncertainty principle for a
"photon" has a simple physical meaning not related to the fundamental
limitations in accuracy of the simultaneous measurement of position and
momentum or time and energy. I argue also that we can avoid the paradoxes
connected with the wave-particle duality of the electron if we consider some
classical wave field - an "electron wave" - instead of electrons as the
particles and consider the wave equations (Dirac, Klein-Gordon, Pauli and
Schrodinger) as the field equations similar to Maxwell equations for the
electromagnetic field. It is shown that such an electron field must have an
electric charge, an intrinsic angular momentum and an intrinsic magnetic moment
continuously distributed in the space. It is shown that from this perspective,
the double-slit experiment for "electrons", the Born rule, the Heisenberg
uncertainty principle and the Compton effect all have a simple explanation
within classical field theory. The proposed perspective allows consideration of
quantum mechanics not as a theory of particles but as a classical field theory
similar to Maxwell electrodynamics.Comment: 61 pages, 3 figures, Quantum Studies: Mathematics and Foundations,
201
Correlated non-perturbative electron dynamics with quantum trajectories
An approach to electron correlation effects in atoms that uses quantum
trajectories is presented. A comparison with the exact quantum mechanical
results for 1D Helium atom shows that the major features of the correlated
ground state distribution and of the strong field ionization dynamics are
reproduced with quantum trajectories. The intra-atomic resonant transitions are
described accurately by a trajectory ensemble. The present approach reduces
significantly the computational time and it can be used for both bound and
ionizing electrons.Comment: 9 pages, 4 figure
Analysis of models for quantum transport of electrons in graphene layers
We present and analyze two mathematical models for the self consistent
quantum transport of electrons in a graphene layer. We treat two situations.
First, when the particles can move in all the plane \RR^2, the model takes
the form of a system of massless Dirac equations coupled together by a
selfconsistent potential, which is the trace in the plane of the graphene of
the 3D Poisson potential associated to surface densities. In this case, we
prove local in time existence and uniqueness of a solution in H^s(\RR^2), for
which includes in particular the energy space H^{1/2}(\RR^2). The
main tools that enable to reach are the dispersive Strichartz
estimates that we generalized here for mixed quantum states. Second, we
consider a situation where the particles are constrained in a regular bounded
domain . In order to take into account Dirichlet boundary conditions
which are not compatible with the Dirac Hamiltonian , we propose a
different model built on a modified Hamiltonian displaying the same energy band
diagram as near the Dirac points. The well-posedness of the system in
this case is proved in , the domain of the fractional order Dirichlet
Laplacian operator, for
Big consequences of small changes (Non-locality and non-linearity of Hartree-Fock equations)
It is demonstrated that non-locality and non-linearity of Hartree-Fock
equations dramatically affect the properties of their solutions that
essentially differ from solutions of Schr?dinger equation with a local
potential. Namely, it acquires extra zeroes, has different coordinate
asymptotic, violates so-called gauge-invariance, has different scattering
phases at zero energy, has in some cases several solutions with the same set of
quantum numbers, usually equivalent expressions of current and Green's
functions became non-equivalent. These features result in a number of
consequences for probabilities of some physical processes, leading e. g. to
extra width of atomic Giant resonances and enhance considerably the ionization
probability of inner atomic electrons by a strong field.Comment: 16 pages, 3 figure
Computational relativistic quantum dynamics and its application to relativistic tunneling and Kapitza-Dirac scattering
Computational methods are indispensable to study the quantum dynamics of
relativistic light-matter interactions in parameter regimes where analytical
methods become inapplicable. We present numerical methods for solving the
time-dependent Dirac equation and the time-dependent Klein-Gordon equation and
their implementation on high performance graphics cards. These methods allow us
to study tunneling from hydrogen-like highly charged ions in strong laser
fields and Kapitza-Dirac scattering in the relativistic regime
Quantum Cellular Neural Networks
We have previously proposed a way of using coupled quantum dots to construct
digital computing elements - quantum-dot cellular automata (QCA). Here we
consider a different approach to using coupled quantum-dot cells in an
architecture which, rather that reproducing Boolean logic, uses a physical
near-neighbor connectivity to construct an analog Cellular Neural Network
(CNN).Comment: 7 pages including 3 figure
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