866 research outputs found
Transmission Resonance in an Infinite Strip of Phason-Defects of a Penrose Approximant Network
An exact method that analytically provides transfer matrices in finite
networks of quasicrystalline approximants of any dimensionality is discussed.
We use these matrices in two ways: a) to exactly determine the band structure
of an infinite approximant network in analytical form; b) to determine, also
analytically, the quantum resistance of a finite strip of a network under
appropriate boundary conditions. As a result of a subtle interplay between
topology and phase interferences, we find that a strip of phason-defects along
a special symmetry direction of a low 2-d Penrose approximant, leads to the
rigorous vanishing of the reflection coefficient for certain energies. A
similar behavior appears in a low 3-d approximant. This type of ``resonance" is
discussed in connection with the gap structure of the corresponding ordered
(undefected) system.Comment: 18 pages special macros jnl.tex,reforder.tex, eqnorder.te
Beyond the Dirac phase factor: Dynamical Quantum Phase-Nonlocalities in the Schroedinger Picture
Generalized solutions of the standard gauge transformation equations are
presented and discussed in physical terms. They go beyond the usual Dirac phase
factors and they exhibit nonlocal quantal behavior, with the well-known
Relativistic Causality of classical fields affecting directly the phases of
wavefunctions in the Schroedinger Picture. These nonlocal phase behaviors,
apparently overlooked in path-integral approaches, give a natural account of
the dynamical nonlocality character of the various (even static) Aharonov-Bohm
phenomena, while at the same time they seem to respect Causality. Indeed, for
particles passing through nonvanishing magnetic or electric fields they lead to
cancellations of Aharonov-Bohm phases at the observation point, generalizing
earlier semiclassical experimental observations (of Werner & Brill) to
delocalized (spread-out) quantum states. This leads to a correction of
previously unnoticed sign-errors in the literature, and to a natural
explanation of the deeper reason why certain time-dependent semiclassical
arguments are consistent with static results in purely quantal Aharonov-Bohm
configurations. These nonlocalities also provide a remedy for misleading
results propagating in the literature (concerning an uncritical use of Dirac
phase factors, that persists since the time of Feynman's work on path
integrals). They are shown to conspire in such a way as to exactly cancel the
instantaneous Aharonov-Bohm phase and recover Relativistic Causality in earlier
"paradoxes" (such as the van Kampen thought-experiment), and to also complete
Peshkin's discussion of the electric Aharonov-Bohm effect in a causal manner.
The present formulation offers a direct way to address time-dependent single-
vs double-slit experiments and the associated causal issues -- issues that have
recently attracted attention, with respect to the inability of current theories
to address them.Comment: 72 pages, 4 figures, v2 minor rephrasing of a sentence on p.4
TOPOLOGICAL INFLUENCE FROM DISTANT FIELDS ON TWO-DIMENSIONAL QUANTUM SYSTEMS
A quantum system that lies nearby a magnetic or time-varying electric field region, and that is under periodic boundary conditions parallel to the interface, is shown to exhibit a hidden Aharonov-Bohm effect (magnetic or electric), caused by fluxes that are not enclosed by, but are merely neighboring to our system – its origin being the absence of magnetic monopoles in 3D space (with corresponding spacetime generalizations). Novel possibilities then arise, where a field-free system can be dramatically affected by manipulating fields in an adjacent or even distant land, provided that these nearby fluxes are not quantized (i.e. they are fractional or irrational parts of the flux quantum). Topological effects (such as Quantum Hall types of behaviors) can therefore be induced from outside our system (that is always fieldfree and can even reside in simply-connected space). Potential novel applications are outlined, and exotic consequences in solid state physics are pointed out (i.e. the violation of Bloch theorem in a field-free quantum periodic system), while formal analogies with certain high energy physics phenomena and with some rather unexplored areas in mechanics and thermodynamics are noted
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