2,790 research outputs found
Periodic and discrete Zak bases
Weyl's displacement operators for position and momentum commute if the
product of the elementary displacements equals Planck's constant. Then, their
common eigenstates constitute the Zak basis, each state specified by two phase
parameters. Upon enforcing a periodic dependence on the phases, one gets a
one-to-one mapping of the Hilbert space on the line onto the Hilbert space on
the torus. The Fourier coefficients of the periodic Zak bases make up the
discrete Zak bases. The two bases are mutually unbiased. We study these bases
in detail, including a brief discussion of their relation to Aharonov's modular
operators, and mention how they can be used to associate with the single degree
of freedom of the line a pair of genuine qubits.Comment: 15 pages, 3 figures; displayed abstract is shortened, see the paper
for the complete abstrac
Entropy on the von Neumann lattice and its evaluation
Based on the recently introduced averaging procedure in phase space, a new
type of entropy is defined on the von Neumann lattice. This quantity can be
interpreted as a measure of uncertainty associated with simultaneous
measurement of the position and momentum observables in the discrete subset of
the phase space. Evaluating for a class of the coherent states, it is shown
that this entropy takes a stationary value for the ground state, modulo a unit
cell of the lattice in such a class. This value for the ground state depends on
the ratio of the position lattice spacing and the momentum lattice spacing. It
is found that its minimum is realized for the perfect square lattice, i.e.,
absence of squeezing. Numerical evaluation of this minimum gives 1.386....Comment: 14 pages, no figures; J. Phys. A, in pres
Mechanism for Multiple Ligand Recognition by the Human Transferrin Receptor
Transferrin receptor 1 (TfR) plays a critical role in cellular iron import for most higher organisms. Cell surface TfR binds to circulating iron-loaded transferrin (Fe-Tf) and transports it to acidic endosomes, where low pH promotes iron to dissociate from transferrin (Tf) in a TfR-assisted process. The iron-free form of Tf (apo-Tf) remains bound to TfR and is recycled to the cell surface, where the complex dissociates upon exposure to the slightly basic pH of the blood. Fe-Tf competes for binding to TfR with HFE, the protein mutated in the iron-overload disease hereditary hemochromatosis. We used a quantitative surface plasmon resonance assay to determine the binding affinities of an extensive set of site-directed TfR mutants to HFE and Fe-Tf at pH 7.4 and to apo-Tf at pH 6.3. These results confirm the previous finding that Fe-Tf and HFE compete for the receptor by binding to an overlapping site on the TfR helical domain. Spatially distant mutations in the TfR protease-like domain affect binding of Fe-Tf, but not iron-loaded Tf C-lobe, apo-Tf, or HFE, and mutations at the edge of the TfR helical domain affect binding of apo-Tf, but not Fe-Tf or HFE. The binding data presented here reveal the binding footprints on TfR for Fe-Tf and apo-Tf. These data support a model in which the Tf C-lobe contacts the TfR helical domain and the Tf N-lobe contacts the base of the TfR protease-like domain. The differential effects of some TfR mutations on binding to Fe-Tf and apo-Tf suggest differences in the contact points between TfR and the two forms of Tf that could be caused by pH-dependent conformational changes in Tf, TfR, or both. From these data, we propose a structure-based model for the mechanism of TfR-assisted iron release from Fe-Tf
Hofstadter Problem on the Honeycomb and Triangular Lattices: Bethe Ansatz Solution
We consider Bloch electrons on the honeycomb lattice under a uniform magnetic
field with flux per cell. It is shown that the problem factorizes
to two triangular lattices. Treating magnetic translations as Heisenberg-Weyl
group and by the use of its irreducible representation on the space of theta
functions, we find a nested set of Bethe equations, which determine the
eigenstates and energy spectrum. The Bethe equations have simple form which
allows to consider them further in the limit by the technique
of Thermodynamic Bethe Ansatz and analyze Hofstadter problem for the irrational
flux.Comment: 7 pages, 2 figures, Revte
Symmetry of Quantum Torus with Crossed Product Algebra
In this paper, we study the symmetry of quantum torus with the concept of
crossed product algebra. As a classical counterpart, we consider the orbifold
of classical torus with complex structure and investigate the transformation
property of classical theta function. An invariant function under the group
action is constructed as a variant of the classical theta function. Then our
main issue, the crossed product algebra representation of quantum torus with
complex structure under the symplectic group is analyzed as a quantum version
of orbifolding.
We perform this analysis with Manin's so-called model II quantum theta
function approach. The symplectic group Sp(2n,Z) satisfies the consistency
condition of crossed product algebra representation. However, only a subgroup
of Sp(2n,Z) satisfies the consistency condition for orbifolding of quantum
torus.Comment: LaTeX 17pages, changes in section 3 on crossed product algebr
Emergent Classicality via Commuting Position and Momentum Operators
Any account of the emergence of classicality from quantum theory must address
the fact that the quantum operators representing positions and momenta do not
commute, whereas their classical counterparts suffer no such restrictions. To
address this, we revive an old idea of von Neumann, and seek a pair of
commuting operators which are, in a specific sense, "close" to the
canonical non-commuting position and momentum operators, . The
construction of such operators is related to the problem of finding complete
sets of orthonormal phase space localized states, a problem severely limited by
the Balian-Low theorem. Here these limitations are avoided by restricting
attention to situations in which the density matrix is reasonably decohered
(i.e., spread out in phase space).Comment: To appear in Proceedings of the 2008 DICE Conferenc
Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
We present a unified theory for wave-packet dynamics of electrons in crystals
subject to perturbations varying slowly in space and time. We derive the
wave-packet energy up to the first order gradient correction and obtain all
kinds of Berry-phase terms for the semiclassical dynamics and the quantization
rule. For electromagnetic perturbations, we recover the orbital magnetization
energy and the anomalous velocity purely within a single-band picture without
invoking inter-band couplings. For deformations in crystals, besides a
deformation potential, we obtain a Berry-phase term in the Lagrangian due to
lattice tracking, which gives rise to new terms in the expressions for the
wave-packet velocity and the semiclassical force. For multiple-valued
displacement fields surrounding dislocations, this term manifests as a Berry
phase, which we show to be proportional to the Burgers vector around each
dislocation.Comment: 12 pages, RevTe
von Neumann Lattices in Finite Dimensions Hilbert Spaces
The prime number decomposition of a finite dimensional Hilbert space reflects
itself in the representations that the space accommodates. The representations
appear in conjugate pairs for factorization to two relative prime factors which
can be viewed as two distinct degrees freedom. These, Schwinger's quantum
degrees of freedom, are uniquely related to a von Neumann lattices in the phase
space that characterizes the Hilbert space and specifies the simultaneous
definitions of both (modular) positions and (modular) momenta. The area in
phase space for each quantum state in each of these quantum degrees of freedom,
is shown to be exactly , Planck's constant.Comment: 16 page
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