29,019 research outputs found
Correlations of chaotic eigenfunctions: a semiclassical analysis
We derive a semiclassical expression for an energy smoothed autocorrelation
function defined on a group of eigenstates of the Schr\"odinger equation. The
system we considered is an energy-conserved Hamiltonian system possessing
time-invariant symmetry. The energy smoothed autocorrelation function is
expressed as a sum of three terms. The first one is analogous to Berry's
conjecture, which is a Bessel function of the zeroth order. The second and the
third terms are trace formulae made from special trajectories. The second term
is found to be direction dependent in the case of spacing averaging, which
agrees qualitatively with previous numerical observations in high-lying
eigenstates of a chaotic billiard.Comment: Revtex, 13 pages, 1 postscript figur
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Kinosternon integrum
Number of Pages: 6Integrative BiologyGeological Science
Lower bounds for communication capacities of two-qudit unitary operations
We show that entangling capacities based on the Jamiolkowski isomorphism may
be used to place lower bounds on the communication capacities of arbitrary
bipartite unitaries. Therefore, for these definitions, the relations which have
been previously shown for two-qubit unitaries also hold for arbitrary
dimensions. These results are closely related to the theory of the
entanglement-assisted capacity of channels. We also present more general
methods for producing ensembles for communication from initial states for
entanglement creation.Comment: 9 pages, 2 figures, comments welcom
Topological Aspects of the Non-adiabatic Berry Phase
The topology of the non-adiabatic parameter space bundle is discussed for
evolution of exact cyclic state vectors in Berry's original example of split
angular momentum eigenstates. It turns out that the change in topology occurs
at a critical frequency. The first Chern number that classifies these bundles
is proportional to angular momentum. The non-adiabatic principal bundle over
the parameter space is not well-defined at the critical frequency.Comment: 14 pages, Dep. of Physics, Uni. of Texas at Austin, Austin, Texas
78712, to appear in J. Physics
Geometric gauge potentials and forces in low-dimensional scattering systems
We introduce and analyze several low-dimensional scattering systems that
exhibit geometric phase phenomena. The systems are fully solvable and we
compare exact solutions of them with those obtained in a Born-Oppenheimer
projection approximation. We illustrate how geometric magnetism manifests in
them, and explore the relationship between solutions obtained in the diabatic
and adiabatic pictures. We provide an example, involving a neutral atom dressed
by an external field, in which the system mimics the behavior of a charged
particle that interacts with, and is scattered by, a ferromagnetic material. We
also introduce a similar system that exhibits Aharonov-Bohm scattering. We
propose some practical applications. We provide a theoretical approach that
underscores universality in the appearance of geometric gauge forces. We do not
insist on degeneracies in the adiabatic Hamiltonian, and we posit that the
emergence of geometric gauge forces is a consequence of symmetry breaking in
the latter.Comment: (Final version, published in Phy. Rev. A. 86, 042704 (2012
Stabilization of solitons in PT models with supersymmetry by periodic management
We introduce a system based on dual-core nonlinear waveguides with the
balanced gain and loss acting separately in the cores. The system features a
"supersymmetry" when the gain and loss are equal to the inter-core coupling.
This system admits a variety of exact solutions (we focus on solitons), which
are subject to a specific subexponential instability. We demonstrate that the
application of a "management", in the form of periodic simultaneous switch of
the sign of the gain, loss, and inter-coupling, effectively stabilizes
solitons, without destroying the supersymmetry. The management turns the
solitons into attractors, for which an attraction basin is identified. The
initial amplitude asymmetry and phase mismatch between the components
transforms the solitons into quasi-stable breathers.Comment: In press EPL 201
On the measurement problem for a two-level quantum system
A geometric approach to quantum mechanics with unitary evolution and
non-unitary collapse processes is developed. In this approach the Schrodinger
evolution of a quantum system is a geodesic motion on the space of states of
the system furnished with an appropriate Riemannian metric. The measuring
device is modeled by a perturbation of the metric. The process of measurement
is identified with a geodesic motion of state of the system in the perturbed
metric. Under the assumption of random fluctuations of the perturbed metric,
the Born rule for probabilities of collapse is derived. The approach is applied
to a two-level quantum system to obtain a simple geometric interpretation of
quantum commutators, the uncertainty principle and Planck's constant. In light
of this, a lucid analysis of the double-slit experiment with collapse and an
experiment on a pair of entangled particles is presented.Comment: for related papers, see http://www.uwc.edu/dept/math/faculty/kryukov
A Class of Parameter Dependent Commuting Matrices
We present a novel class of real symmetric matrices in arbitrary dimension
, linearly dependent on a parameter . The matrix elements satisfy a set
of nontrivial constraints that arise from asking for commutation of pairs of
such matrices for all , and an intuitive sufficiency condition for the
solvability of certain linear equations that arise therefrom. This class of
matrices generically violate the Wigner von Neumann non crossing rule, and is
argued to be intimately connected with finite dimensional Hamiltonians of
quantum integrable systems.Comment: Latex, Added References, Typos correcte
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