586 research outputs found
Quantum Speed Limit for Perfect State Transfer in One Dimension
The basic idea of spin chain engineering for perfect quantum state transfer
(QST) is to find a set of coupling constants in the Hamiltonian, such that a
particular state initially encoded on one site will evolve freely to the
opposite site without any dynamical controls. The minimal possible evolution
time represents a speed limit for QST. We prove that the optimal solution is
the one simulating the precession of a spin in a static magnetic field. We also
argue that, at least for solid-state systems where interactions are local, it
is more realistic to characterize the computation power by the couplings than
the initial energy.Comment: 5 pages, no figure; improved versio
Effective non-Markovian description of a system interacting with a bath
We study a harmonic system coupled to chain of first neighbor interacting
oscillators. After deriving the exact dynamics of the system, we prove that one
can effectively describe the exact dynamics by considering a suitable shorter
chain. We provide the explicit expression for such an effective dynamics and we
provide an upper bound on the error one makes considering it instead of the
dynamics of the full chain. We eventually prove how error, timescale and number
of modes in the truncated chain are related
How to construct spin chains with perfect state transfer
It is shown how to systematically construct the quantum spin chains with
nearest-neighbor interactions that allow perfect state transfer (PST). Sets of
orthogonal polynomials (OPs) are in correspondence with such systems. The key
observation is that for any admissible one-excitation energy spectrum, the
weight function of the associated OPs is uniquely prescribed. This entails the
complete characterization of these PST models with the mirror symmetry property
arising as a corollary. A simple and efficient algorithm to obtain the
corresponding Hamiltonians is presented. A new model connected to a special
case of the symmetric -Racah polynomials is offered. It is also explained
how additional models with PST can be derived from a parent system by removing
energy levels from the one-excitation spectrum of the latter. This is achieved
through Christoffel transformations and is also completely constructive in
regards to the Hamiltonians.Comment: 7 page
Inverse eigenvalue problem for discrete three-diagonal Sturm-Liouville operator and the continuum limit
In present article the self-contained derivation of eigenvalue inverse
problem results is given by using a discrete approximation of the Schroedinger
operator on a bounded interval as a finite three-diagonal symmetric Jacobi
matrix. This derivation is more correct in comparison with previous works which
used only single-diagonal matrix. It is demonstrated that inverse problem
procedure is nothing else than well known Gram-Schmidt orthonormalization in
Euclidean space for special vectors numbered by the space coordinate index. All
the results of usual inverse problem with continuous coordinate are reobtained
by employing a limiting procedure, including the Goursat problem -- equation in
partial derivatives for the solutions of the inversion integral equation.Comment: 19 pages There were made some additions (and reformulations) to the
text making the derivation of the results more precise and understandabl
Perfect State Transfer, Effective Gates and Entanglement Generation in Engineered Bosonic and Fermionic Networks
We show how to achieve perfect quantum state transfer and construct effective
two-qubit gates between distant sites in engineered bosonic and fermionic
networks. The Hamiltonian for the system can be determined by choosing an
eigenvalue spectrum satisfying a certain condition, which is shown to be both
sufficient and necessary in mirror-symmetrical networks. The natures of the
effective two-qubit gates depend on the exchange symmetry for fermions and
bosons. For fermionic networks, the gates are entangling (and thus universal
for quantum computation). For bosonic networks, though the gates are not
entangling, they allow two-way simultaneous communications. Protocols of
entanglement generation in both bosonic and fermionic engineered networks are
discussed.Comment: RevTeX4, 6 pages, 1 figure; replaced with a more general example and
clarified the sufficient and necessary condition for perfect state transfe
Hamiltonian tomography in an access-limited setting without state initialization
We propose a scheme for the determination of the coupling parameters in a
chain of interacting spins. This requires only time-resolved measurements over
a single particle, simple data post-processing and no state initialization or
prior knowledge of the state of the chain. The protocol fits well into the
context of quantum-dynamics characterization and is efficient even when the
spin-chain is affected by general dissipative and dephasing channels. We
illustrate the performance of the scheme by analyzing explicit examples and
discuss possible extensions.Comment: 4 pages, 2 figures, RevTeX
On an initial value Reissner-Sagoci problem
A rigid circular cylinder is cemented to the otherwise stress-free surface of a homogeneous isotropic elastic half-space. The cylinder is rotated through a small angle and then released from rest. During the subsequent motion the cylinder remains cemented to the half-space and the problem is the determination of its motion. The problem is solved by setting up an integral equation for the Laplace transform of the angular displacement. Numerical values for the solution of this equation for large and small values of the Laplace parameter s = i[omega] can be obtained from the known results for the steady-state Reissner-Sagoci problem. For intermediate values of the parameter the equation is solved by means of Chebyshev approximation. The inversion of the Laplace transform is carried out by using a Laguerre polynomial approximation technique.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32750/1/0000119.pd
The Amplitude of Non-Equilibrium Quantum Interference in Metallic Mesoscopic Systems
We study the influence of a DC bias voltage V on quantum interference
corrections to the measured differential conductance in metallic mesoscopic
wires and rings. The amplitude of both universal conductance fluctuations (UCF)
and Aharonov-Bohm effect (ABE) is enhanced several times for voltages larger
than the Thouless energy. The enhancement persists even in the presence of
inelastic electron-electron scattering up to V ~ 1 mV. For larger voltages
electron-phonon collisions lead to the amplitude decaying as a power law for
the UCF and exponentially for the ABE. We obtain good agreement of the
experimental data with a model which takes into account the decrease of the
electron phase-coherence length due to electron-electron and electron-phonon
scattering.Comment: New title, refined analysis. 7 pages, 3 figures, to be published in
Europhysics Letter
Multi-indexed (q-)Racah Polynomials
As the second stage of the project multi-indexed orthogonal polynomials, we
present, in the framework of `discrete quantum mechanics' with real shifts in
one dimension, the multi-indexed (q-)Racah polynomials. They are obtained from
the (q-)Racah polynomials by multiple application of the discrete analogue of
the Darboux transformations or the Crum-Krein-Adler deletion of `virtual state'
vectors, in a similar way to the multi-indexed Laguerre and Jacobi polynomials
reported earlier. The virtual state vectors are the `solutions' of the matrix
Schr\"odinger equation with negative `eigenvalues', except for one of the two
boundary points.Comment: 29 pages. The type II (q-)Racah polynomials are deleted because they
can be obtained from the type I polynomials. To appear in J.Phys.
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