246 research outputs found
Spectroscopy of a Cooper-Pair box in the Autler-Townes configuration
A theoretical spectroscopic analysis of a microwave driven superconducting
charge qubit (Cooper-pair box coupled) to an RLC oscillator model is performed.
By treating the oscillator as a probe through the backreaction effect of the
qubit on the oscillator circuit, we extract frequency splitting features
analogous to the Autler-Townes effect from quantum optics, thereby extending
the analogies between superconducting and quantum optical phenomenology. These
features are found in a frequency band that avoids the need for high frequency
measurement systems and therefore may be of use in qubit characterization and
coupling schemes. In addition we find this frequency band can be adjusted to
suit an experimental frequency regime by changing the oscillator frequency.Comment: 13 pages, 7 figures. v2: Revised version after referee comments.
Accepted for publication by Physical Review
Edgeworth Expansion of the Largest Eigenvalue Distribution Function of GUE Revisited
We derive expansions of the resolvent
Rn(x;y;t)=(Qn(x;t)Pn(y;t)-Qn(y;t)Pn(x;t))/(x-y) of the Hermite kernel Kn at the
edge of the spectrum of the finite n Gaussian Unitary Ensemble (GUEn) and the
finite n expansion of Qn(x;t) and Pn(x;t). Using these large n expansions, we
give another proof of the derivation of an Edgeworth type theorem for the
largest eigenvalue distribution function of GUEn. We conclude with a brief
discussion on the derivation of the probability distribution function of the
corresponding largest eigenvalue in the Gaussian Orthogonal Ensemble (GOEn) and
Gaussian Symplectic Ensembles (GSEn)
The Coulomb phase shift revisited
We investigate the Coulomb phase shift, and derive and analyze new and more
precise analytical formulae. We consider next to leading order terms to the
Stirling approximation, and show that they are important at small values of the
angular momentum and other regimes. We employ the uniform approximation.
The use of our expressions in low energy scattering of charged particles is
discussed and some comparisons are made with other approximation methods.Comment: 13 pages, 5 figures, 1 tabl
Spherical harmonics and integration in superspace
In this paper the classical theory of spherical harmonics in R^m is extended
to superspace using techniques from Clifford analysis. After defining a
super-Laplace operator and studying some basic properties of polynomial
null-solutions of this operator, a new type of integration over the supersphere
is introduced by exploiting the formal equivalence with an old result of
Pizzetti. This integral is then used to prove orthogonality of spherical
harmonics of different degree, Green-like theorems and also an extension of the
important Funk-Hecke theorem to superspace. Finally, this integration over the
supersphere is used to define an integral over the whole superspace and it is
proven that this is equivalent with the Berezin integral, thus providing a more
sound definition of the Berezin integral.Comment: 22 pages, accepted for publication in J. Phys.
Decoherence, Correlation, and Unstable Quantum States in Semiclassical Cosmology
It is demonstrated that almost any S-matrix of quantum field theory in curved
spaces posses an infinite set of complex poles (or branch cuts). These poles
can be transformed into complex eigenvalues, the corresponding eigenvectors
being Gamow vectors. All this formalism, which is heuristic in ordinary Hilbert
space, becomes a rigorous one within the framework of a properly chosen rigged
Hilbert space. Then complex eigenvalues produce damping or growing factors. It
is known that the growth of entropy, decoherence, and the appearance of
correlations, occur in the universe evolution, but only under a restricted set
of initial conditions. It is proved that the damping factors allow to enlarge
this set up to almost any initial conditions.Comment: 19 pgs. Latex fil
Inverse spectral problems for Sturm-Liouville operators with singular potentials
The inverse spectral problem is solved for the class of Sturm-Liouville
operators with singular real-valued potentials from the space .
The potential is recovered via the eigenvalues and the corresponding norming
constants. The reconstruction algorithm is presented and its stability proved.
Also, the set of all possible spectral data is explicitly described and the
isospectral sets are characterized.Comment: Submitted to Inverse Problem
Quantum Statistics and Entanglement of Two Electromagnetic Field Modes Coupled via a Mesoscopic SQUID Ring
In this paper we investigate the behaviour of a fully quantum mechanical
system consisting of a mesoscopic SQUID ring coupled to one or two
electromagnetic field modes. We show that we can use a static magnetic flux
threading the SQUID ring to control the transfer of energy, the entanglement
and the statistical properties of the fields coupled to the ring. We also
demonstrate that at, and around, certain values of static flux the effective
coupling between the components of the system is large. The position of these
regions in static flux is dependent on the energy level structure of the ring
and the relative field mode frequencies, In these regions we find that the
entanglement of states in the coupled system, and the energy transfer between
its components, is strong.Comment: 15 pages, 19 figures, Uploaded as implementing a policy of arXiving
old paper
On Density of State of Quantized Willmore Surface-A Way to Quantized Extrinsic String in R^3
Recently I quantized an elastica with Bernoulli-Euler functional in
two-dimensional space using the modified KdV hierarchy. In this article, I will
quantize a Willmore surface, or equivalently a surface with the Polyakov
extrinsic curvature action, using the modified Novikov-Veselov (MNV) equation.
In other words, I show that the density of state of the partition function for
the quantized Willmore surface is expressed by volume of a subspace of the
moduli of the MNV equation.Comment: AMS-Tex Us
Stateful Contracts for Affine Types
Abstract. Affine type systems manage resources by preventing some values from being used more than once. This offers expressiveness and performance benefits, but difficulty arises in interacting with components written in a conventional language whose type system provides no way to maintain the affine type system’s aliasing invariants. We propose and implement a technique that uses behavioral contracts to mediate between code written in an affine language and code in a conventional typed language. We formalize our approach via a typed calculus with both affine-typed and conventionally-typed modules. We show how to preserve the guarantees of both type systems despite both languages being able to call into each other and exchange higher-order values.
Tunneling of quantum rotobreathers
We analyze the quantum properties of a system consisting of two nonlinearly
coupled pendula. This non-integrable system exhibits two different symmetries:
a permutational symmetry (permutation of the pendula) and another one related
to the reversal of the total momentum of the system. Each of these symmetries
is responsible for the existence of two kinds of quasi-degenerated states. At
sufficiently high energy, pairs of symmetry-related states glue together to
form quadruplets. We show that, starting from the anti-continuous limit,
particular quadruplets allow us to construct quantum states whose properties
are very similar to those of classical rotobreathers. By diagonalizing
numerically the quantum Hamiltonian, we investigate their properties and show
that such states are able to store the main part of the total energy on one of
the pendula. Contrary to the classical situation, the coupling between pendula
necessarily introduces a periodic exchange of energy between them with a
frequency which is proportional to the energy splitting between
quasi-degenerated states related to the permutation symmetry. This splitting
may remain very small as the coupling strength increases and is a decreasing
function of the pair energy. The energy may be therefore stored in one pendulum
during a time period very long as compared to the inverse of the internal
rotobreather frequency.Comment: 20 pages, 11 figures, REVTeX4 styl
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