1,652 research outputs found
Nonlinear oscillations of gas bubbles submerged in water: implications for plasma breakdown
Gas bubbles submerged in a dielectric liquid and driven by an electric field can undergo dramatic changes in both shape and volume. In certain cases, this deformation can enhance the distribution of the applied field inside the bubble as well as decrease the internal gas pressure. Both effects will tend to facilitate plasma formation in the gas volume. A practical realization of these two effects could have a broad impact on the viability of liquid plasma technologies, which tend to suffer from high voltage requirements. In this experiment, bubbles of diameter 0.4–0.7 mm are suspended in the node of a 26.4 kHz underwater acoustic standing wave and excited into nonlinear shape oscillations using ac electric fields with amplitudes of 5–15 kV cm ‚à Ã1 . Oscillations of the deformed bubble are photographed with a high-speed camera operating at 5130 frames s ‚à Ã1 and the resulting images are decomposed into their axisymmetric spherical harmonic modes, ##IMG## [http://ej.iop.org/images/0022-3727/45/41/415203/jphysd431220ieqn001.gif] { , using an edge detection algorithm. Overall, the bubble motion is dominated by the first three even modes l = 0, 2 and 4. Electrostatic simulations of the deformed bubble's internal electric field indicate that the applied field is enhanced by as much as a factor of 2.3 above the nominal applied field. Further simulation of both the pure l = 2 and l = 4 modes predicts that with additional deformation, the field enhancement factors could reach as much as 10–50.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98592/1/0022-3727_45_41_415203.pd
Nonlinear statistics of quantum transport in chaotic cavities
Copyright © 2008 The American Physical Society.In the framework of the random matrix approach, we apply the theory of Selberg’s integral to problems of quantum transport in chaotic cavities. All the moments of transmission eigenvalues are calculated analytically up to the fourth order. As a result, we derive exact explicit expressions for the skewness and kurtosis of the conductance and transmitted charge as well as for the variance of the shot-noise power in chaotic cavities. The obtained results are generally valid at arbitrary numbers of propagating channels in the two attached leads. In the particular limit of large (and equal) channel numbers, the shot-noise variance attends the universal value 1∕64β that determines a universal Gaussian statistics of shot-noise fluctuations in this case.DFG and BRIEF
Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
Assuming the validity of random matrices for describing the statistics of a
closed chaotic quantum system, we study analytically some statistical
properties of the S-matrix characterizing scattering in its open counterpart.
In the first part of the paper we attempt to expose systematically ideas
underlying the so-called stochastic (Heidelberg) approach to chaotic quantum
scattering. Then we concentrate on systems with broken time-reversal invariance
coupled to continua via M open channels. By using the supersymmetry method we
derive:
(i) an explicit expression for the density of S-matrix poles (resonances) in
the complex energy plane
(ii) an explicit expression for the parametric correlation function of
densities of eigenphases of the S-matrix.
We use it to find the distribution of derivatives of these eigenphases with
respect to the energy ("partial delay times" ) as well as with respect to an
arbitrary external parameter.Comment: 51 pages, RevTEX , three figures are available on request. To be
published in the special issue of the Journal of Mathematical Physic
Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices
We apply the method of skew-orthogonal polynomials (SOP) in the complex plane to asymmetric random matrices with real elements, belonging to two different classes. Explicit integral representations valid for arbitrary weight functions are derived for the SOP and for their Cauchy transforms, given as expectation values of traces and determinants or their inverses, respectively. Our proof uses the fact that the joint probability distribution function for all combinations of real eigenvalues and complex conjugate eigenvalue pairs can be written as a product. Examples for the SOP are given in terms of Laguerre polynomials for the chiral ensemble (also called the non-Hermitian real Wishart-Laguerre ensemble), both without and with the insertion of characteristic polynomials. Such characteristic polynomials play the role of mass terms in applications to complex Dirac spectra in field theory. In addition, for the elliptic real Ginibre ensemble we recover the SOP of Forrester and Nagao in terms of Hermite polynomials
Probability distributions of Linear Statistics in Chaotic Cavities and associated phase transitions
We establish large deviation formulas for linear statistics on the
transmission eigenvalues of a chaotic cavity, in the framework of
Random Matrix Theory. Given any linear statistics of interest , the probability distribution of generically
satisfies the large deviation formula
, where
is a rate function that we compute explicitly in many cases
(conductance, shot noise, moments) and corresponds to different
symmetry classes. Using these large deviation expressions, it is possible to
recover easily known results and to produce new formulas, such as a closed form
expression for (where
) for arbitrary integer . The universal limit
is also computed exactly. The
distributions display a central Gaussian region flanked on both sides by
non-Gaussian tails. At the junction of the two regimes, weakly non-analytical
points appear, a direct consequence of phase transitions in an associated
Coulomb gas problem. Numerical checks are also provided, which are in full
agreement with our asymptotic results in both real and Laplace space even for
moderately small . Part of the results have been announced in [P. Vivo, S.N.
Majumdar and O. Bohigas, {\it Phys. Rev. Lett.} {\bf 101}, 216809 (2008)].Comment: 31 pages, 16 figures. To appear in Phys. Rev. B. Added section IVD
about comparison with other theories and numerical simulation
Statistical properties of random density matrices
Statistical properties of ensembles of random density matrices are
investigated. We compute traces and von Neumann entropies averaged over
ensembles of random density matrices distributed according to the Bures
measure. The eigenvalues of the random density matrices are analyzed: we derive
the eigenvalue distribution for the Bures ensemble which is shown to be broader
then the quarter--circle distribution characteristic of the Hilbert--Schmidt
ensemble. For measures induced by partial tracing over the environment we
compute exactly the two-point eigenvalue correlation function.Comment: 8 revtex pages with one eps file included, ver. 2 - minor misprints
correcte
Volume of the quantum mechanical state space
The volume of the quantum mechanical state space over -dimensional real,
complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean
measure is computed, and explicit formulas are presented for the expected value
of the determinant in the general setting too. The case when the state space is
endowed with a monotone metric or a pull-back metric is considered too, we give
formulas to compute the volume of the state space with respect to the given
Riemannian metric. We present the volume of the space of qubits with respect to
various monotone metrics. It turns out that the volume of the space of qubits
can be infinite too. We characterize those monotone metrics which generates
infinite volume.Comment: 17 page
Calculation of the unitary part of the Bures measure for N-level quantum systems
We use the canonical coset parameterization and provide a formula with the
unitary part of the Bures measure for non-degenerate systems in terms of the
product of even Euclidean balls. This formula is shown to be consistent with
the sampling of random states through the generation of random unitary
matrices
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